0.00/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s 0.12/0.32 % Computer : n011.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 960 0.12/0.32 % WCLimit : 120 0.12/0.32 % DateTime : Tue Aug 9 03:06:21 EDT 2022 0.12/0.32 % CPUTime : 0.17/0.56 start to proof:theBenchmark 7.66/7.72 %------------------------------------------- 7.66/7.72 % File :CSE---1.5 7.66/7.72 % Problem :theBenchmark 7.66/7.72 % Transform :cnf 7.66/7.72 % Format :tptp:raw 7.66/7.72 % Command :java -jar mcs_scs.jar %d %s 7.66/7.72 7.66/7.72 % Result :Theorem 6.090000s 7.66/7.72 % Output :CNFRefutation 6.090000s 7.66/7.72 %------------------------------------------- 7.66/7.73 fof(fact_322_insert__subset,axiom, 7.66/7.73 ! [X_3,A_1,B_6] : 7.66/7.73 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.66/7.73 & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) ) 7.66/7.73 <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X_3,A_1)),B_6)) ) ). 7.66/7.73 7.66/7.73 fof(conj_0,hypothesis, 7.66/7.73 hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)) ). 7.66/7.73 7.66/7.73 fof(fact_521_xt1_I4_J,axiom, 7.66/7.73 ! [C_1,B_1,A_3] : 7.66/7.73 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),A_3)) 7.66/7.73 <= C_1 = B_1 ) 7.66/7.73 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_1),A_3)) ) ). 7.66/7.73 7.66/7.73 fof(fact_184_lift__Suc__mono__le,axiom, 7.66/7.73 ! [Na,N_3,F] : 7.66/7.73 ( ! [N_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,N_2)),hAPP_n1699378549t_bool(F,hAPP_nat_nat(suc,N_2)))) 7.66/7.73 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Na)),hAPP_n1699378549t_bool(F,N_3))) 7.66/7.73 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) ) ) ). 7.66/7.73 7.66/7.73 fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc,axiom, 7.66/7.73 is_fun949378684l_bool(bot_bo1389914601l_bool) ). 7.66/7.73 7.66/7.73 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_002,axiom, 7.66/7.73 ! [B_1_1,B_2_1] : 7.66/7.73 ( is_fun1661590463l_bool(B_2_1) 7.66/7.73 => is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2_1)) ) ). 7.66/7.73 7.66/7.73 fof(gsy_c_Set_Oinsert_000t__a,hypothesis, 7.66/7.73 ! [B_1_1,B_2_1] : 7.66/7.73 ( is_fun_a_bool(insert_a(B_1_1,B_2_1)) 7.66/7.73 <= ( is_fun_a_bool(B_2_1) 7.66/7.73 & is_a(B_1_1) ) ) ). 7.66/7.73 7.66/7.73 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom, 7.66/7.73 ! [P,Q,R] : hAPP_nat_bool(cOMBB_bool_bool_nat(P,Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R)) ). 7.66/7.73 7.66/7.73 fof(fact_347_subset__image__iff,axiom, 7.66/7.73 ! [B_6,F,A_1] : 7.66/7.73 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1))) 7.66/7.73 <=> ? [AA] : 7.66/7.73 ( B_6 = image_pname_a(F,AA) 7.66/7.73 & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A_1)) 7.66/7.73 & is_fun_pname_bool(AA) ) ) 7.66/7.73 <= is_fun_a_bool(B_6) ) ). 7.66/7.73 7.66/7.73 fof(fact_374_le__fun__def,axiom, 7.66/7.73 ! [F,G_1] : 7.66/7.73 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1)) 7.66/7.73 <=> ! [X_1] : 7.66/7.73 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G_1,X_1))) 7.66/7.73 <= is_pname(X_1) ) ) ). 7.66/7.73 7.66/7.73 fof(fact_635_less__Suc__eq,axiom, 7.66/7.73 ! [M_1,Na] : 7.66/7.73 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) 7.66/7.73 | M_1 = Na ) 7.66/7.73 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na))) ) ). 7.66/7.73 7.66/7.73 fof(fact_588_trans__le__add1,axiom, 7.66/7.73 ! [M,I,J_2] : 7.66/7.73 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) 7.66/7.73 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(plus_plus_nat(J_2),M))) ) ). 7.66/7.73 7.66/7.73 fof(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom, 7.66/7.73 ! [X,Y] : 7.66/7.73 ( ( is_pname(Y) 7.66/7.73 & is_pname(X) ) 7.66/7.73 => ( ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)) 7.66/7.73 | X = Y ) ) ). 7.66/7.73 7.66/7.73 fof(fact_48_card__seteq,axiom, 7.66/7.73 ! [A_1,B_6] : 7.66/7.73 ( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6)) 7.68/7.73 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,B_6)),hAPP_f696928925ol_nat(finite346522414t_bool,A_1))) 7.68/7.73 => B_6 = A_1 ) ) 7.68/7.73 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ) ). 7.68/7.73 7.68/7.73 fof(fact_29_card__image__le,axiom, 7.68/7.73 ! [F,A_1] : 7.68/7.73 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.73 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1))) ) ). 7.68/7.73 7.68/7.73 fof(fact_26_finite_OinsertI,axiom, 7.68/7.73 ! [A_3,A_1] : 7.68/7.73 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_3,A_1))) 7.68/7.73 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.73 7.68/7.73 fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.73 ! [B_1_1,B_2_1] : 7.68/7.73 ( is_pname(B_2_1) 7.68/7.73 => is_fun_a_bool(hAPP_p1534023578a_bool(B_1_1,B_2_1)) ) ). 7.68/7.73 7.68/7.73 fof(fact_209_pigeonhole__infinite,axiom, 7.68/7.73 ! [F,A_1] : 7.68/7.73 ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) 7.68/7.73 => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(F,A_1))) 7.68/7.73 => ? [X_1] : 7.68/7.73 ( is_a(X_1) 7.68/7.73 & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,F)),hAPP_a_fun_a_bool(F,X_1)))))) 7.68/7.73 & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) ) ) ) ). 7.68/7.73 7.68/7.73 fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom, 7.68/7.73 ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) = hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(P),Q),R) ). 7.68/7.74 7.68/7.74 fof(fact_411_empty__Collect__eq,axiom, 7.68/7.74 ! [Pa] : 7.68/7.74 ( bot_bot_fun_a_bool = collect_a(Pa) 7.68/7.74 <=> ! [X_1] : 7.68/7.74 ( is_a(X_1) 7.68/7.74 => ~ hBOOL(hAPP_a_bool(Pa,X_1)) ) ) ). 7.68/7.74 7.68/7.74 fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U,axiom, 7.68/7.74 ! [P,Q] : 7.68/7.74 ( is_bool(P) 7.68/7.74 => hAPP_a_bool(cOMBK_bool_a(P),Q) = P ) ). 7.68/7.74 7.68/7.74 fof(fact_603_le__add__diff,axiom, 7.68/7.74 ! [M,K,N] : 7.68/7.74 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),K))) 7.68/7.74 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) ) ). 7.68/7.74 7.68/7.74 fof(fact_246_insert__absorb2,axiom, 7.68/7.74 ! [X_3,A_1] : insert_nat(X_3,insert_nat(X_3,A_1)) = insert_nat(X_3,A_1) ). 7.68/7.74 7.68/7.74 fof(fact_574_nat__add__right__cancel,axiom, 7.68/7.74 ! [M_1,K_2,Na] : 7.68/7.74 ( M_1 = Na 7.68/7.74 <=> hAPP_nat_nat(plus_plus_nat(Na),K_2) = hAPP_nat_nat(plus_plus_nat(M_1),K_2) ) ). 7.68/7.74 7.68/7.74 fof(fact_375_le__fun__def,axiom, 7.68/7.74 ! [F,G_1] : 7.68/7.74 ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G_1,X_1))) 7.68/7.74 <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) ) ). 7.68/7.74 7.68/7.74 fof(fact_666_add__diff__inverse,axiom, 7.68/7.74 ! [M,N] : 7.68/7.74 ( hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M 7.68/7.74 <= ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ). 7.68/7.74 7.68/7.74 fof(fact_354_imageE,axiom, 7.68/7.74 ! [B_1,F,A_1] : 7.68/7.74 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1))) 7.68/7.74 => ~ ! [X_1] : 7.68/7.74 ( is_pname(X_1) 7.68/7.74 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.74 <= B_1 = hAPP_pname_nat(F,X_1) ) ) ) ). 7.68/7.74 7.68/7.74 fof(fact_471_Collect__conv__if,axiom, 7.68/7.74 ! [Pa,A_3] : 7.68/7.74 ( ( bot_bo844097828e_bool = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),Pa)) 7.68/7.74 <= ~ hBOOL(hAPP_pname_bool(Pa,A_3)) ) 7.68/7.74 & ( hBOOL(hAPP_pname_bool(Pa,A_3)) 7.68/7.74 => insert_pname(A_3,bot_bo844097828e_bool) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),Pa)) ) ) ). 7.68/7.74 7.68/7.74 fof(fact_625_not__add__less1,axiom, 7.68/7.74 ! [I,J_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),J_2)),I)) ). 7.68/7.74 7.68/7.74 fof(fact_50_card__seteq,axiom, 7.68/7.74 ! [A_1,B_6] : 7.68/7.74 ( ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,B_6)),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))) 7.68/7.74 => B_6 = A_1 ) 7.68/7.74 <= hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6)) ) 7.68/7.74 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) ) 7.68/7.74 <= ( is_fun949378684l_bool(B_6) 7.68/7.74 & is_fun949378684l_bool(A_1) ) ) ). 7.68/7.74 7.68/7.74 fof(fact_117_le__SucI,axiom, 7.68/7.74 ! [M,N] : 7.68/7.74 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))) 7.68/7.74 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ). 7.68/7.74 7.68/7.74 fof(fact_416_all__not__in__conv,axiom, 7.68/7.74 ! [A_1] : 7.68/7.74 ( ! [X_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) 7.68/7.74 <=> bot_bot_fun_nat_bool = A_1 ) ). 7.68/7.74 7.68/7.74 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On,axiom, 7.68/7.74 ! [P,Q,R] : hAPP_bool_bool(P,hAPP_f54304608l_bool(Q,R)) = hAPP_f54304608l_bool(cOMBB_238756964t_bool(P,Q),R) ). 7.68/7.74 7.68/7.74 fof(fact_476_Collect__conv__if2,axiom, 7.68/7.74 ! [Pa,A_3] : 7.68/7.74 ( ( hBOOL(hAPP_nat_bool(Pa,A_3)) 7.68/7.74 => insert_nat(A_3,bot_bot_fun_nat_bool) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_3)),Pa)) ) 7.68/7.74 & ( ~ hBOOL(hAPP_nat_bool(Pa,A_3)) 7.68/7.74 => collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_3)),Pa)) = bot_bot_fun_nat_bool ) ) ). 7.68/7.74 7.68/7.74 fof(fact_464_subset__empty,axiom, 7.68/7.74 ! [A_1] : 7.68/7.74 ( A_1 = bot_bot_fun_nat_bool 7.68/7.74 <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),bot_bot_fun_nat_bool)) ) ). 7.68/7.74 7.68/7.74 fof(fact_17_finite__imageI,axiom, 7.68/7.74 ! [H,F_1] : 7.68/7.74 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) 7.68/7.74 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(H,F_1))) ) ). 7.68/7.74 7.68/7.74 fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__022,axiom, 7.68/7.74 ! [P,Q,R] : hAPP_f103356543l_bool(P,hAPP_p1499970991t_bool(Q,R)) = hAPP_p130839763l_bool(cOMBB_928955006_pname(P,Q),R) ). 7.68/7.74 7.68/7.74 fof(fact_292_Collect__def,axiom, 7.68/7.74 ! [Pa] : collect_fun_nat_bool(Pa) = Pa ). 7.68/7.74 7.68/7.74 fof(fact_160_finite__subset__image,axiom, 7.68/7.74 ! [F,A_1,B_6] : 7.68/7.74 ( ( ( ? [C_7] : 7.68/7.74 ( is_fun_a_bool(C_7) 7.68/7.74 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) 7.68/7.74 & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) 7.68/7.74 & image_819518260e_bool(F,C_7) = B_6 ) 7.68/7.74 <= hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_819518260e_bool(F,A_1))) ) 7.68/7.74 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) ) 7.68/7.74 <= is_fun1661590463l_bool(B_6) ) ). 7.68/7.74 7.68/7.74 fof(fact_413_ex__in__conv,axiom, 7.68/7.74 ! [A_1] : 7.68/7.74 ( ? [X_1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) 7.68/7.74 <=> bot_bot_fun_nat_bool != A_1 ) ). 7.68/7.74 7.68/7.74 fof(fact_508_xt1_I5_J,axiom, 7.68/7.74 ! [Y_6,X_7] : 7.68/7.74 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_6)) 7.68/7.74 => X_7 = Y_6 ) 7.68/7.74 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),X_7)) ) ). 7.68/7.74 7.68/7.74 fof(fact_289_mem__def,axiom, 7.68/7.74 ! [X_3,A_1] : 7.68/7.74 ( hBOOL(hAPP_a_bool(A_1,X_3)) 7.68/7.74 <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) ). 7.68/7.74 7.68/7.74 fof(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom, 7.68/7.74 ! [B_1_1,B_2_1] : 7.68/7.74 ( is_fun_pname_bool(image_1854862208_pname(B_1_1,B_2_1)) 7.68/7.74 <= is_fun949378684l_bool(B_2_1) ) ). 7.68/7.74 7.68/7.74 fof(fact_74_finite__Collect__conjI,axiom, 7.68/7.74 ! [Q_1,Pa] : 7.68/7.74 ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1))) 7.68/7.74 | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) ) 7.68/7.74 => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,Pa),Q_1)))) ) ). 7.68/7.74 7.68/7.74 fof(gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom, 7.68/7.74 ! [B_1_1,B_2_1] : 7.68/7.74 ( is_a(B_2_1) 7.68/7.74 => is_fun_pname_bool(hAPP_a93125764e_bool(B_1_1,B_2_1)) ) ). 7.68/7.74 7.68/7.74 fof(fact_478_Collect__conv__if2,axiom, 7.68/7.74 ! [Pa,A_3] : 7.68/7.74 ( ( ~ hBOOL(hAPP_a_bool(Pa,A_3)) 7.68/7.74 => collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_3)),Pa)) = bot_bot_fun_a_bool ) 7.68/7.74 & ( hBOOL(hAPP_a_bool(Pa,A_3)) 7.68/7.74 => collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_3)),Pa)) = insert_a(A_3,bot_bot_fun_a_bool) ) ) ). 7.68/7.74 7.68/7.74 fof(fact_259_insert__ident,axiom, 7.68/7.74 ! [B_6,X_3,A_1] : 7.68/7.74 ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) 7.68/7.74 => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) 7.68/7.74 => ( insert_a(X_3,A_1) = insert_a(X_3,B_6) 7.68/7.74 <=> B_6 = A_1 ) ) ) 7.68/7.74 <= ( is_fun_a_bool(B_6) 7.68/7.74 & is_fun_a_bool(A_1) ) ) ). 7.68/7.74 7.68/7.74 fof(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom, 7.68/7.74 ! [X,Y] : 7.68/7.74 ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) 7.68/7.74 | Y = X ) ). 7.68/7.74 7.68/7.74 fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.74 ! [B_1_1,B_2_1] : 7.68/7.74 ( is_fun_pname_bool(B_2_1) 7.68/7.74 => is_fun949378684l_bool(image_112932426a_bool(B_1_1,B_2_1)) ) ). 7.68/7.74 7.68/7.74 fof(fact_323_insert__subset,axiom, 7.68/7.74 ! [X_3,A_1,B_6] : 7.68/7.74 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.74 & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) ) 7.68/7.74 <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_3,A_1)),B_6)) ) ). 7.68/7.74 7.68/7.74 fof(fact_284_set__mp,axiom, 7.68/7.74 ! [X_3,A_1,B_6] : 7.68/7.74 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.68/7.74 => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) 7.68/7.74 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) ) ) ). 7.68/7.74 7.68/7.74 fof(fact_166_finite__subset__image,axiom, 7.68/7.74 ! [F,A_1,B_6] : 7.68/7.74 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) 7.68/7.74 => ( ? [C_7] : 7.68/7.74 ( is_fun_a_bool(C_7) 7.68/7.74 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) 7.68/7.74 & B_6 = image_a_nat(F,C_7) 7.68/7.74 & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) ) 7.68/7.74 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1))) ) ) ). 7.68/7.74 7.68/7.74 fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna,axiom, 7.68/7.74 ! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f654413245e_bool(B_1_1,B_2_1)) ). 7.68/7.74 7.68/7.74 fof(fact_651_nat__less__cases,axiom, 7.68/7.74 ! [Pa,M_1,Na] : 7.68/7.74 ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) 7.68/7.74 <= ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) 7.68/7.74 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) ) ) 7.68/7.74 <= ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) 7.68/7.74 <= M_1 = Na ) ) 7.68/7.74 <= ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) 7.68/7.74 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) ) ) ). 7.68/7.74 7.68/7.74 fof(fact_275_equalityD2,axiom, 7.68/7.74 ! [A_1,B_6] : 7.68/7.74 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1)) 7.68/7.74 <= B_6 = A_1 ) ). 7.68/7.74 7.68/7.74 fof(help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_,axiom, 7.68/7.74 ! [P,Q,R] : hAPP_bool_bool(hAPP_f198738859l_bool(P,R),hAPP_fun_a_bool_bool(Q,R)) = hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(P,Q),R) ). 7.68/7.74 7.68/7.74 fof(gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom, 7.68/7.74 ! [B_1_1] : 7.68/7.74 ( is_bool(B_1_1) 7.68/7.74 => is_fun1661590463l_bool(cOMBK_1857069011e_bool(B_1_1)) ) ). 7.68/7.74 7.68/7.74 fof(fact_696_Zero__not__Suc,axiom, 7.68/7.74 ! [M] : zero_zero_nat != hAPP_nat_nat(suc,M) ). 7.68/7.74 7.68/7.74 fof(fact_663_le__less__Suc__eq,axiom, 7.68/7.74 ! [M_1,Na] : 7.68/7.74 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) 7.68/7.74 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) 7.68/7.74 <=> M_1 = Na ) ) ). 7.68/7.74 7.68/7.74 fof(fact_260_insertI2,axiom, 7.68/7.74 ! [B_1,A_3,B_6] : 7.68/7.74 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,B_6))) 7.68/7.74 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),B_6)) ) ). 7.68/7.74 7.68/7.74 fof(fact_297_subset__trans,axiom, 7.68/7.74 ! [C_6,A_1,B_6] : 7.68/7.74 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),C_6)) 7.68/7.74 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),C_6)) ) 7.68/7.74 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ) ). 7.68/7.74 7.68/7.74 fof(fact_10_finite__imageI,axiom, 7.68/7.74 ! [H,F_1] : 7.68/7.74 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) 7.68/7.74 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(H,F_1))) ) ). 7.68/7.74 7.68/7.74 fof(help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom, 7.68/7.74 ! [P,Q,R] : hAPP_nat_bool(hAPP_a_fun_nat_bool(P,R),Q) = hAPP_a_bool(hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(P),Q),R) ). 7.68/7.74 7.68/7.74 fof(fact_406_empty__iff,axiom, 7.68/7.74 ! [C_1] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),bot_bot_fun_a_bool)) ). 7.68/7.74 7.68/7.74 fof(fact_682_one__is__add,axiom, 7.68/7.74 ! [M_1,Na] : 7.68/7.74 ( hAPP_nat_nat(plus_plus_nat(M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat) 7.68/7.74 <=> ( ( Na = zero_zero_nat 7.68/7.74 & M_1 = hAPP_nat_nat(suc,zero_zero_nat) ) 7.68/7.74 | ( M_1 = zero_zero_nat 7.68/7.74 & Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ). 7.68/7.74 7.68/7.74 fof(fact_56_card__insert__le,axiom, 7.68/7.74 ! [X_3,A_1] : 7.68/7.74 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)))) 7.68/7.74 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ) ). 7.68/7.74 7.68/7.74 fof(fact_33_card__image__le,axiom, 7.68/7.74 ! [F,A_1] : 7.68/7.74 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(F,A_1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))) 7.68/7.74 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ) ). 7.68/7.74 7.68/7.74 fof(fact_224_insertCI,axiom, 7.68/7.74 ! [B_1,A_3,B_6] : 7.68/7.74 ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),B_6)) 7.68/7.74 => A_3 = B_1 ) 7.68/7.74 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,B_6))) ) ). 7.68/7.74 7.68/7.74 fof(fact_539_ord__eq__le__trans,axiom, 7.68/7.74 ! [C_1,A_3,B_1] : 7.68/7.74 ( B_1 = A_3 7.68/7.74 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),C_1)) 7.68/7.74 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_1),C_1)) ) ) ). 7.68/7.74 7.68/7.74 fof(fact_569_diff__Suc__1,axiom, 7.68/7.74 ! [N] : N = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,N)),one_one_nat) ). 7.68/7.74 7.68/7.74 fof(fact_647_linorder__neqE__nat,axiom, 7.68/7.74 ! [X,Y] : 7.68/7.74 ( X != Y 7.68/7.74 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X)) 7.68/7.74 <= ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) ) ) ). 7.68/7.74 7.68/7.74 fof(fact_321_subset__insertI,axiom, 7.68/7.74 ! [B_6,A_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),insert_a(A_3,B_6))) ). 7.68/7.74 7.68/7.74 fof(fact_340_insert__image,axiom, 7.68/7.74 ! [F,X_3,A_1] : 7.68/7.74 ( insert_pname(hAPP_a_pname(F,X_3),image_a_pname(F,A_1)) = image_a_pname(F,A_1) 7.68/7.74 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) ). 7.68/7.74 7.68/7.74 fof(fact_433_le__bot,axiom, 7.68/7.74 ! [A_3] : 7.68/7.74 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),bot_bot_fun_nat_bool)) 7.68/7.74 => A_3 = bot_bot_fun_nat_bool ) ). 7.68/7.74 7.68/7.74 fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_006,axiom, 7.68/7.74 ! [P,Q,R] : hAPP_n1025906991e_bool(cOMBB_1212655066ol_nat(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_nat_pname(Q,R)) ). 7.68/7.74 7.68/7.74 fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_,axiom, 7.68/7.74 ! [B_1_1,B_2_1] : 7.68/7.74 ( is_fun1661590463l_bool(cOMBB_307249310e_bool(B_1_1,B_2_1)) 7.68/7.74 <= is_fun1661590463l_bool(B_2_1) ) ). 7.68/7.74 7.68/7.74 fof(fact_649_less__not__refl2,axiom, 7.68/7.74 ! [N,M] : 7.68/7.74 ( N != M 7.68/7.74 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) ) ). 7.68/7.74 7.68/7.74 fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc,axiom, 7.68/7.74 ! [P,Q,R] : hAPP_a_bool(hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_a217006258l_bool(P,R),Q) ). 7.68/7.74 7.68/7.74 fof(fact_242_insert__Collect,axiom, 7.68/7.74 ! [A_3,Pa] : insert_fun_a_bool(A_3,collect_fun_a_bool(Pa)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3))),Pa)) ). 7.68/7.74 7.68/7.74 fof(fact_63_card__insert__if,axiom, 7.68/7.74 ! [X_3,A_1] : 7.68/7.74 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.74 => ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) 7.68/7.74 => hAPP_f22106695ol_nat(finite_card_nat,A_1) = hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) ) 7.68/7.74 & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) 7.68/7.74 => hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A_1)) ) ) ) ). 7.68/7.74 7.68/7.74 fof(fact_475_Collect__conv__if,axiom, 7.68/7.74 ! [Pa,A_3] : 7.68/7.74 ( ( insert_fun_a_bool(A_3,bot_bo1389914601l_bool) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),Pa)) 7.68/7.74 <= hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) ) 7.68/7.74 & ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) 7.68/7.74 => collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),Pa)) = bot_bo1389914601l_bool ) ) ). 7.68/7.74 7.68/7.74 fof(fact_318_insert__compr__raw,axiom, 7.68/7.74 ! [X_1,Xa] : collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),Xa))) = insert_a(X_1,Xa) ). 7.68/7.74 7.68/7.74 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,axiom, 7.68/7.74 ! [B_1_1,B_2_1] : 7.68/7.74 ( is_fun1661590463l_bool(B_2_1) 7.68/7.74 => is_bool(hAPP_f1935102916l_bool(B_1_1,B_2_1)) ) ). 7.68/7.74 7.68/7.74 fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool,axiom, 7.68/7.74 ! [B_1_1,B_2_1] : 7.68/7.74 ( is_fun949378684l_bool(B_2_1) 7.68/7.74 => is_fun949378684l_bool(cOMBB_2140588453a_bool(B_1_1,B_2_1)) ) ). 7.68/7.74 7.68/7.74 fof(fact_282_set__rev__mp,axiom, 7.68/7.74 ! [B_6,X_3,A_1] : 7.68/7.74 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.74 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) ) 7.68/7.74 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ) ). 7.68/7.74 7.68/7.74 fof(fact_221_subsetD,axiom, 7.68/7.74 ! [C_1,A_1,B_6] : 7.68/7.74 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),A_1)) 7.68/7.74 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),B_6)) ) 7.68/7.74 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ). 7.68/7.74 7.68/7.74 fof(fact_568_diff__Suc__eq__diff__pred,axiom, 7.68/7.74 ! [M,N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N) = hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,N)) ). 7.68/7.74 7.68/7.74 fof(help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom, 7.68/7.74 ! [P,Q,R] : hAPP_a_bool(cOMBS_a_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_a_fun_bool_bool(P,R),hAPP_a_bool(Q,R)) ). 7.68/7.74 7.68/7.74 fof(fact_86_le__trans,axiom, 7.68/7.74 ! [K,I,J_2] : 7.68/7.74 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) 7.68/7.74 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),K)) 7.68/7.75 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K)) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_477_Collect__conv__if2,axiom, 7.68/7.75 ! [Pa,A_3] : 7.68/7.75 ( ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_3)),Pa)) = bot_bo844097828e_bool 7.68/7.75 <= ~ hBOOL(hAPP_pname_bool(Pa,A_3)) ) 7.68/7.75 & ( hBOOL(hAPP_pname_bool(Pa,A_3)) 7.68/7.75 => insert_pname(A_3,bot_bo844097828e_bool) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_3)),Pa)) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_614_finite__Collect__less__nat,axiom, 7.68/7.75 ! [K_2] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),K_2)))) ). 7.68/7.75 7.68/7.75 fof(fact_425_bot__fun__def,axiom, 7.68/7.75 ! [X_1] : 7.68/7.75 ( hBOOL(bot_bot_bool) 7.68/7.75 <=> hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_619_add__less__mono,axiom, 7.68/7.75 ! [K,L,I,J_2] : 7.68/7.75 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),L))) 7.68/7.75 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L)) ) 7.68/7.75 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ) ). 7.68/7.75 7.68/7.75 fof(fact_332_insert__mono,axiom, 7.68/7.75 ! [A_3,C_6,D_1] : 7.68/7.75 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(A_3,C_6)),insert_nat(A_3,D_1))) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),D_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_198_pigeonhole__infinite,axiom, 7.68/7.75 ! [F,A_1] : 7.68/7.75 ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) 7.68/7.75 => ( ? [X_1] : 7.68/7.75 ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A_1)) 7.68/7.75 & ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),A_1)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,F)),hAPP_fun_a_bool_nat(F,X_1)))))) 7.68/7.75 & is_fun_a_bool(X_1) ) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(F,A_1))) ) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : is_fun1661590463l_bool(image_1655916159e_bool(B_1_1,B_2_1)) ). 7.68/7.75 7.68/7.75 fof(fact_205_pigeonhole__infinite,axiom, 7.68/7.75 ! [F,A_1] : 7.68/7.75 ( ( ? [X_1] : 7.68/7.75 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.75 & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,F)),hAPP_p1534023578a_bool(F,X_1)))))) 7.68/7.75 & is_pname(X_1) ) 7.68/7.75 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(F,A_1))) ) 7.68/7.75 <= ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_206_pigeonhole__infinite,axiom, 7.68/7.75 ! [F,A_1] : 7.68/7.75 ( ( ? [X_1] : 7.68/7.75 ( is_a(X_1) 7.68/7.75 & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) 7.68/7.75 & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,F)),hAPP_a_a(F,X_1)))))) ) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(F,A_1))) ) 7.68/7.75 <= ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(conj_4,hypothesis, 7.68/7.75 hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)) ). 7.68/7.75 7.68/7.75 fof(fact_608_diff__Suc__diff__eq2,axiom, 7.68/7.75 ! [M,K,J_2] : 7.68/7.75 ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J_2),K))),M) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,J_2)),hAPP_nat_nat(plus_plus_nat(K),M)) 7.68/7.75 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ) ). 7.68/7.75 7.68/7.75 fof(fact_693_nat_Osimps_I3_J,axiom, 7.68/7.75 ! [Nat_1] : zero_zero_nat != hAPP_nat_nat(suc,Nat_1) ). 7.68/7.75 7.68/7.75 fof(fact_659_less__Suc__eq__le,axiom, 7.68/7.75 ! [M_1,Na] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na))) 7.68/7.75 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ). 7.68/7.75 7.68/7.75 fof(fact_620_add__less__mono1,axiom, 7.68/7.75 ! [K,I,J_2] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) 7.68/7.75 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),K))) ) ). 7.68/7.75 7.68/7.75 fof(fact_543_order__antisym__conv,axiom, 7.68/7.75 ! [Y_2,X_3] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_3)) 7.68/7.75 => ( Y_2 = X_3 7.68/7.75 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_2)) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_169_finite__subset__image,axiom, 7.68/7.75 ! [F,A_1,B_6] : 7.68/7.75 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_fun_a_bool_nat(F,A_1))) 7.68/7.75 => ? [C_7] : 7.68/7.75 ( image_fun_a_bool_nat(F,C_7) = B_6 7.68/7.75 & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7)) 7.68/7.75 & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1)) 7.68/7.75 & is_fun949378684l_bool(C_7) ) ) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ). 7.68/7.75 7.68/7.75 fof(fact_447_singleton__inject,axiom, 7.68/7.75 ! [A_3,B_1] : 7.68/7.75 ( insert_nat(A_3,bot_bot_fun_nat_bool) = insert_nat(B_1,bot_bot_fun_nat_bool) 7.68/7.75 => B_1 = A_3 ) ). 7.68/7.75 7.68/7.75 fof(fact_57_card__insert__le,axiom, 7.68/7.75 ! [X_3,A_1] : 7.68/7.75 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.75 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A_1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)))) ) ). 7.68/7.75 7.68/7.75 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(P,R),Q) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(P),Q),R) ). 7.68/7.75 7.68/7.75 fof(fact_341_insert__image,axiom, 7.68/7.75 ! [F,X_3,A_1] : 7.68/7.75 ( insert_nat(hAPP_a_nat(F,X_3),image_a_nat(F,A_1)) = image_a_nat(F,A_1) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_617_add__lessD1,axiom, 7.68/7.75 ! [I,J_2,K] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),J_2)),K)) 7.68/7.75 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)) ) ). 7.68/7.75 7.68/7.75 fof(fact_337_image__insert,axiom, 7.68/7.75 ! [F,A_3,B_6] : image_pname_a(F,insert_pname(A_3,B_6)) = insert_a(hAPP_pname_a(F,A_3),image_pname_a(F,B_6)) ). 7.68/7.75 7.68/7.75 fof(fact_263_insert__absorb,axiom, 7.68/7.75 ! [A_3,A_1] : 7.68/7.75 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1)) 7.68/7.75 => A_1 = insert_nat(A_3,A_1) ) ). 7.68/7.75 7.68/7.75 fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_a85458249l_bool(cOMBB_472261505bool_a(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_a_fun_a_bool(Q,R)) ). 7.68/7.75 7.68/7.75 fof(fact_188_pigeonhole__infinite,axiom, 7.68/7.75 ! [F,A_1] : 7.68/7.75 ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(F,A_1))) 7.68/7.75 => ? [X_1] : 7.68/7.75 ( is_a(X_1) 7.68/7.75 & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) 7.68/7.75 & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,F)),hAPP_a_pname(F,X_1)))))) ) ) 7.68/7.75 <= ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_527_ord__le__eq__trans,axiom, 7.68/7.75 ! [C_1,A_3,B_1] : 7.68/7.75 ( ( C_1 = B_1 7.68/7.75 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),C_1)) ) 7.68/7.75 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),B_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_545_order__eq__refl,axiom, 7.68/7.75 ! [Y_2,X_3] : 7.68/7.75 ( ( hBOOL(X_3) 7.68/7.75 <=> hBOOL(Y_2) ) 7.68/7.75 => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) ) ). 7.68/7.75 7.68/7.75 fof(fact_563_finite__induct,axiom, 7.68/7.75 ! [Pa,F_1] : 7.68/7.75 ( ( hBOOL(hAPP_f1637334154l_bool(Pa,bot_bo1701429464l_bool)) 7.68/7.75 => ( hBOOL(hAPP_f1637334154l_bool(Pa,F_1)) 7.68/7.75 <= ! [X_1,F_2] : 7.68/7.75 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_2)) 7.68/7.75 => ( ( hBOOL(hAPP_f1637334154l_bool(Pa,insert_fun_nat_bool(X_1,F_2))) 7.68/7.75 <= hBOOL(hAPP_f1637334154l_bool(Pa,F_2)) ) 7.68/7.75 <= ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),F_2)) ) ) ) ) 7.68/7.75 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_405_empty__iff,axiom, 7.68/7.75 ! [C_1] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),bot_bo844097828e_bool)) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000t__a_000t__a,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : 7.68/7.75 ( is_a(B_2_1) 7.68/7.75 => is_a(hAPP_a_a(B_1_1,B_2_1)) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1)) ). 7.68/7.75 7.68/7.75 fof(help_fdisj_2_1_U,axiom, 7.68/7.75 ! [P,Q] : 7.68/7.75 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) 7.68/7.75 | ~ hBOOL(Q) ) ). 7.68/7.75 7.68/7.75 fof(fact_291_Collect__def,axiom, 7.68/7.75 ! [Pa] : 7.68/7.75 ( Pa = collect_pname(Pa) 7.68/7.75 <= is_fun_pname_bool(Pa) ) ). 7.68/7.75 7.68/7.75 fof(help_fNot_1_1_U,axiom, 7.68/7.75 ! [P] : 7.68/7.75 ( ~ hBOOL(hAPP_bool_bool(fNot,P)) 7.68/7.75 | ~ hBOOL(P) ) ). 7.68/7.75 7.68/7.75 fof(fact_245_insert__absorb2,axiom, 7.68/7.75 ! [X_3,A_1] : insert_pname(X_3,A_1) = insert_pname(X_3,insert_pname(X_3,A_1)) ). 7.68/7.75 7.68/7.75 fof(fact_610_termination__basic__simps_I3_J,axiom, 7.68/7.75 ! [Z,X,Y] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))) 7.68/7.75 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ) ). 7.68/7.75 7.68/7.75 fof(fact_487_singleton__conv,axiom, 7.68/7.75 ! [A_3] : collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool) ). 7.68/7.75 7.68/7.75 fof(gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : 7.68/7.75 ( is_fun1661590463l_bool(insert1325755072e_bool(B_1_1,B_2_1)) 7.68/7.75 <= ( is_fun_pname_bool(B_1_1) 7.68/7.75 & is_fun1661590463l_bool(B_2_1) ) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : is_bool(hAPP_f937997336l_bool(B_1_1,B_2_1)) ). 7.68/7.75 7.68/7.75 fof(fact_630_Suc__lessI,axiom, 7.68/7.75 ! [M,N] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) 7.68/7.75 => ( N != hAPP_nat_nat(suc,M) 7.68/7.75 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N)) ) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : 7.68/7.75 ( is_pname(hAPP_pname_pname(B_1_1,B_2_1)) 7.68/7.75 <= is_pname(B_2_1) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.75 ! [B_1_1] : 7.68/7.75 ( is_fun949378684l_bool(B_1_1) 7.68/7.75 => is_fun949378684l_bool(collect_fun_a_bool(B_1_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_187_pigeonhole__infinite,axiom, 7.68/7.75 ! [F,A_1] : 7.68/7.75 ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.75 => ( ? [X_1] : 7.68/7.75 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) 7.68/7.75 & ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A_1)),hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,F)),hAPP_nat_pname(F,X_1)))))) ) 7.68/7.75 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(F,A_1))) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_247_insert__absorb2,axiom, 7.68/7.75 ! [X_3,A_1] : insert_a(X_3,insert_a(X_3,A_1)) = insert_a(X_3,A_1) ). 7.68/7.75 7.68/7.75 fof(fact_61_card__insert__if,axiom, 7.68/7.75 ! [X_3,A_1] : 7.68/7.75 ( ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,A_1) = hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1)) ) 7.68/7.75 & ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1)) 7.68/7.75 => hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)) ) ) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_626_Suc__less__SucD,axiom, 7.68/7.75 ! [M,N] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) 7.68/7.75 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_n1025906991e_bool(B_1_1,B_2_1)) ). 7.68/7.75 7.68/7.75 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(P,R),Q) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(P),Q),R) ). 7.68/7.75 7.68/7.75 fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_025,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_f434788991l_bool(P,hAPP_p61793385e_bool(Q,R)) = hAPP_p338031245l_bool(cOMBB_408569982_pname(P,Q),R) ). 7.68/7.75 7.68/7.75 fof(fact_307_imageI,axiom, 7.68/7.75 ! [F,X_3,A_1] : 7.68/7.75 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.75 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_3)),image_pname_a(F,A_1))) ) ). 7.68/7.75 7.68/7.75 fof(fact_570_less__eq__nat_Osimps_I2_J,axiom, 7.68/7.75 ! [M_1,Na] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na)) 7.68/7.75 <=> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),Na)) ) ). 7.68/7.75 7.68/7.75 fof(fact_225_insertE,axiom, 7.68/7.75 ! [A_3,B_1,A_1] : 7.68/7.75 ( ( A_3 != B_1 7.68/7.75 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1)) ) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,A_1))) ) ). 7.68/7.75 7.68/7.75 fof(fact_204_pigeonhole__infinite,axiom, 7.68/7.75 ! [F,A_1] : 7.68/7.75 ( ( ? [X_1] : 7.68/7.75 ( is_pname(X_1) 7.68/7.75 & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.75 & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,F)),hAPP_p61793385e_bool(F,X_1)))))) ) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(F,A_1))) ) 7.68/7.75 <= ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_602_le__add__diff__inverse,axiom, 7.68/7.75 ! [N,M] : 7.68/7.75 ( M = hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) 7.68/7.75 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) ) ). 7.68/7.75 7.68/7.75 fof(fact_213_image__eqI,axiom, 7.68/7.75 ! [A_1,B_1,F,X_3] : 7.68/7.75 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1))) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ) 7.68/7.75 <= hAPP_nat_pname(F,X_3) = B_1 ) ). 7.68/7.75 7.68/7.75 fof(fact_470_Collect__conv__if,axiom, 7.68/7.75 ! [Pa,A_3] : 7.68/7.75 ( ( ~ hBOOL(hAPP_nat_bool(Pa,A_3)) 7.68/7.75 => collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),Pa)) = bot_bot_fun_nat_bool ) 7.68/7.75 & ( insert_nat(A_3,bot_bot_fun_nat_bool) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),Pa)) 7.68/7.75 <= hBOOL(hAPP_nat_bool(Pa,A_3)) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_90_diff__commute,axiom, 7.68/7.75 ! [I,J_2,K] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),K)),J_2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J_2)),K) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000t__a_000tc__Com__Opname,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : 7.68/7.75 ( is_a(B_2_1) 7.68/7.75 => is_pname(hAPP_a_pname(B_1_1,B_2_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_394_empty__subsetI,axiom, 7.68/7.75 ! [A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_1)) ). 7.68/7.75 7.68/7.75 fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_nat_bool(hAPP_f282463732t_bool(P,R),Q) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(cOMBC_619334683t_bool(P),Q),R) ). 7.68/7.75 7.68/7.75 fof(fact_553_order__eq__iff,axiom, 7.68/7.75 ! [X_3,Y_2] : 7.68/7.75 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_2)) 7.68/7.75 & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_3)) ) 7.68/7.75 <=> X_3 = Y_2 ) ). 7.68/7.75 7.68/7.75 fof(fact_82_nat_Oinject,axiom, 7.68/7.75 ! [Nat_3,Nat_2] : 7.68/7.75 ( hAPP_nat_nat(suc,Nat_3) = hAPP_nat_nat(suc,Nat_2) 7.68/7.75 <=> Nat_3 = Nat_2 ) ). 7.68/7.75 7.68/7.75 fof(fact_230_insertI1,axiom, 7.68/7.75 ! [A_3,B_6] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(A_3,B_6))) ). 7.68/7.75 7.68/7.75 fof(fact_59_card__insert__le,axiom, 7.68/7.75 ! [X_3,A_1] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A_1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)))) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_54_card__insert__le,axiom, 7.68/7.75 ! [X_3,A_1] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)))) 7.68/7.75 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_79_finite__Collect__le__nat,axiom, 7.68/7.75 ! [K_2] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),K_2)))) ). 7.68/7.75 7.68/7.75 fof(fact_43_card__mono,axiom, 7.68/7.75 ! [A_1,B_6] : 7.68/7.75 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)),hAPP_f55526627ol_nat(finite1340463720e_bool,B_6))) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6)) ) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) ) ). 7.68/7.75 7.68/7.75 fof(fact_564_finite__induct,axiom, 7.68/7.75 ! [Pa,F_1] : 7.68/7.75 ( ( hBOOL(hAPP_f1935102916l_bool(Pa,bot_bo1649642514l_bool)) 7.68/7.75 => ( ! [X_1,F_2] : 7.68/7.75 ( ( is_fun1661590463l_bool(F_2) 7.68/7.75 & is_fun_pname_bool(X_1) ) 7.68/7.75 => ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),F_2)) 7.68/7.75 => ( hBOOL(hAPP_f1935102916l_bool(Pa,F_2)) 7.68/7.75 => hBOOL(hAPP_f1935102916l_bool(Pa,insert1325755072e_bool(X_1,F_2))) ) ) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2)) ) ) 7.68/7.75 => hBOOL(hAPP_f1935102916l_bool(Pa,F_1)) ) ) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_492_singleton__conv2,axiom, 7.68/7.75 ! [A_3] : insert1325755072e_bool(A_3,bot_bo1649642514l_bool) = collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,A_3)) ). 7.68/7.75 7.68/7.75 fof(fact_241_insert__Collect,axiom, 7.68/7.75 ! [A_3,Pa] : insert1325755072e_bool(A_3,collec1974731493e_bool(Pa)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3))),Pa)) ). 7.68/7.75 7.68/7.75 fof(fact_534_xt1_I3_J,axiom, 7.68/7.75 ! [C_1,A_3,B_1] : 7.68/7.75 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),B_1)) 7.68/7.75 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),A_3)) ) 7.68/7.75 <= A_3 = B_1 ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__Nat__Onat_000t__a,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : is_a(hAPP_nat_a(B_1_1,B_2_1)) ). 7.68/7.75 7.68/7.75 fof(fact_583_diff__cancel2,axiom, 7.68/7.75 ! [M,K,N] : hAPP_nat_nat(minus_minus_nat(M),N) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K)),hAPP_nat_nat(plus_plus_nat(N),K)) ). 7.68/7.75 7.68/7.75 fof(fact_252_insert__iff,axiom, 7.68/7.75 ! [A_3,B_1,A_1] : 7.68/7.75 ( ( is_pname(B_1) 7.68/7.75 & is_pname(A_3) ) 7.68/7.75 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,A_1))) 7.68/7.75 <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)) 7.68/7.75 | B_1 = A_3 ) ) ) ). 7.68/7.75 7.68/7.75 fof(conj_6,conjecture, 7.68/7.75 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))) ). 7.68/7.75 7.68/7.75 fof(fact_364_image__subsetI,axiom, 7.68/7.75 ! [F,B_6,A_1] : 7.68/7.75 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(F,A_1)),B_6)) 7.68/7.75 <= ! [X_1] : 7.68/7.75 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) 7.68/7.75 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(F,X_1)),B_6)) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_11_finite__imageI,axiom, 7.68/7.75 ! [H,F_1] : 7.68/7.75 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(H,F_1))) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_144_finite__surj,axiom, 7.68/7.75 ! [B_6,F,A_1] : 7.68/7.75 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_nat_pname(F,A_1))) 7.68/7.75 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_496_subset__singletonD,axiom, 7.68/7.75 ! [A_1,X_3] : 7.68/7.75 ( ( ( A_1 = insert_a(X_3,bot_bot_fun_a_bool) 7.68/7.75 | bot_bot_fun_a_bool = A_1 ) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(X_3,bot_bot_fun_a_bool))) ) 7.68/7.75 <= is_fun_a_bool(A_1) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : 7.68/7.75 ( is_bool(hAPP_bool_bool(B_1_1,B_2_1)) 7.68/7.75 <= is_bool(B_2_1) ) ). 7.68/7.75 7.68/7.75 fof(help_fconj_1_1_U,axiom, 7.68/7.75 ! [Q,P] : 7.68/7.75 ( ~ hBOOL(Q) 7.68/7.75 | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) 7.68/7.75 | ~ hBOOL(P) ) ). 7.68/7.75 7.68/7.75 fof(fact_485_singleton__conv,axiom, 7.68/7.75 ! [A_3] : insert_fun_nat_bool(A_3,bot_bo1701429464l_bool) = collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)) ). 7.68/7.75 7.68/7.75 fof(fact_554_order__eq__iff,axiom, 7.68/7.75 ! [X_3,Y_2] : 7.68/7.75 ( ( is_fun_a_bool(X_3) 7.68/7.75 & is_fun_a_bool(Y_2) ) 7.68/7.75 => ( X_3 = Y_2 7.68/7.75 <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3)) 7.68/7.75 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) ) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_531_xt1_I3_J,axiom, 7.68/7.75 ! [C_1,A_3,B_1] : 7.68/7.75 ( A_3 = B_1 7.68/7.75 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),B_1)) 7.68/7.75 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),A_3)) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_31_card__image__le,axiom, 7.68/7.75 ! [F,A_1] : 7.68/7.75 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) 7.68/7.75 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(F,A_1))),hAPP_f696928925ol_nat(finite346522414t_bool,A_1))) ) ). 7.68/7.75 7.68/7.75 fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_a_bool(hAPP_f1549043526a_bool(cOMBC_777206479l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_a1392362872l_bool(P,R),Q) ). 7.68/7.75 7.68/7.75 fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_p61793385e_bool(P,hAPP_f1291551745_pname(Q,R)) = hAPP_f654413245e_bool(cOMBB_141086128t_bool(P,Q),R) ). 7.68/7.75 7.68/7.75 fof(fact_313_insert__compr__raw,axiom, 7.68/7.75 ! [X_1,Xa] : collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),Xa))) = insert_fun_nat_bool(X_1,Xa) ). 7.68/7.75 7.68/7.75 fof(gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : 7.68/7.75 ( is_fun1661590463l_bool(B_2_1) 7.68/7.75 => is_fun1661590463l_bool(cOMBS_350070575l_bool(B_1_1,B_2_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_511_order__trans,axiom, 7.68/7.75 ! [Z_1,X_3,Y_2] : 7.68/7.75 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1)) 7.68/7.75 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Z_1)) ) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) ) ). 7.68/7.75 7.68/7.75 fof(fact_514_order__trans,axiom, 7.68/7.75 ! [Z_1,X_3,Y_2] : 7.68/7.75 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),Z_1)) 7.68/7.75 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Z_1)) ) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) ) ). 7.68/7.75 7.68/7.75 fof(conj_1,hypothesis, 7.68/7.75 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))) ). 7.68/7.75 7.68/7.75 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_bool_bool(P,hAPP_a_bool(Q,R)) = hAPP_a_bool(cOMBB_bool_bool_a(P,Q),R) ). 7.68/7.75 7.68/7.75 fof(fact_660_Suc__le__eq,axiom, 7.68/7.75 ! [M_1,Na] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na)) 7.68/7.75 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : 7.68/7.75 ( is_fun_pname_bool(B_2_1) 7.68/7.75 => is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_112_rev__finite__subset,axiom, 7.68/7.75 ! [A_1,B_6] : 7.68/7.75 ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ). 7.68/7.75 7.68/7.75 fof(fact_342_insert__image,axiom, 7.68/7.75 ! [F,X_3,A_1] : 7.68/7.75 ( image_nat_a(F,A_1) = insert_a(hAPP_nat_a(F,X_3),image_nat_a(F,A_1)) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_22_finite__imageI,axiom, 7.68/7.75 ! [H,F_1] : 7.68/7.75 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) 7.68/7.75 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(H,F_1))) ) ). 7.68/7.75 7.68/7.75 fof(fact_680_zero__less__Suc,axiom, 7.68/7.75 ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N))) ). 7.68/7.75 7.68/7.75 fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool,axiom, 7.68/7.75 ! [P,Q] : 7.68/7.75 ( is_bool(P) 7.68/7.75 => hAPP_f54304608l_bool(cOMBK_1994329625t_bool(P),Q) = P ) ). 7.68/7.75 7.68/7.75 fof(fact_131_finite__surj,axiom, 7.68/7.75 ! [B_6,F,A_1] : 7.68/7.75 ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_a_a(F,A_1))) ) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_633_not__less__less__Suc__eq,axiom, 7.68/7.75 ! [Na,M_1] : 7.68/7.75 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) 7.68/7.75 <=> M_1 = Na ) 7.68/7.75 <= ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_524_xt1_I4_J,axiom, 7.68/7.75 ! [C_1,B_1,A_3] : 7.68/7.75 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_1),A_3)) 7.68/7.75 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),A_3)) 7.68/7.75 <= C_1 = B_1 ) ) ). 7.68/7.75 7.68/7.75 fof(fact_507_xt1_I5_J,axiom, 7.68/7.75 ! [Y_2,X_3] : 7.68/7.75 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3)) 7.68/7.75 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) 7.68/7.75 => Y_2 = X_3 ) ) 7.68/7.75 <= ( is_fun_pname_bool(Y_2) 7.68/7.75 & is_fun_pname_bool(X_3) ) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : is_fun1661590463l_bool(hAPP_n850744903l_bool(B_1_1,B_2_1)) ). 7.68/7.75 7.68/7.75 fof(fact_644_termination__basic__simps_I5_J,axiom, 7.68/7.75 ! [X,Y] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) 7.68/7.75 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : is_fun949378684l_bool(hAPP_n1414589940l_bool(B_1_1,B_2_1)) ). 7.68/7.75 7.68/7.75 fof(fact_350_image__mono,axiom, 7.68/7.75 ! [F,A_1,B_6] : 7.68/7.75 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.68/7.75 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(F,A_1)),image_nat_a(F,B_6))) ) ). 7.68/7.75 7.68/7.75 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_004,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)) = hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(P,Q),R) ). 7.68/7.75 7.68/7.75 fof(fact_326_subset__insert,axiom, 7.68/7.75 ! [B_6,X_3,A_1] : 7.68/7.75 ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.75 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(X_3,B_6))) 7.68/7.75 <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_439_bot__unique,axiom, 7.68/7.75 ! [A_3] : 7.68/7.75 ( ( A_3 = bot_bot_fun_a_bool 7.68/7.75 <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),bot_bot_fun_a_bool)) ) 7.68/7.75 <= is_fun_a_bool(A_3) ) ). 7.68/7.75 7.68/7.75 fof(fact_398_Collect__empty__eq,axiom, 7.68/7.75 ! [Pa] : 7.68/7.75 ( ! [X_1] : 7.68/7.75 ( ~ hBOOL(hAPP_pname_bool(Pa,X_1)) 7.68/7.75 <= is_pname(X_1) ) 7.68/7.75 <=> bot_bo844097828e_bool = collect_pname(Pa) ) ). 7.68/7.75 7.68/7.75 fof(fact_137_finite__surj,axiom, 7.68/7.75 ! [B_6,F,A_1] : 7.68/7.75 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.75 => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_112932426a_bool(F,A_1))) 7.68/7.75 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_28_finite_OinsertI,axiom, 7.68/7.75 ! [A_3,A_1] : 7.68/7.75 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_3,A_1))) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_525_ord__le__eq__trans,axiom, 7.68/7.75 ! [C_1,A_3,B_1] : 7.68/7.75 ( ( ( hBOOL(C_1) 7.68/7.75 <=> hBOOL(B_1) ) 7.68/7.75 => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),C_1)) ) 7.68/7.75 <= hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),B_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_15_finite__imageI,axiom, 7.68/7.75 ! [H,F_1] : 7.68/7.75 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(H,F_1))) 7.68/7.75 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_6_finite__Collect__subsets,axiom, 7.68/7.75 ! [A_1] : 7.68/7.75 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.75 => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),A_1)))) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,hypothesis, 7.68/7.75 ! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)) ). 7.68/7.75 7.68/7.75 fof(fact_497_image__constant,axiom, 7.68/7.75 ! [C_1,X_3,A_1] : 7.68/7.75 ( image_pname_a(cOMBK_a_pname(C_1),A_1) = insert_a(C_1,bot_bot_fun_a_bool) 7.68/7.75 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ) ). 7.68/7.75 7.68/7.75 fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_f759274231e_bool(cOMBB_598082538e_bool(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_f1297739591_pname(Q,R)) ). 7.68/7.75 7.68/7.75 fof(fact_495_subset__singletonD,axiom, 7.68/7.75 ! [A_1,X_3] : 7.68/7.75 ( is_fun_pname_bool(A_1) 7.68/7.75 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(X_3,bot_bo844097828e_bool))) 7.68/7.75 => ( A_1 = bot_bo844097828e_bool 7.68/7.75 | A_1 = insert_pname(X_3,bot_bo844097828e_bool) ) ) ) ). 7.68/7.75 7.68/7.75 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R)) = hAPP_p393069232l_bool(cOMBB_675860798_pname(P,Q),R) ). 7.68/7.75 7.68/7.75 fof(fact_673_less__imp__Suc__add,axiom, 7.68/7.75 ! [M,N] : 7.68/7.75 ( ? [K_1] : N = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),K_1)) 7.68/7.75 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ). 7.68/7.75 7.68/7.75 fof(fact_155_finite__subset__image,axiom, 7.68/7.75 ! [F,A_1,B_6] : 7.68/7.75 ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_nat_bool_a(F,A_1))) 7.68/7.75 => ? [C_7] : 7.68/7.75 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7)) 7.68/7.75 & image_fun_nat_bool_a(F,C_7) = B_6 7.68/7.75 & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) ) ) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) 7.68/7.75 <= is_fun_a_bool(B_6) ) ). 7.68/7.75 7.68/7.75 fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(P),Q),R) = hAPP_a_bool(hAPP_p1534023578a_bool(P,R),Q) ). 7.68/7.75 7.68/7.75 fof(fact_191_pigeonhole__infinite,axiom, 7.68/7.75 ! [F,A_1] : 7.68/7.75 ( ( ? [X_1] : 7.68/7.75 ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) 7.68/7.75 & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),A_1)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,F)),hAPP_f1297739591_pname(F,X_1)))))) 7.68/7.75 & is_fun_pname_bool(X_1) ) 7.68/7.75 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(F,A_1))) ) 7.68/7.75 <= ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,axiom, 7.68/7.75 ! [X,Y] : 7.68/7.75 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X),Y)) 7.68/7.75 | X != Y ) ). 7.68/7.75 7.68/7.75 fof(fact_604_le__diff__conv,axiom, 7.68/7.75 ! [J_1,K_2,I_1] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(plus_plus_nat(I_1),K_2))) 7.68/7.75 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_1),K_2)),I_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_605_diff__diff__right,axiom, 7.68/7.75 ! [I,K,J_2] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) 7.68/7.75 => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),K)),J_2) = hAPP_nat_nat(minus_minus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)) ) ). 7.68/7.75 7.68/7.75 fof(fact_481_Collect__conv__if2,axiom, 7.68/7.75 ! [Pa,A_3] : 7.68/7.75 ( ( bot_bo1389914601l_bool = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)),Pa)) 7.68/7.75 <= ~ hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) ) 7.68/7.75 & ( insert_fun_a_bool(A_3,bot_bo1389914601l_bool) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)),Pa)) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_451_singletonE,axiom, 7.68/7.75 ! [B_1,A_3] : 7.68/7.75 ( ( B_1 = A_3 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),insert_a(A_3,bot_bot_fun_a_bool))) ) 7.68/7.75 <= ( is_a(B_1) 7.68/7.75 & is_a(A_3) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_25_finite_OinsertI,axiom, 7.68/7.75 ! [A_3,A_1] : 7.68/7.75 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) 7.68/7.75 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_3,A_1))) ) ). 7.68/7.75 7.68/7.75 fof(fact_581_diff__diff__left,axiom, 7.68/7.75 ! [I,J_2,K] : hAPP_nat_nat(minus_minus_nat(I),hAPP_nat_nat(plus_plus_nat(J_2),K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J_2)),K) ). 7.68/7.75 7.68/7.75 fof(fact_24_finite_OinsertI,axiom, 7.68/7.75 ! [A_3,A_1] : 7.68/7.75 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_3,A_1))) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_80_card__Collect__le__nat,axiom, 7.68/7.75 ! [Na] : hAPP_nat_nat(suc,Na) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),Na))) ). 7.68/7.75 7.68/7.75 fof(fact_304_imageI,axiom, 7.68/7.75 ! [F,X_3,A_1] : 7.68/7.75 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(F,X_3)),image_a_nat(F,A_1))) 7.68/7.75 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_330_subset__insertI2,axiom, 7.68/7.75 ! [B_1,A_1,B_6] : 7.68/7.75 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) 7.68/7.75 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(B_1,B_6))) ) ). 7.68/7.75 7.68/7.75 fof(fact_116_le__SucE,axiom, 7.68/7.75 ! [M,N] : 7.68/7.75 ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) 7.68/7.75 => M = hAPP_nat_nat(suc,N) ) 7.68/7.75 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))) ) ). 7.68/7.75 7.68/7.75 fof(fact_560_finite__subset__induct,axiom, 7.68/7.75 ! [Pa,A_1,F_1] : 7.68/7.75 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) 7.68/7.75 => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,F_1),A_1)) 7.68/7.75 => ( hBOOL(hAPP_f1935102916l_bool(Pa,bot_bo1649642514l_bool)) 7.68/7.75 => ( hBOOL(hAPP_f1935102916l_bool(Pa,F_1)) 7.68/7.75 <= ! [A_2,F_2] : 7.68/7.75 ( ( is_fun_pname_bool(A_2) 7.68/7.75 & is_fun1661590463l_bool(F_2) ) 7.68/7.75 => ( ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A_1)) 7.68/7.75 => ( ( hBOOL(hAPP_f1935102916l_bool(Pa,insert1325755072e_bool(A_2,F_2))) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(Pa,F_2)) ) 7.68/7.75 <= ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),F_2)) ) ) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2)) ) ) ) ) ) ) ). 7.68/7.75 7.68/7.75 fof(gsy_v_wt,axiom, 7.68/7.75 ! [B_1_1] : is_bool(wt(B_1_1)) ). 7.68/7.75 7.68/7.75 fof(fact_384_emptyE,axiom, 7.68/7.75 ! [A_3] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),bot_bo844097828e_bool)) ). 7.68/7.75 7.68/7.75 fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__,axiom, 7.68/7.75 is_fun1661590463l_bool(bot_bo1649642514l_bool) ). 7.68/7.75 7.68/7.75 fof(fact_591_add__le__mono,axiom, 7.68/7.75 ! [K,L,I,J_2] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) 7.68/7.75 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),L))) 7.68/7.75 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),L)) ) ) ). 7.68/7.75 7.68/7.75 fof(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : 7.68/7.75 ( is_fun949378684l_bool(B_2_1) 7.68/7.75 => is_bool(hAPP_f621171935l_bool(B_1_1,B_2_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_52_card__seteq,axiom, 7.68/7.75 ! [A_1,B_6] : 7.68/7.75 ( ( is_fun_a_bool(A_1) 7.68/7.75 & is_fun_a_bool(B_6) ) 7.68/7.75 => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) 7.68/7.75 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) 7.68/7.75 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,B_6)),hAPP_fun_a_bool_nat(finite_card_a,A_1))) 7.68/7.75 => B_6 = A_1 ) ) ) ) ). 7.68/7.75 7.68/7.75 fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,axiom, 7.68/7.75 ! [P,Q,R] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1476298914l_bool(P,R),hAPP_f1664156314l_bool(Q,R)) ). 7.68/7.75 7.68/7.75 fof(fact_302_image__iff,axiom, 7.68/7.75 ! [Z_1,F,A_1] : 7.68/7.75 ( ( ? [X_1] : 7.68/7.75 ( is_pname(X_1) 7.68/7.75 & Z_1 = hAPP_pname_a(F,X_1) 7.68/7.75 & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) ) 7.68/7.75 <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z_1),image_pname_a(F,A_1))) ) 7.68/7.75 <= is_a(Z_1) ) ). 7.68/7.75 7.68/7.75 fof(fact_299_equalityE,axiom, 7.68/7.75 ! [A_1,B_6] : 7.68/7.75 ( ~ ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1)) 7.68/7.75 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ) 7.68/7.75 <= B_6 = A_1 ) ). 7.68/7.75 7.68/7.75 fof(fact_121_Suc__n__not__le__n,axiom, 7.68/7.75 ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N)) ). 7.68/7.75 7.68/7.75 fof(gsy_c_Set_Oimage_000tc__Com__Opname_000t__a,hypothesis, 7.68/7.75 ! [B_1_1,B_2_1] : 7.68/7.75 ( is_fun_pname_bool(B_2_1) 7.68/7.75 => is_fun_a_bool(image_pname_a(B_1_1,B_2_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_152_finite__surj,axiom, 7.68/7.75 ! [B_6,F,A_1] : 7.68/7.75 ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_1551609309ol_nat(F,A_1))) ) 7.68/7.75 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_324_insert__subset,axiom, 7.68/7.75 ! [X_3,A_1,B_6] : 7.68/7.75 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_3,A_1)),B_6)) 7.68/7.75 <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) 7.68/7.75 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ) ). 7.68/7.75 7.68/7.75 fof(fact_670_less__eq__Suc__le__raw,axiom, 7.68/7.75 ! [X_1] : hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1)) ). 7.68/7.75 7.68/7.75 fof(fact_139_finite__surj,axiom, 7.68/7.75 ! [B_6,F,A_1] : 7.68/7.75 ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) 7.68/7.75 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_pname_nat(F,A_1))) ) 7.68/7.75 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_662_Suc__leI,axiom, 7.68/7.75 ! [M,N] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) 7.68/7.75 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) ) ). 7.68/7.75 7.68/7.75 fof(fact_386_finite_OemptyI,axiom, 7.68/7.75 hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,bot_bo1701429464l_bool)) ). 7.68/7.75 7.68/7.75 fof(fact_16_finite__imageI,axiom, 7.68/7.75 ! [H,F_1] : 7.68/7.75 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) 7.68/7.75 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(H,F_1))) ) ). 7.68/7.75 7.68/7.75 fof(fact_244_insert__Collect,axiom, 7.68/7.75 ! [A_3,Pa] : collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3))),Pa)) = insert_a(A_3,collect_a(Pa)) ). 7.68/7.75 7.68/7.75 fof(conj_2,hypothesis, 7.68/7.75 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ). 7.68/7.75 7.68/7.75 fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,axiom, 7.68/7.75 ! [B_1_1,B_2_1] : 7.68/7.75 ( is_fun_pname_bool(B_2_1) 7.68/7.75 => is_fun_pname_bool(image_pname_pname(B_1_1,B_2_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_85_le__antisym,axiom, 7.68/7.75 ! [M,N] : 7.68/7.75 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) 7.68/7.75 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) 7.68/7.75 => N = M ) ) ). 7.68/7.75 7.68/7.75 fof(fact_202_pigeonhole__infinite,axiom, 7.68/7.75 ! [F,A_1] : 7.68/7.75 ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(F,A_1))) 7.68/7.75 => ? [X_1] : 7.68/7.75 ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A_1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,F)),hAPP_nat_fun_a_bool(F,X_1)))))) 7.68/7.75 & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) 7.68/7.75 <= ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ) ). 7.68/7.75 7.68/7.75 fof(fact_395_equals0D,axiom, 7.68/7.75 ! [A_3,A_1] : 7.68/7.76 ( bot_bot_fun_nat_bool = A_1 7.68/7.76 => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_303_imageI,axiom, 7.68/7.76 ! [F,X_3,A_1] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.76 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(F,X_3)),image_pname_nat(F,A_1))) ) ). 7.68/7.76 7.68/7.76 fof(fact_294_Collect__def,axiom, 7.68/7.76 ! [Pa] : 7.68/7.76 ( is_fun949378684l_bool(Pa) 7.68/7.76 => collect_fun_a_bool(Pa) = Pa ) ). 7.68/7.76 7.68/7.76 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__021,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(P,R),Q) ). 7.68/7.76 7.68/7.76 fof(fact_325_subset__insert,axiom, 7.68/7.76 ! [B_6,X_3,A_1] : 7.68/7.76 ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) 7.68/7.76 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.68/7.76 <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(X_3,B_6))) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_503_xt1_I6_J,axiom, 7.68/7.76 ! [Z_3,Y_7,X_8] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_8)) 7.68/7.76 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_3),X_8)) 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_3),Y_7)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_64_card__insert__if,axiom, 7.68/7.76 ! [X_3,A_1] : 7.68/7.76 ( ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.76 => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A_1)) ) 7.68/7.76 & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.76 => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_f921600141ol_nat(finite_card_pname,A_1) ) ) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_a_fun_nat_bool(cOMBB_1321347587bool_a(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_a_nat(Q,R)) ). 7.68/7.76 7.68/7.76 fof(fact_256_insert__code,axiom, 7.68/7.76 ! [Y_2,A_1,X_3] : 7.68/7.76 ( ( hBOOL(hAPP_a_bool(insert_a(Y_2,A_1),X_3)) 7.68/7.76 <=> ( hBOOL(hAPP_a_bool(A_1,X_3)) 7.68/7.76 | X_3 = Y_2 ) ) 7.68/7.76 <= ( is_a(X_3) 7.68/7.76 & is_a(Y_2) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_267_subset__refl,axiom, 7.68/7.76 ! [A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),A_1)) ). 7.68/7.76 7.68/7.76 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : is_bool(hAPP_f389811538l_bool(B_1_1,B_2_1)) ). 7.68/7.76 7.68/7.76 fof(fact_37_card__image__le,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) 7.68/7.76 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(F,A_1))),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))) ) ). 7.68/7.76 7.68/7.76 fof(fact_621_trans__less__add2,axiom, 7.68/7.76 ! [M,I,J_2] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(plus_plus_nat(M),J_2))) 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ) ). 7.68/7.76 7.68/7.76 fof(fact_142_finite__surj,axiom, 7.68/7.76 ! [B_6,F,A_1] : 7.68/7.76 ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) 7.68/7.76 <= hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_1655916159e_bool(F,A_1))) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_185_lift__Suc__mono__le,axiom, 7.68/7.76 ! [Na,N_3,F] : 7.68/7.76 ( ! [N_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,N_2)),hAPP_nat_fun_a_bool(F,hAPP_nat_nat(suc,N_2)))) 7.68/7.76 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,Na)),hAPP_nat_fun_a_bool(F,N_3))) 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_536_ord__eq__le__trans,axiom, 7.68/7.76 ! [C_1,A_3,B_1] : 7.68/7.76 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_1),C_1)) 7.68/7.76 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),C_1)) ) 7.68/7.76 <= A_3 = B_1 ) ). 7.68/7.76 7.68/7.76 fof(fact_208_pigeonhole__infinite,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) 7.68/7.76 => ( ? [X_1] : 7.68/7.76 ( is_a(X_1) 7.68/7.76 & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) 7.68/7.76 & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,F)),hAPP_a93125764e_bool(F,X_1)))))) ) 7.68/7.76 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(F,A_1))) ) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_Set_Oimage_000t__a_000t__a,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : 7.68/7.76 ( is_fun_a_bool(image_a_a(B_1_1,B_2_1)) 7.68/7.76 <= is_fun_a_bool(B_2_1) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1)) ). 7.68/7.76 7.68/7.76 fof(fact_469_empty__is__image,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( ( bot_bo844097828e_bool = A_1 7.68/7.76 <=> image_pname_a(F,A_1) = bot_bot_fun_a_bool ) 7.68/7.76 <= is_fun_pname_bool(A_1) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_pname_bool(cOMBB_647938656_pname(P,Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R)) ). 7.68/7.76 7.68/7.76 fof(fact_45_card__mono,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.76 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A_1)),hAPP_f921600141ol_nat(finite_card_pname,B_6))) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) ). 7.68/7.76 7.68/7.76 fof(fact_417_all__not__in__conv,axiom, 7.68/7.76 ! [A_1] : 7.68/7.76 ( ( bot_bo844097828e_bool = A_1 7.68/7.76 <=> ! [X_1] : 7.68/7.76 ( is_pname(X_1) 7.68/7.76 => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) ) ) 7.68/7.76 <= is_fun_pname_bool(A_1) ) ). 7.68/7.76 7.68/7.76 fof(fact_667_less__diff__conv,axiom, 7.68/7.76 ! [I_1,J_1,K_2] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_2))) 7.68/7.76 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_2)),J_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_124_le__diff__iff,axiom, 7.68/7.76 ! [Na,K_2,M_1] : 7.68/7.76 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) 7.68/7.76 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_2)),hAPP_nat_nat(minus_minus_nat(Na),K_2))) 7.68/7.76 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ) 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_480_Collect__conv__if2,axiom, 7.68/7.76 ! [Pa,A_3] : 7.68/7.76 ( ( insert1325755072e_bool(A_3,bot_bo1649642514l_bool) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_3)),Pa)) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) ) 7.68/7.76 & ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) 7.68/7.76 => bot_bo1649642514l_bool = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_3)),Pa)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_652_finite__nat__set__iff__bounded,axiom, 7.68/7.76 ! [N_1] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1)) 7.68/7.76 <=> ? [M_2] : 7.68/7.76 ! [X_1] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) 7.68/7.76 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M_2)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_119_le__Suc__eq,axiom, 7.68/7.76 ! [M_1,Na] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,Na))) 7.68/7.76 <=> ( M_1 = hAPP_nat_nat(suc,Na) 7.68/7.76 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_627_Suc__lessD,axiom, 7.68/7.76 ! [M,N] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N)) 7.68/7.76 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_nat_bool(hAPP_p1499970991t_bool(P,R),Q) = hAPP_pname_bool(hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(P),Q),R) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_fun_a_bool_bool(Q,R)) ). 7.68/7.76 7.68/7.76 fof(fact_365_image__subsetI,axiom, 7.68/7.76 ! [F,B_6,A_1] : 7.68/7.76 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(F,A_1)),B_6)) 7.68/7.76 <= ! [X_1] : 7.68/7.76 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(F,X_1)),B_6)) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_312_rev__image__eqI,axiom, 7.68/7.76 ! [B_1,F,X_3,A_1] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.76 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) 7.68/7.76 <= hAPP_pname_a(F,X_3) = B_1 ) ) ). 7.68/7.76 7.68/7.76 fof(fact_220_subsetD,axiom, 7.68/7.76 ! [C_1,A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.76 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B_6)) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A_1)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_278_in__mono,axiom, 7.68/7.76 ! [X_3,A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.68/7.76 => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) 7.68/7.76 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_215_image__eqI,axiom, 7.68/7.76 ! [A_1,B_1,F,X_3] : 7.68/7.76 ( hAPP_pname_a(F,X_3) = B_1 7.68/7.76 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.76 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) ) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_hAPP_000tc__Com__Opname_000t__a,hypothesis, 7.68/7.76 ! [B_1_1,B_2_1] : 7.68/7.76 ( is_pname(B_2_1) 7.68/7.76 => is_a(hAPP_pname_a(B_1_1,B_2_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_103_finite__subset,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6)) 7.68/7.76 => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) 7.68/7.76 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_316_insert__compr__raw,axiom, 7.68/7.76 ! [X_1,Xa] : collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),Xa))) = insert_nat(X_1,Xa) ). 7.68/7.76 7.68/7.76 fof(fact_698_le__0__eq,axiom, 7.68/7.76 ! [Na] : 7.68/7.76 ( zero_zero_nat = Na 7.68/7.76 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat)) ) ). 7.68/7.76 7.68/7.76 fof(fact_109_rev__finite__subset,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) 7.68/7.76 => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6)) 7.68/7.76 => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_5_finite__Collect__subsets,axiom, 7.68/7.76 ! [A_1] : 7.68/7.76 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A_1)))) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_240_insert__Collect,axiom, 7.68/7.76 ! [A_3,Pa] : insert_fun_nat_bool(A_3,collect_fun_nat_bool(Pa)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3))),Pa)) ). 7.68/7.76 7.68/7.76 fof(fact_565_finite__induct,axiom, 7.68/7.76 ! [Pa,F_1] : 7.68/7.76 ( ( ( ! [X_1,F_2] : 7.68/7.76 ( ( is_fun949378684l_bool(F_2) 7.68/7.76 & is_fun_a_bool(X_1) ) 7.68/7.76 => ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),F_2)) 7.68/7.76 => ( hBOOL(hAPP_f621171935l_bool(Pa,insert_fun_a_bool(X_1,F_2))) 7.68/7.76 <= hBOOL(hAPP_f621171935l_bool(Pa,F_2)) ) ) 7.68/7.76 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_2)) ) ) 7.68/7.76 => hBOOL(hAPP_f621171935l_bool(Pa,F_1)) ) 7.68/7.76 <= hBOOL(hAPP_f621171935l_bool(Pa,bot_bo1389914601l_bool)) ) 7.68/7.76 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_92_finite__Collect__disjI,axiom, 7.68/7.76 ! [Pa,Q_1] : 7.68/7.76 ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1))) 7.68/7.76 & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) ) 7.68/7.76 <=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_1)))) ) ). 7.68/7.76 7.68/7.76 fof(fact_295_Collect__def,axiom, 7.68/7.76 ! [Pa] : collect_nat(Pa) = Pa ). 7.68/7.76 7.68/7.76 fof(fact_441_bot__least,axiom, 7.68/7.76 ! [A_3] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_3)) ). 7.68/7.76 7.68/7.76 fof(fact_459_insert__not__empty,axiom, 7.68/7.76 ! [A_3,A_1] : insert_nat(A_3,A_1) != bot_bot_fun_nat_bool ). 7.68/7.76 7.68/7.76 fof(fact_661_le__imp__less__Suc,axiom, 7.68/7.76 ! [M,N] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) 7.68/7.76 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) ) ). 7.68/7.76 7.68/7.76 fof(fact_434_le__bot,axiom, 7.68/7.76 ! [A_3] : 7.68/7.76 ( is_fun_a_bool(A_3) 7.68/7.76 => ( bot_bot_fun_a_bool = A_3 7.68/7.76 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),bot_bot_fun_a_bool)) ) ) ). 7.68/7.76 7.68/7.76 fof(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom, 7.68/7.76 ! [X,Y] : 7.68/7.76 ( Y != X 7.68/7.76 | hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)) ) ). 7.68/7.76 7.68/7.76 fof(fact_360_image__subsetI,axiom, 7.68/7.76 ! [F,B_6,A_1] : 7.68/7.76 ( ! [X_1] : 7.68/7.76 ( is_pname(X_1) 7.68/7.76 => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(F,X_1)),B_6)) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) ) ) 7.68/7.76 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(F,A_1)),B_6)) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__012,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_f800510211t_bool(cOMBB_1250273980t_bool(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_f22106695ol_nat(Q,R)) ). 7.68/7.76 7.68/7.76 fof(fact_99_finite__insert,axiom, 7.68/7.76 ! [A_3,A_1] : 7.68/7.76 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) 7.68/7.76 <=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_3,A_1))) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__020,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_n1699378549t_bool(Q,R)) ). 7.68/7.76 7.68/7.76 fof(fact_499_linorder__le__cases,axiom, 7.68/7.76 ! [X_9,Y_8] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_8),X_9)) 7.68/7.76 <= ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_9),Y_8)) ) ). 7.68/7.76 7.68/7.76 fof(fact_203_pigeonhole__infinite,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( ( ? [X_1] : 7.68/7.76 ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,F)),hAPP_p1499970991t_bool(F,X_1)))))) 7.68/7.76 & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.76 & is_pname(X_1) ) 7.68/7.76 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(F,A_1))) ) 7.68/7.76 <= ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_424_empty__def,axiom, 7.68/7.76 bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)) ). 7.68/7.76 7.68/7.76 fof(fact_255_insert__code,axiom, 7.68/7.76 ! [Y_2,A_1,X_3] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(insert_nat(Y_2,A_1),X_3)) 7.68/7.76 <=> ( X_3 = Y_2 7.68/7.76 | hBOOL(hAPP_nat_bool(A_1,X_3)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_270_set__eq__subset,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.76 ( A_1 = B_6 7.68/7.76 <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.68/7.76 & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_194_pigeonhole__infinite,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(F,A_1))) 7.68/7.76 => ? [X_1] : 7.68/7.76 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) 7.68/7.76 & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,F)),hAPP_a_nat(F,X_1)))))) 7.68/7.76 & is_a(X_1) ) ) 7.68/7.76 <= ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_566_finite__less__ub,axiom, 7.68/7.76 ! [U,F] : 7.68/7.76 ( ! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),hAPP_nat_nat(F,N_2))) 7.68/7.76 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,F)),U)))) ) ). 7.68/7.76 7.68/7.76 fof(fact_672_inc__induct,axiom, 7.68/7.76 ! [Pa,I_1,J_1] : 7.68/7.76 ( ( ( ! [I_2] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) 7.68/7.76 => ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_2))) 7.68/7.76 => hBOOL(hAPP_nat_bool(Pa,I_2)) ) ) 7.68/7.76 => hBOOL(hAPP_nat_bool(Pa,I_1)) ) 7.68/7.76 <= hBOOL(hAPP_nat_bool(Pa,J_1)) ) 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R)) ). 7.68/7.76 7.68/7.76 fof(gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,hypothesis, 7.68/7.76 is_fun1661590463l_bool(finite_finite_pname) ). 7.68/7.76 7.68/7.76 fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : 7.68/7.76 ( is_fun_a_bool(hAPP_f2050579477a_bool(B_1_1,B_2_1)) 7.68/7.76 <= is_fun_a_bool(B_2_1) ) ). 7.68/7.76 7.68/7.76 fof(fact_123_diff__Suc__Suc,axiom, 7.68/7.76 ! [M,N] : hAPP_nat_nat(minus_minus_nat(M),N) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) ). 7.68/7.76 7.68/7.76 fof(fact_114_rev__finite__subset,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.76 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.68/7.76 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ). 7.68/7.76 7.68/7.76 fof(gsy_v_G,hypothesis, 7.68/7.76 is_fun_a_bool(g) ). 7.68/7.76 7.68/7.76 fof(gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J,hypothesis, 7.68/7.76 ! [B_1_1,B_2_1] : 7.68/7.76 ( is_fun949378684l_bool(hAPP_a85458249l_bool(B_1_1,B_2_1)) 7.68/7.76 <= is_a(B_2_1) ) ). 7.68/7.76 7.68/7.76 fof(fact_686_One__nat__def,axiom, 7.68/7.76 one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ). 7.68/7.76 7.68/7.76 fof(fact_653_card__Collect__less__nat,axiom, 7.68/7.76 ! [Na] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),Na))) = Na ). 7.68/7.76 7.68/7.76 fof(fact_167_finite__subset__image,axiom, 7.68/7.76 ! [F,A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) 7.68/7.76 => ( ? [C_7] : 7.68/7.76 ( image_496248727ol_nat(F,C_7) = B_6 7.68/7.76 & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7)) 7.68/7.76 & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_496248727ol_nat(F,A_1))) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_331_insert__mono,axiom, 7.68/7.76 ! [A_3,C_6,D_1] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_3,C_6)),insert_pname(A_3,D_1))) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_6),D_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_572_add__Suc,axiom, 7.68/7.76 ! [M,N] : hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) ). 7.68/7.76 7.68/7.76 fof(fact_91_finite__Collect__disjI,axiom, 7.68/7.76 ! [Pa,Q_1] : 7.68/7.76 ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1))) 7.68/7.76 & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) ) 7.68/7.76 <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_1)))) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : is_fun_a_bool(image_nat_a(B_1_1,B_2_1)) ). 7.68/7.76 7.68/7.76 fof(fact_446_singleton__inject,axiom, 7.68/7.76 ! [A_3,B_1] : 7.68/7.76 ( ( is_pname(B_1) 7.68/7.76 & is_pname(A_3) ) 7.68/7.76 => ( insert_pname(B_1,bot_bo844097828e_bool) = insert_pname(A_3,bot_bo844097828e_bool) 7.68/7.76 => B_1 = A_3 ) ) ). 7.68/7.76 7.68/7.76 fof(fact_35_card__image__le,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1))) 7.68/7.76 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : 7.68/7.76 ( is_fun949378684l_bool(insert_fun_a_bool(B_1_1,B_2_1)) 7.68/7.76 <= ( is_fun_a_bool(B_1_1) 7.68/7.76 & is_fun949378684l_bool(B_2_1) ) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_HOL_Oundefined_000t__a,axiom, 7.68/7.76 is_a(undefined_a(x_a)) ). 7.68/7.76 7.68/7.76 fof(fact_345_subset__image__iff,axiom, 7.68/7.76 ! [B_6,F,A_1] : 7.68/7.76 ( is_fun_pname_bool(B_6) 7.68/7.76 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1))) 7.68/7.76 <=> ? [AA] : 7.68/7.76 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,AA),A_1)) 7.68/7.76 & image_a_pname(F,AA) = B_6 7.68/7.76 & is_fun_a_bool(AA) ) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_129_diff__le__mono2,axiom, 7.68/7.76 ! [L,M,N] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M))) 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ). 7.68/7.76 7.68/7.76 fof(fact_228_zero__induct__lemma,axiom, 7.68/7.76 ! [I_1,Pa,K_2] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(Pa,K_2)) 7.68/7.76 => ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K_2),I_1))) 7.68/7.76 <= ! [N_2] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2))) 7.68/7.76 => hBOOL(hAPP_nat_bool(Pa,N_2)) ) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_699_less__eq__nat_Osimps_I1_J,axiom, 7.68/7.76 ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)) ). 7.68/7.76 7.68/7.76 fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : 7.68/7.76 ( is_fun_pname_bool(B_2_1) 7.68/7.76 => is_pname(hAPP_f1297739591_pname(B_1_1,B_2_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_601_add__diff__assoc,axiom, 7.68/7.76 ! [I,K,J_2] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) 7.68/7.76 => hAPP_nat_nat(plus_plus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),J_2)),K) ) ). 7.68/7.76 7.68/7.76 fof(fact_104_finite__subset,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6)) 7.68/7.76 => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) 7.68/7.76 => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_196_pigeonhole__infinite,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) 7.68/7.76 => ( ? [X_1] : 7.68/7.76 ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),A_1)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,F)),hAPP_f22106695ol_nat(F,X_1)))))) 7.68/7.76 & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A_1)) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(F,A_1))) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_319_subset__insertI,axiom, 7.68/7.76 ! [B_6,A_3] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),insert_pname(A_3,B_6))) ). 7.68/7.76 7.68/7.76 fof(fact_383_emptyE,axiom, 7.68/7.76 ! [A_3] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),bot_bot_fun_nat_bool)) ). 7.68/7.76 7.68/7.76 fof(fact_89_le__refl,axiom, 7.68/7.76 ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N)) ). 7.68/7.76 7.68/7.76 fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_pname_bool(cOMBS_568398431l_bool(P,Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R)) ). 7.68/7.76 7.68/7.76 fof(fact_146_finite__surj,axiom, 7.68/7.76 ! [B_6,F,A_1] : 7.68/7.76 ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1))) ) 7.68/7.76 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_309_rev__image__eqI,axiom, 7.68/7.76 ! [B_1,F,X_3,A_1] : 7.68/7.76 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) 7.68/7.76 => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1))) 7.68/7.76 <= B_1 = hAPP_a_nat(F,X_3) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_556_finite__subset__induct,axiom, 7.68/7.76 ! [Pa,A_1,F_1] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) 7.68/7.76 => ( ( ( ! [A_2,F_2] : 7.68/7.76 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1)) 7.68/7.76 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),F_2)) 7.68/7.76 => ( hBOOL(hAPP_f54304608l_bool(Pa,insert_nat(A_2,F_2))) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(Pa,F_2)) ) ) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) ) 7.68/7.76 => hBOOL(hAPP_f54304608l_bool(Pa,F_1)) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F_1),A_1)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_58_card__insert__le,axiom, 7.68/7.76 ! [X_3,A_1] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.76 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)))) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(P),Q),R) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(P,R),Q) ). 7.68/7.76 7.68/7.76 fof(fact_687_diffs0__imp__equal,axiom, 7.68/7.76 ! [M,N] : 7.68/7.76 ( ( hAPP_nat_nat(minus_minus_nat(N),M) = zero_zero_nat 7.68/7.76 => M = N ) 7.68/7.76 <= zero_zero_nat = hAPP_nat_nat(minus_minus_nat(M),N) ) ). 7.68/7.76 7.68/7.76 fof(fact_571_add__Suc__right,axiom, 7.68/7.76 ! [M,N] : hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N)) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N)) ). 7.68/7.76 7.68/7.76 fof(fact_143_finite__surj,axiom, 7.68/7.76 ! [B_6,F,A_1] : 7.68/7.76 ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) 7.68/7.76 <= hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_nat_fun_a_bool(F,A_1))) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_281_set__rev__mp,axiom, 7.68/7.76 ! [B_6,X_3,A_1] : 7.68/7.76 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_p1499970991t_bool(cOMBB_523834888_pname(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_pname_nat(Q,R)) ). 7.68/7.76 7.68/7.76 fof(fact_689_minus__nat_Odiff__0,axiom, 7.68/7.76 ! [M] : M = hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat) ). 7.68/7.76 7.68/7.76 fof(help_fconj_2_1_U,axiom, 7.68/7.76 ! [P,Q] : 7.68/7.76 ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) 7.68/7.76 | hBOOL(P) ) ). 7.68/7.76 7.68/7.76 fof(fact_32_card__image__le,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(F,A_1))),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))) 7.68/7.76 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_1_finite__Collect__subsets,axiom, 7.68/7.76 ! [A_1] : 7.68/7.76 ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),A_1)))) 7.68/7.76 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_49_card__seteq,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.76 ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) 7.68/7.76 => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,B_6)),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))) 7.68/7.76 => B_6 = A_1 ) 7.68/7.76 <= hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6)) ) ) 7.68/7.76 <= ( is_fun1661590463l_bool(B_6) 7.68/7.76 & is_fun1661590463l_bool(A_1) ) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.76 ! [B_1_1] : 7.68/7.76 ( is_bool(B_1_1) 7.68/7.76 => is_fun949378684l_bool(cOMBK_324466864a_bool(B_1_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_548_order__eq__refl,axiom, 7.68/7.76 ! [X_4,Y_3] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_3)) 7.68/7.76 <= X_4 = Y_3 ) ). 7.68/7.76 7.68/7.76 fof(fact_437_bot__unique,axiom, 7.68/7.76 ! [A_3] : 7.68/7.76 ( ( hBOOL(A_3) 7.68/7.76 <=> hBOOL(bot_bot_bool) ) 7.68/7.76 <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),bot_bot_bool)) ) ). 7.68/7.76 7.68/7.76 fof(fact_493_singleton__conv2,axiom, 7.68/7.76 ! [A_3] : collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool) ). 7.68/7.76 7.68/7.76 fof(fact_584_le__add2,axiom, 7.68/7.76 ! [N,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(M),N))) ). 7.68/7.76 7.68/7.76 fof(fact_201_pigeonhole__infinite,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.76 => ( ? [X_1] : 7.68/7.76 ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A_1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,F)),hAPP_n1025906991e_bool(F,X_1)))))) 7.68/7.76 & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) 7.68/7.76 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(F,A_1))) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_465_subset__empty,axiom, 7.68/7.76 ! [A_1] : 7.68/7.76 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),bot_bo844097828e_bool)) 7.68/7.76 <=> bot_bo844097828e_bool = A_1 ) 7.68/7.76 <= is_fun_pname_bool(A_1) ) ). 7.68/7.76 7.68/7.76 fof(fact_458_insert__not__empty,axiom, 7.68/7.76 ! [A_3,A_1] : bot_bo844097828e_bool != insert_pname(A_3,A_1) ). 7.68/7.76 7.68/7.76 fof(fact_697_bot__nat__def,axiom, 7.68/7.76 zero_zero_nat = bot_bot_nat ). 7.68/7.76 7.68/7.76 fof(fact_163_finite__subset__image,axiom, 7.68/7.76 ! [F,A_1,B_6] : 7.68/7.76 ( ( ( ? [C_7] : 7.68/7.76 ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) 7.68/7.76 & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7)) 7.68/7.76 & B_6 = image_1921560913_pname(F,C_7) ) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1921560913_pname(F,A_1))) ) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) 7.68/7.76 <= is_fun_pname_bool(B_6) ) ). 7.68/7.76 7.68/7.76 fof(fact_429_bot__apply,axiom, 7.68/7.76 ! [X_3] : 7.68/7.76 ( hBOOL(bot_bot_bool) 7.68/7.76 <=> hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_3)) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.76 is_fun_a_bool(bot_bot_fun_a_bool) ). 7.68/7.76 7.68/7.76 fof(gsy_c_Set_OCollect_000tc__Com__Opname,axiom, 7.68/7.76 ! [B_1_1] : 7.68/7.76 ( is_fun_pname_bool(collect_pname(B_1_1)) 7.68/7.76 <= is_fun_pname_bool(B_1_1) ) ). 7.68/7.76 7.68/7.76 fof(fact_468_image__empty,axiom, 7.68/7.76 ! [F] : bot_bot_fun_a_bool = image_pname_a(F,bot_bo844097828e_bool) ). 7.68/7.76 7.68/7.76 fof(fact_523_xt1_I4_J,axiom, 7.68/7.76 ! [C_5,B_5,A_7] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_5),A_7)) 7.68/7.76 => ( C_5 = B_5 7.68/7.76 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_5),A_7)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_368_order__refl,axiom, 7.68/7.76 ! [X_3] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),X_3)) ). 7.68/7.76 7.68/7.76 fof(fact_67_card__insert__disjoint,axiom, 7.68/7.76 ! [X_3,A_1] : 7.68/7.76 ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)) 7.68/7.76 <= ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1)) ) 7.68/7.76 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_598_le__imp__diff__is__add,axiom, 7.68/7.76 ! [K_2,I_1,J_1] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) 7.68/7.76 => ( hAPP_nat_nat(minus_minus_nat(J_1),I_1) = K_2 7.68/7.76 <=> J_1 = hAPP_nat_nat(plus_plus_nat(K_2),I_1) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_501_xt1_I6_J,axiom, 7.68/7.76 ! [Z_1,Y_2,X_3] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) 7.68/7.76 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),X_3)) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_369_order__refl,axiom, 7.68/7.76 ! [X_3] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),X_3)) ). 7.68/7.76 7.68/7.76 fof(help_fFalse_1_1_T,axiom, 7.68/7.76 ! [P] : 7.68/7.76 ( is_bool(P) 7.68/7.76 => ( fFalse = P 7.68/7.76 | fTrue = P ) ) ). 7.68/7.76 7.68/7.76 fof(fact_66_card__insert__disjoint,axiom, 7.68/7.76 ! [X_3,A_1] : 7.68/7.76 ( ( hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)) = hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) 7.68/7.76 <= ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1)) ) 7.68/7.76 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_175_finite__subset__image,axiom, 7.68/7.76 ! [F,A_1,B_6] : 7.68/7.76 ( is_fun_a_bool(B_6) 7.68/7.76 => ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1))) 7.68/7.76 => ? [C_7] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) 7.68/7.76 & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) 7.68/7.76 & B_6 = image_nat_a(F,C_7) ) ) 7.68/7.76 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_679_le0,axiom, 7.68/7.76 ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)) ). 7.68/7.76 7.68/7.76 fof(fact_676_Suc__lessE,axiom, 7.68/7.76 ! [I,K] : 7.68/7.76 ( ~ ! [J] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) 7.68/7.76 => K != hAPP_nat_nat(suc,J) ) 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K)) ) ). 7.68/7.76 7.68/7.76 fof(fact_258_insert__ident,axiom, 7.68/7.76 ! [B_6,X_3,A_1] : 7.68/7.76 ( ( is_fun_pname_bool(A_1) 7.68/7.76 & is_fun_pname_bool(B_6) ) 7.68/7.76 => ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) 7.68/7.76 => ( insert_pname(X_3,B_6) = insert_pname(X_3,A_1) 7.68/7.76 <=> A_1 = B_6 ) ) 7.68/7.76 <= ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_226_insertE,axiom, 7.68/7.76 ! [A_3,B_1,A_1] : 7.68/7.76 ( ( is_pname(B_1) 7.68/7.76 & is_pname(A_3) ) 7.68/7.76 => ( ( A_3 != B_1 7.68/7.76 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)) ) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,A_1))) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_14_finite__imageI,axiom, 7.68/7.76 ! [H,F_1] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(H,F_1))) 7.68/7.76 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_016,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R)) ). 7.68/7.76 7.68/7.76 fof(fact_168_finite__subset__image,axiom, 7.68/7.76 ! [F,A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) 7.68/7.76 => ( ? [C_7] : 7.68/7.76 ( is_fun1661590463l_bool(C_7) 7.68/7.76 & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7)) 7.68/7.76 & B_6 = image_1551609309ol_nat(F,C_7) 7.68/7.76 & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1)) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_1551609309ol_nat(F,A_1))) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_490_singleton__conv2,axiom, 7.68/7.76 ! [A_3] : insert_a(A_3,bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(fequal_a,A_3)) ). 7.68/7.76 7.68/7.76 fof(fact_509_xt1_I5_J,axiom, 7.68/7.76 ! [Y_2,X_3] : 7.68/7.76 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3)) 7.68/7.76 => ( Y_2 = X_3 7.68/7.76 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) ) ) 7.68/7.76 <= ( is_fun_a_bool(Y_2) 7.68/7.76 & is_fun_a_bool(X_3) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_482_singleton__conv,axiom, 7.68/7.76 ! [A_3] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)) = insert_nat(A_3,bot_bot_fun_nat_bool) ). 7.68/7.76 7.68/7.76 fof(fact_377_le__funD,axiom, 7.68/7.76 ! [X_3,F,G_1] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1)) 7.68/7.76 => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_3)),hAPP_pname_bool(G_1,X_3))) ) ). 7.68/7.76 7.68/7.76 fof(fact_658_less__eq__Suc__le,axiom, 7.68/7.76 ! [Na,M_1] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) 7.68/7.76 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_498_image__constant__conv,axiom, 7.68/7.76 ! [C_1,A_1] : 7.68/7.76 ( is_fun_pname_bool(A_1) 7.68/7.76 => ( ( bot_bot_fun_a_bool = image_pname_a(cOMBK_a_pname(C_1),A_1) 7.68/7.76 <= bot_bo844097828e_bool = A_1 ) 7.68/7.76 & ( insert_a(C_1,bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(C_1),A_1) 7.68/7.76 <= A_1 != bot_bo844097828e_bool ) ) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_Set_Oinsert_000tc__Com__Opname,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : 7.68/7.76 ( is_fun_pname_bool(insert_pname(B_1_1,B_2_1)) 7.68/7.76 <= ( is_pname(B_1_1) 7.68/7.76 & is_fun_pname_bool(B_2_1) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_125_Nat_Odiff__diff__eq,axiom, 7.68/7.76 ! [N,K,M] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) 7.68/7.76 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) 7.68/7.76 => hAPP_nat_nat(minus_minus_nat(M),N) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),K)),hAPP_nat_nat(minus_minus_nat(N),K)) ) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_b589554111l_bool(P,hAPP_a_bool(Q,R)) = hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(P,Q),R) ). 7.68/7.76 7.68/7.76 fof(fact_346_subset__image__iff,axiom, 7.68/7.76 ! [B_6,F,A_1] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1))) 7.68/7.76 <=> ? [AA] : 7.68/7.76 ( is_fun_a_bool(AA) 7.68/7.76 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,AA),A_1)) 7.68/7.76 & image_a_nat(F,AA) = B_6 ) ) ). 7.68/7.76 7.68/7.76 fof(fact_640_le__eq__less__or__eq,axiom, 7.68/7.76 ! [M_1,Na] : 7.68/7.76 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) 7.68/7.76 | Na = M_1 ) 7.68/7.76 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ). 7.68/7.76 7.68/7.76 fof(fact_427_bot__fun__def,axiom, 7.68/7.76 ! [X_1] : 7.68/7.76 ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_1)) 7.68/7.76 <=> hBOOL(bot_bot_bool) ) ). 7.68/7.76 7.68/7.76 fof(fact_688_diff__self__eq__0,axiom, 7.68/7.76 ! [M] : zero_zero_nat = hAPP_nat_nat(minus_minus_nat(M),M) ). 7.68/7.76 7.68/7.76 fof(fact_356_imageE,axiom, 7.68/7.76 ! [B_1,F,A_1] : 7.68/7.76 ( is_a(B_1) 7.68/7.76 => ( ~ ! [X_1] : 7.68/7.76 ( is_pname(X_1) 7.68/7.76 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.76 <= hAPP_pname_a(F,X_1) = B_1 ) ) 7.68/7.76 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_616_termination__basic__simps_I2_J,axiom, 7.68/7.76 ! [Y,X,Z] : 7.68/7.76 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))) 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z)) ) ). 7.68/7.76 7.68/7.76 fof(fact_279_in__mono,axiom, 7.68/7.76 ! [X_3,A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.76 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_222_insertCI,axiom, 7.68/7.76 ! [B_1,A_3,B_6] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,B_6))) 7.68/7.76 <= ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),B_6)) 7.68/7.76 => A_3 = B_1 ) ) ). 7.68/7.76 7.68/7.76 fof(fact_349_image__mono,axiom, 7.68/7.76 ! [F,A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) 7.68/7.76 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(F,A_1)),image_a_nat(F,B_6))) ) ). 7.68/7.76 7.68/7.76 fof(fact_400_Collect__empty__eq,axiom, 7.68/7.76 ! [Pa] : 7.68/7.76 ( ! [X_1] : 7.68/7.76 ( is_fun_pname_bool(X_1) 7.68/7.76 => ~ hBOOL(hAPP_f1664156314l_bool(Pa,X_1)) ) 7.68/7.76 <=> bot_bo1649642514l_bool = collec1974731493e_bool(Pa) ) ). 7.68/7.76 7.68/7.76 fof(fact_576_nat__add__assoc,axiom, 7.68/7.76 ! [M,N,K] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),K) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(plus_plus_nat(N),K)) ). 7.68/7.76 7.68/7.76 fof(fact_418_all__not__in__conv,axiom, 7.68/7.76 ! [A_1] : 7.68/7.76 ( ( A_1 = bot_bot_fun_a_bool 7.68/7.76 <=> ! [X_1] : 7.68/7.76 ( is_a(X_1) 7.68/7.76 => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) ) ) 7.68/7.76 <= is_fun_a_bool(A_1) ) ). 7.68/7.76 7.68/7.76 fof(fact_388_finite_OemptyI,axiom, 7.68/7.76 hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,bot_bo1389914601l_bool)) ). 7.68/7.76 7.68/7.76 fof(fact_135_finite__surj,axiom, 7.68/7.76 ! [B_6,F,A_1] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.76 => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) 7.68/7.76 <= hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_2129980159t_bool(F,A_1))) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_690_diff__0__eq__0,axiom, 7.68/7.76 ! [N] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N) = zero_zero_nat ). 7.68/7.76 7.68/7.76 fof(fact_2_finite__Collect__subsets,axiom, 7.68/7.76 ! [A_1] : 7.68/7.76 ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A_1)))) 7.68/7.76 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(P,R),Q) ). 7.68/7.76 7.68/7.76 fof(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : is_fun_a_bool(image_fun_nat_bool_a(B_1_1,B_2_1)) ). 7.68/7.76 7.68/7.76 fof(fact_261_insertI2,axiom, 7.68/7.76 ! [B_1,A_3,B_6] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),B_6)) 7.68/7.76 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,B_6))) ) ). 7.68/7.76 7.68/7.76 fof(fact_336_image__insert,axiom, 7.68/7.76 ! [F,A_3,B_6] : insert_a(hAPP_nat_a(F,A_3),image_nat_a(F,B_6)) = image_nat_a(F,insert_nat(A_3,B_6)) ). 7.68/7.76 7.68/7.76 fof(fact_148_finite__surj,axiom, 7.68/7.76 ! [B_6,F,A_1] : 7.68/7.76 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1283814551_pname(F,A_1))) 7.68/7.76 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) 7.68/7.76 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_656_less__add__Suc2,axiom, 7.68/7.76 ! [I,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),I)))) ). 7.68/7.76 7.68/7.76 fof(fact_538_ord__eq__le__trans,axiom, 7.68/7.76 ! [C_2,A_4,B_2] : 7.68/7.76 ( B_2 = A_4 7.68/7.76 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_4),C_2)) 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),C_2)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_51_card__seteq,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.76 ( ( is_fun_pname_bool(A_1) 7.68/7.76 & is_fun_pname_bool(B_6) ) 7.68/7.76 => ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.76 => ( A_1 = B_6 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,B_6)),hAPP_f921600141ol_nat(finite_card_pname,A_1))) ) ) 7.68/7.76 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_310_rev__image__eqI,axiom, 7.68/7.76 ! [B_1,F,X_3,A_1] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) 7.68/7.76 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1))) 7.68/7.76 <= B_1 = hAPP_nat_pname(F,X_3) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_391_finite_OemptyI,axiom, 7.68/7.76 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)) ). 7.68/7.76 7.68/7.76 fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opname_Mtc__H,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : 7.68/7.76 ( is_fun_pname_bool(hAPP_f1794073134e_bool(B_1_1,B_2_1)) 7.68/7.76 <= is_fun_a_bool(B_2_1) ) ). 7.68/7.76 7.68/7.76 fof(fact_311_rev__image__eqI,axiom, 7.68/7.76 ! [B_1,F,X_3,A_1] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) 7.68/7.76 => ( hAPP_nat_a(F,X_3) = B_1 7.68/7.76 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1))) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_357_subsetI,axiom, 7.68/7.76 ! [B_6,A_1] : 7.68/7.76 ( ! [X_1] : 7.68/7.76 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) 7.68/7.76 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_6)) ) 7.68/7.76 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_Set_Oimage_000t__a_000tc__Com__Opname,axiom, 7.68/7.76 ! [B_1_1,B_2_1] : 7.68/7.76 ( is_fun_a_bool(B_2_1) 7.68/7.76 => is_fun_pname_bool(image_a_pname(B_1_1,B_2_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_78_Suc__diff__le,axiom, 7.68/7.76 ! [N,M] : 7.68/7.76 ( hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M),N)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N) 7.68/7.76 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) ) ). 7.68/7.76 7.68/7.76 fof(fact_443_bot__least,axiom, 7.68/7.76 ! [A_3] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_3)) ). 7.68/7.76 7.68/7.76 fof(fact_390_finite_OemptyI,axiom, 7.68/7.76 hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ). 7.68/7.76 7.68/7.76 fof(fact_399_Collect__empty__eq,axiom, 7.68/7.76 ! [Pa] : 7.68/7.76 ( bot_bo1701429464l_bool = collect_fun_nat_bool(Pa) 7.68/7.76 <=> ! [X_1] : ~ hBOOL(hAPP_f54304608l_bool(Pa,X_1)) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U,axiom, 7.68/7.76 ! [P,Q] : 7.68/7.76 ( is_bool(P) 7.68/7.76 => P = hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(P),Q) ) ). 7.68/7.76 7.68/7.76 fof(fact_683_diff__add__0,axiom, 7.68/7.76 ! [N,M] : zero_zero_nat = hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(plus_plus_nat(N),M)) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_fun_a_bool_bool(Q,R)) ). 7.68/7.76 7.68/7.76 fof(conj_3,hypothesis, 7.68/7.76 hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)) ). 7.68/7.76 7.68/7.76 fof(fact_512_order__trans,axiom, 7.68/7.76 ! [Z_1,X_3,Y_2] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) 7.68/7.76 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),Z_1)) 7.68/7.76 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Z_1)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_195_pigeonhole__infinite,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.76 => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(F,A_1))) 7.68/7.76 => ? [X_1] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.76 & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,F)),hAPP_pname_nat(F,X_1)))))) 7.68/7.76 & is_pname(X_1) ) ) ) ). 7.68/7.76 7.68/7.76 fof(gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom, 7.68/7.76 ! [B_1_1] : 7.68/7.76 ( is_fun1661590463l_bool(collec1974731493e_bool(B_1_1)) 7.68/7.76 <= is_fun1661590463l_bool(B_1_1) ) ). 7.68/7.76 7.68/7.76 fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom, 7.68/7.76 ! [P,Q,R] : hAPP_a1392362872l_bool(cOMBB_743407885bool_a(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_a_fun_nat_bool(Q,R)) ). 7.68/7.76 7.68/7.76 fof(fact_286_set__mp,axiom, 7.68/7.76 ! [X_3,A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) 7.68/7.76 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) 7.68/7.76 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_445_bot__least,axiom, 7.68/7.76 ! [A_8] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_8)) ). 7.68/7.76 7.68/7.76 fof(fact_436_bot__unique,axiom, 7.68/7.76 ! [A_3] : 7.68/7.76 ( is_fun_pname_bool(A_3) 7.68/7.76 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),bot_bo844097828e_bool)) 7.68/7.76 <=> bot_bo844097828e_bool = A_3 ) ) ). 7.68/7.76 7.68/7.76 fof(fact_98_finite__insert,axiom, 7.68/7.76 ! [A_3,A_1] : 7.68/7.76 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_3,A_1))) 7.68/7.76 <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ). 7.68/7.76 7.68/7.76 fof(fact_520_xt1_I4_J,axiom, 7.68/7.76 ! [C_1,B_1,A_3] : 7.68/7.76 ( ( ( hBOOL(C_1) 7.68/7.76 <=> hBOOL(B_1) ) 7.68/7.76 => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),A_3)) ) 7.68/7.76 <= hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),A_3)) ) ). 7.68/7.76 7.68/7.76 fof(fact_665_diff__less__Suc,axiom, 7.68/7.76 ! [M,N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N)),hAPP_nat_nat(suc,M))) ). 7.68/7.76 7.68/7.76 fof(fact_110_rev__finite__subset,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) 7.68/7.76 => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) 7.68/7.76 <= hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_606_Suc__eq__plus1,axiom, 7.68/7.76 ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(N),one_one_nat) ). 7.68/7.76 7.68/7.76 fof(fact_540_order__antisym__conv,axiom, 7.68/7.76 ! [Y_2,X_3] : 7.68/7.76 ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) 7.68/7.76 <=> ( hBOOL(Y_2) 7.68/7.76 <=> hBOOL(X_3) ) ) 7.68/7.76 <= hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) ) ). 7.68/7.76 7.68/7.76 fof(fact_654_finite__M__bounded__by__nat,axiom, 7.68/7.76 ! [Pa,I_1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),I_1))))) ). 7.68/7.76 7.68/7.76 fof(fact_646_nat__neq__iff,axiom, 7.68/7.76 ! [M_1,Na] : 7.68/7.76 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) 7.68/7.76 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) ) 7.68/7.76 <=> M_1 != Na ) ). 7.68/7.76 7.68/7.76 fof(fact_174_finite__subset__image,axiom, 7.68/7.76 ! [F,A_1,B_6] : 7.68/7.76 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_pname_nat(F,A_1))) 7.68/7.76 => ? [C_7] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) 7.68/7.76 & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) 7.68/7.76 & image_pname_nat(F,C_7) = B_6 7.68/7.76 & is_fun_pname_bool(C_7) ) ) 7.68/7.76 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ). 7.68/7.76 7.68/7.76 fof(fact_339_insert__image,axiom, 7.68/7.76 ! [F,X_3,A_1] : 7.68/7.76 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.76 => insert_nat(hAPP_pname_nat(F,X_3),image_pname_nat(F,A_1)) = image_pname_nat(F,A_1) ) ). 7.68/7.76 7.68/7.76 fof(fact_186_lift__Suc__mono__le,axiom, 7.68/7.76 ! [Na,N_3,F] : 7.68/7.76 ( ! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_2)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2)))) 7.68/7.76 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) 7.68/7.76 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Na)),hAPP_nat_nat(F,N_3))) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_106_finite__subset,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.76 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) 7.68/7.76 => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) 7.68/7.76 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ) ). 7.68/7.76 7.68/7.76 fof(fact_467_image__is__empty,axiom, 7.68/7.76 ! [F,A_1] : 7.68/7.76 ( ( image_pname_a(F,A_1) = bot_bot_fun_a_bool 7.68/7.76 <=> bot_bo844097828e_bool = A_1 ) 7.68/7.76 <= is_fun_pname_bool(A_1) ) ). 7.68/7.76 7.68/7.76 fof(fact_404_empty__iff,axiom, 7.68/7.76 ! [C_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),bot_bot_fun_nat_bool)) ). 7.68/7.76 7.68/7.76 fof(fact_108_finite__subset,axiom, 7.68/7.76 ! [A_1,B_6] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.68/7.77 => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_393_empty__subsetI,axiom, 7.68/7.77 ! [A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_1)) ). 7.68/7.77 7.68/7.77 fof(fact_172_finite__subset__image,axiom, 7.68/7.77 ! [F,A_1,B_6] : 7.68/7.77 ( is_fun949378684l_bool(B_6) 7.68/7.77 => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) 7.68/7.77 => ( ? [C_7] : 7.68/7.77 ( is_fun_pname_bool(C_7) 7.68/7.77 & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) 7.68/7.77 & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) 7.68/7.77 & image_112932426a_bool(F,C_7) = B_6 ) 7.68/7.77 <= hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_112932426a_bool(F,A_1))) ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_197_pigeonhole__infinite,axiom, 7.68/7.77 ! [F,A_1] : 7.68/7.77 ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) 7.68/7.77 => ( ? [X_1] : 7.68/7.77 ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) 7.68/7.77 & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),A_1)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,F)),hAPP_f921600141ol_nat(F,X_1)))))) 7.68/7.77 & is_fun_pname_bool(X_1) ) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(F,A_1))) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_335_image__insert,axiom, 7.68/7.77 ! [F,A_3,B_6] : insert_nat(hAPP_a_nat(F,A_3),image_a_nat(F,B_6)) = image_a_nat(F,insert_a(A_3,B_6)) ). 7.68/7.77 7.68/7.77 fof(gsy_c_fTrue,axiom, 7.68/7.77 is_bool(fTrue) ). 7.68/7.77 7.68/7.77 fof(fact_159_finite__subset__image,axiom, 7.68/7.77 ! [F,A_1,B_6] : 7.68/7.77 ( ( ? [C_7] : 7.68/7.77 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) 7.68/7.77 & B_6 = image_a_fun_nat_bool(F,C_7) 7.68/7.77 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) 7.68/7.77 & is_fun_a_bool(C_7) ) 7.68/7.77 <= hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_a_fun_nat_bool(F,A_1))) ) 7.68/7.77 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ) ). 7.68/7.77 7.68/7.77 fof(fact_378_le__funD,axiom, 7.68/7.77 ! [X_3,F,G_1] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) 7.68/7.77 => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_3)),hAPP_nat_bool(G_1,X_3))) ) ). 7.68/7.77 7.68/7.77 fof(fact_285_set__mp,axiom, 7.68/7.77 ! [X_3,A_1,B_6] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.77 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_435_le__bot,axiom, 7.68/7.77 ! [A_9] : 7.68/7.77 ( A_9 = bot_bot_nat 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),bot_bot_nat)) ) ). 7.68/7.77 7.68/7.77 fof(fact_567_assms_I4_J,axiom, 7.68/7.77 ! [Pn] : 7.68/7.77 ( hBOOL(wt(the_com(body(Pn)))) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn),u)) ) ). 7.68/7.77 7.68/7.77 fof(fact_607_Suc__eq__plus1__left,axiom, 7.68/7.77 ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(one_one_nat),N) ). 7.68/7.77 7.68/7.77 fof(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( is_fun_a_bool(image_876012084bool_a(B_1_1,B_2_1)) 7.68/7.77 <= is_fun1661590463l_bool(B_2_1) ) ). 7.68/7.77 7.68/7.77 fof(fact_145_finite__surj,axiom, 7.68/7.77 ! [B_6,F,A_1] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.77 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_nat_nat(F,A_1))) 7.68/7.77 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_428_bot__apply,axiom, 7.68/7.77 ! [X_3] : 7.68/7.77 ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_3)) 7.68/7.77 <=> hBOOL(bot_bot_bool) ) ). 7.68/7.77 7.68/7.77 fof(fact_101_finite__insert,axiom, 7.68/7.77 ! [A_3,A_1] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.77 <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_3,A_1))) ) ). 7.68/7.77 7.68/7.77 fof(fact_190_pigeonhole__infinite,axiom, 7.68/7.77 ! [F,A_1] : 7.68/7.77 ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) 7.68/7.77 => ( ? [X_1] : 7.68/7.77 ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),A_1)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,F)),hAPP_f1291551745_pname(F,X_1)))))) 7.68/7.77 & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A_1)) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(F,A_1))) ) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : is_fun949378684l_bool(image_nat_fun_a_bool(B_1_1,B_2_1)) ). 7.68/7.77 7.68/7.77 fof(fact_317_insert__compr__raw,axiom, 7.68/7.77 ! [X_1,Xa] : collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa))) = insert_pname(X_1,Xa) ). 7.68/7.77 7.68/7.77 fof(fact_589_trans__le__add2,axiom, 7.68/7.77 ! [M,I,J_2] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) 7.68/7.77 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(plus_plus_nat(M),J_2))) ) ). 7.68/7.77 7.68/7.77 fof(fact_515_order__antisym,axiom, 7.68/7.77 ! [X_3,Y_2] : 7.68/7.77 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) 7.68/7.77 => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) 7.68/7.77 => ( hBOOL(Y_2) 7.68/7.77 <=> hBOOL(X_3) ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_432_le__bot,axiom, 7.68/7.77 ! [A_3] : 7.68/7.77 ( ( hBOOL(A_3) 7.68/7.77 <=> hBOOL(bot_bot_bool) ) 7.68/7.77 <= hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),bot_bot_bool)) ) ). 7.68/7.77 7.68/7.77 fof(fact_60_card__insert__if,axiom, 7.68/7.77 ! [X_3,A_1] : 7.68/7.77 ( ( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1)) 7.68/7.77 => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_f696928925ol_nat(finite346522414t_bool,A_1) ) 7.68/7.77 & ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1)) 7.68/7.77 => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)) ) ) 7.68/7.77 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_675_less__mono__imp__le__mono,axiom, 7.68/7.77 ! [I_1,J_1,F] : 7.68/7.77 ( ! [I_2,J] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J))) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) ) 7.68/7.77 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) 7.68/7.77 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1))) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_587_nat__add__left__cancel__le,axiom, 7.68/7.77 ! [K_2,M_1,Na] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) 7.68/7.77 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K_2),M_1)),hAPP_nat_nat(plus_plus_nat(K_2),Na))) ) ). 7.68/7.77 7.68/7.77 fof(help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,axiom, 7.68/7.77 ! [X,Y] : 7.68/7.77 ( Y != X 7.68/7.77 | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)) ) ). 7.68/7.77 7.68/7.77 fof(fact_561_finite__subset__induct,axiom, 7.68/7.77 ! [Pa,A_1,F_1] : 7.68/7.77 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) 7.68/7.77 => ( ( ( hBOOL(hAPP_f621171935l_bool(Pa,F_1)) 7.68/7.77 <= ! [A_2,F_2] : 7.68/7.77 ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_2)) 7.68/7.77 => ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,A_2),A_1)) 7.68/7.77 => ( ( hBOOL(hAPP_f621171935l_bool(Pa,insert_fun_a_bool(A_2,F_2))) 7.68/7.77 <= hBOOL(hAPP_f621171935l_bool(Pa,F_2)) ) 7.68/7.77 <= ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,A_2),F_2)) ) ) ) 7.68/7.77 <= ( is_fun_a_bool(A_2) 7.68/7.77 & is_fun949378684l_bool(F_2) ) ) ) 7.68/7.77 <= hBOOL(hAPP_f621171935l_bool(Pa,bot_bo1389914601l_bool)) ) 7.68/7.77 <= hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,F_1),A_1)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_120_not__less__eq__eq,axiom, 7.68/7.77 ! [M_1,Na] : 7.68/7.77 ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) 7.68/7.77 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_253_insert__iff,axiom, 7.68/7.77 ! [A_3,B_1,A_1] : 7.68/7.77 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1))) 7.68/7.77 <=> ( B_1 = A_3 7.68/7.77 | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) ) ) 7.68/7.77 <= ( is_a(B_1) 7.68/7.77 & is_a(A_3) ) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( is_pname(hAPP_f1128469712_pname(B_1_1,B_2_1)) 7.68/7.77 <= is_fun_a_bool(B_2_1) ) ). 7.68/7.77 7.68/7.77 fof(fact_582_diff__cancel,axiom, 7.68/7.77 ! [K,M,N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(K),M)),hAPP_nat_nat(plus_plus_nat(K),N)) = hAPP_nat_nat(minus_minus_nat(M),N) ). 7.68/7.77 7.68/7.77 fof(fact_277_equalityD2,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1)) 7.68/7.77 <= A_1 = B_6 ) ). 7.68/7.77 7.68/7.77 fof(fact_541_order__antisym__conv,axiom, 7.68/7.77 ! [Y_2,X_3] : 7.68/7.77 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) 7.68/7.77 <=> Y_2 = X_3 ) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) ) ). 7.68/7.77 7.68/7.77 fof(fact_133_finite__surj,axiom, 7.68/7.77 ! [B_6,F,A_1] : 7.68/7.77 ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) 7.68/7.77 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_876012084bool_a(F,A_1))) ) 7.68/7.77 <= hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_f621171935l_bool(hAPP_f285962445l_bool(P,R),Q) = hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(P),Q),R) ). 7.68/7.77 7.68/7.77 fof(fact_69_card__insert__disjoint,axiom, 7.68/7.77 ! [X_3,A_1] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.77 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) 7.68/7.77 => hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A_1)) = hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) ) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(P,R),Q) = hAPP_pname_bool(hAPP_f1794073134e_bool(cOMBC_445755039l_bool(P),Q),R) ). 7.68/7.77 7.68/7.77 fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom, 7.68/7.77 is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))) ). 7.68/7.77 7.68/7.77 fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom, 7.68/7.77 ! [P,Q] : 7.68/7.77 ( is_bool(P) 7.68/7.77 => hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(P),Q) = P ) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q) ). 7.68/7.77 7.68/7.77 fof(fact_229_Suc__le__D,axiom, 7.68/7.77 ! [N,M_3] : 7.68/7.77 ( ? [M_2] : M_3 = hAPP_nat_nat(suc,M_2) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_3)) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : is_fun_pname_bool(image_1921560913_pname(B_1_1,B_2_1)) ). 7.68/7.77 7.68/7.77 fof(fact_577_nat__add__left__commute,axiom, 7.68/7.77 ! [X,Y,Z] : hAPP_nat_nat(plus_plus_nat(X),hAPP_nat_nat(plus_plus_nat(Y),Z)) = hAPP_nat_nat(plus_plus_nat(Y),hAPP_nat_nat(plus_plus_nat(X),Z)) ). 7.68/7.77 7.68/7.77 fof(fact_351_image__mono,axiom, 7.68/7.77 ! [F,A_1,B_6] : 7.68/7.77 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A_1)),image_pname_a(F,B_6))) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ) ). 7.68/7.77 7.68/7.77 fof(fact_127_diff__diff__cancel,axiom, 7.68/7.77 ! [I,N] : 7.68/7.77 ( hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(minus_minus_nat(N),I)) = I 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N)) ) ). 7.68/7.77 7.68/7.77 fof(fact_396_equals0D,axiom, 7.68/7.77 ! [A_3,A_1] : 7.68/7.77 ( A_1 = bot_bo844097828e_bool 7.68/7.77 => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_479_Collect__conv__if2,axiom, 7.68/7.77 ! [Pa,A_3] : 7.68/7.77 ( ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)),Pa)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(Pa,A_3)) ) 7.68/7.77 & ( ~ hBOOL(hAPP_f54304608l_bool(Pa,A_3)) 7.68/7.77 => bot_bo1701429464l_bool = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)),Pa)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_236_insert__compr,axiom, 7.68/7.77 ! [A_3,B_6] : collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B_6))) = insert_nat(A_3,B_6) ). 7.68/7.77 7.68/7.77 fof(fact_486_singleton__conv,axiom, 7.68/7.77 ! [A_3] : insert1325755072e_bool(A_3,bot_bo1649642514l_bool) = collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)) ). 7.68/7.77 7.68/7.77 fof(fact_223_insertCI,axiom, 7.68/7.77 ! [B_1,A_3,B_6] : 7.68/7.77 ( ( A_3 = B_1 7.68/7.77 <= ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),B_6)) ) 7.68/7.77 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,B_6))) ) ). 7.68/7.77 7.68/7.77 fof(fact_200_pigeonhole__infinite,axiom, 7.68/7.77 ! [F,A_1] : 7.68/7.77 ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.77 => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(F,A_1))) 7.68/7.77 => ? [X_1] : 7.68/7.77 ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,F)),hAPP_n1699378549t_bool(F,X_1)))))) 7.68/7.77 & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_272_equalityD1,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.77 <= B_6 = A_1 ) ). 7.68/7.77 7.68/7.77 fof(fact_97_finite__insert,axiom, 7.68/7.77 ! [A_3,A_1] : 7.68/7.77 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) 7.68/7.77 <=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_3,A_1))) ) ). 7.68/7.77 7.68/7.77 fof(fact_227_insertE,axiom, 7.68/7.77 ! [A_3,B_1,A_1] : 7.68/7.77 ( ( is_a(A_3) 7.68/7.77 & is_a(B_1) ) 7.68/7.77 => ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) 7.68/7.77 <= B_1 != A_3 ) 7.68/7.77 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1))) ) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( is_fun949378684l_bool(B_2_1) 7.68/7.77 => is_fun_a_bool(image_fun_a_bool_a(B_1_1,B_2_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_637_less__or__eq__imp__le,axiom, 7.68/7.77 ! [M,N] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) 7.68/7.77 <= ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) 7.68/7.77 | N = M ) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname,axiom, 7.68/7.77 ! [B_1_1] : 7.68/7.77 ( is_bool(B_1_1) 7.68/7.77 => is_fun_pname_bool(cOMBK_bool_pname(B_1_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_111_rev__finite__subset,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) 7.68/7.77 <= hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6)) ) 7.68/7.77 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) ) ). 7.68/7.77 7.68/7.77 fof(fact_47_card__mono,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) 7.68/7.77 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_1)),hAPP_f22106695ol_nat(finite_card_nat,B_6))) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_hAPP_000t__a_000tc__HOL__Obool,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( is_bool(hAPP_a_bool(B_1_1,B_2_1)) 7.68/7.77 <= ( is_a(B_2_1) 7.68/7.77 & is_fun_a_bool(B_1_1) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_624_not__add__less2,axiom, 7.68/7.77 ! [J_2,I] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(J_2),I)),I)) ). 7.68/7.77 7.68/7.77 fof(fact_234_insert__compr,axiom, 7.68/7.77 ! [A_3,B_6] : collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B_6))) = insert1325755072e_bool(A_3,B_6) ). 7.68/7.77 7.68/7.77 fof(fact_72_finite__Collect__conjI,axiom, 7.68/7.77 ! [Q_1,Pa] : 7.68/7.77 ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) 7.68/7.77 | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1))) ) 7.68/7.77 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,Pa),Q_1)))) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( is_fun_pname_bool(image_1283814551_pname(B_1_1,B_2_1)) 7.68/7.77 <= is_fun1661590463l_bool(B_2_1) ) ). 7.68/7.77 7.68/7.77 fof(fact_193_pigeonhole__infinite,axiom, 7.68/7.77 ! [F,A_1] : 7.68/7.77 ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.77 => ( ? [X_1] : 7.68/7.77 ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A_1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,F)),hAPP_nat_nat(F,X_1)))))) 7.68/7.77 & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(F,A_1))) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_273_equalityD1,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( B_6 = A_1 7.68/7.77 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ) ). 7.68/7.77 7.68/7.77 fof(fact_590_add__le__mono1,axiom, 7.68/7.77 ! [K,I,J_2] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),K))) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ) ). 7.68/7.77 7.68/7.77 fof(fact_513_order__trans,axiom, 7.68/7.77 ! [Z_2,X_6,Y_5] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Y_5)) 7.68/7.77 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Z_2)) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),Z_2)) ) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,hypothesis, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( is_pname(B_2_1) 7.68/7.77 => is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2_1)) ) ). 7.68/7.77 7.68/7.77 fof(help_fconj_3_1_U,axiom, 7.68/7.77 ! [P,Q] : 7.68/7.77 ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) 7.68/7.77 | hBOOL(Q) ) ). 7.68/7.77 7.68/7.77 fof(fact_249_insert__commute,axiom, 7.68/7.77 ! [X_3,Y_2,A_1] : insert_nat(Y_2,insert_nat(X_3,A_1)) = insert_nat(X_3,insert_nat(Y_2,A_1)) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q) = hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(P),Q),R) ). 7.68/7.77 7.68/7.77 fof(fact_128_diff__le__mono,axiom, 7.68/7.77 ! [L,M,N] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) 7.68/7.77 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),L)),hAPP_nat_nat(minus_minus_nat(N),L))) ) ). 7.68/7.77 7.68/7.77 fof(fact_118_Suc__le__mono,axiom, 7.68/7.77 ! [Na,M_1] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_1))) 7.68/7.77 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_257_insert__ident,axiom, 7.68/7.77 ! [B_6,X_3,A_1] : 7.68/7.77 ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) 7.68/7.77 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) 7.68/7.77 => ( insert_nat(X_3,A_1) = insert_nat(X_3,B_6) 7.68/7.77 <=> A_1 = B_6 ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_410_empty__Collect__eq,axiom, 7.68/7.77 ! [Pa] : 7.68/7.77 ( ! [X_1] : 7.68/7.77 ( is_fun_a_bool(X_1) 7.68/7.77 => ~ hBOOL(hAPP_fun_a_bool_bool(Pa,X_1)) ) 7.68/7.77 <=> collect_fun_a_bool(Pa) = bot_bo1389914601l_bool ) ). 7.68/7.77 7.68/7.77 fof(fact_557_finite__subset__induct,axiom, 7.68/7.77 ! [Pa,A_1,F_1] : 7.68/7.77 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F_1),A_1)) 7.68/7.77 => ( ( ! [A_2,F_2] : 7.68/7.77 ( ( ( ( ( hBOOL(hAPP_f1664156314l_bool(Pa,insert_pname(A_2,F_2))) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(Pa,F_2)) ) 7.68/7.77 <= ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),F_2)) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1)) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2)) ) 7.68/7.77 <= ( is_pname(A_2) 7.68/7.77 & is_fun_pname_bool(F_2) ) ) 7.68/7.77 => hBOOL(hAPP_f1664156314l_bool(Pa,F_1)) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool)) ) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom, 7.68/7.77 is_fun_pname_bool(bot_bo844097828e_bool) ). 7.68/7.77 7.68/7.77 fof(fact_692_Zero__neq__Suc,axiom, 7.68/7.77 ! [M] : zero_zero_nat != hAPP_nat_nat(suc,M) ). 7.68/7.77 7.68/7.77 fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( ( is_fun949378684l_bool(B_1_1) 7.68/7.77 & is_fun_a_bool(B_2_1) ) 7.68/7.77 => is_bool(hAPP_fun_a_bool_bool(B_1_1,B_2_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_62_card__insert__if,axiom, 7.68/7.77 ! [X_3,A_1] : 7.68/7.77 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) 7.68/7.77 => ( ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1)) 7.68/7.77 => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1) ) 7.68/7.77 & ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1)) 7.68/7.77 => hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_444_bot__least,axiom, 7.68/7.77 ! [A_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_3)) ). 7.68/7.77 7.68/7.77 fof(fact_547_order__eq__refl,axiom, 7.68/7.77 ! [X_3,Y_2] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) 7.68/7.77 <= Y_2 = X_3 ) ). 7.68/7.77 7.68/7.77 fof(fact_30_card__image__le,axiom, 7.68/7.77 ! [F,A_1] : 7.68/7.77 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) 7.68/7.77 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1))) ) ). 7.68/7.77 7.68/7.77 fof(fact_65_card__insert__if,axiom, 7.68/7.77 ! [X_3,A_1] : 7.68/7.77 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) 7.68/7.77 => ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) 7.68/7.77 => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_fun_a_bool_nat(finite_card_a,A_1) ) 7.68/7.77 & ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) 7.68/7.77 => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A_1)) ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_192_pigeonhole__infinite,axiom, 7.68/7.77 ! [F,A_1] : 7.68/7.77 ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) 7.68/7.77 => ( ? [X_1] : 7.68/7.77 ( is_fun_a_bool(X_1) 7.68/7.77 & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A_1)) 7.68/7.77 & ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),A_1)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,F)),hAPP_f1128469712_pname(F,X_1)))))) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(F,A_1))) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_376_le__fun__def,axiom, 7.68/7.77 ! [F,G_1] : 7.68/7.77 ( ! [X_1] : 7.68/7.77 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_1)),hAPP_a_bool(G_1,X_1))) 7.68/7.77 <= is_a(X_1) ) 7.68/7.77 <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) ) ). 7.68/7.77 7.68/7.77 fof(help_fequal_1_1_fequal_000t__a_T,axiom, 7.68/7.77 ! [X,Y] : 7.68/7.77 ( ( is_a(X) 7.68/7.77 & is_a(Y) ) 7.68/7.77 => ( ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X),Y)) 7.68/7.77 | X = Y ) ) ). 7.68/7.77 7.68/7.77 fof(fact_455_singleton__iff,axiom, 7.68/7.77 ! [B_1,A_3] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),insert_nat(A_3,bot_bot_fun_nat_bool))) 7.68/7.77 <=> A_3 = B_1 ) ). 7.68/7.77 7.68/7.77 fof(gsy_v_mgt,axiom, 7.68/7.77 ! [B_1_1] : is_a(mgt(B_1_1)) ). 7.68/7.77 7.68/7.77 fof(fact_262_insertI2,axiom, 7.68/7.77 ! [B_1,A_3,B_6] : 7.68/7.77 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,B_6))) 7.68/7.77 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),B_6)) ) ). 7.68/7.77 7.68/7.77 fof(fact_392_empty__subsetI,axiom, 7.68/7.77 ! [A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_1)) ). 7.68/7.77 7.68/7.77 fof(gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( is_fun_pname_bool(B_2_1) 7.68/7.77 => is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_19_finite__imageI,axiom, 7.68/7.77 ! [H,F_1] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(H,F_1))) 7.68/7.77 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_419_empty__def,axiom, 7.68/7.77 bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)) ). 7.68/7.77 7.68/7.77 fof(fact_8_finite__imageI,axiom, 7.68/7.77 ! [H,F_1] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) 7.68/7.77 => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(H,F_1))) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom, 7.68/7.77 is_bool(bot_bot_bool) ). 7.68/7.77 7.68/7.77 fof(fact_677_lessE,axiom, 7.68/7.77 ! [I,K] : 7.68/7.77 ( ( ~ ! [J] : 7.68/7.77 ( hAPP_nat_nat(suc,J) != K 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) ) 7.68/7.77 <= hAPP_nat_nat(suc,I) != K ) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)) ) ). 7.68/7.77 7.68/7.77 fof(fact_613_Suc__mono,axiom, 7.68/7.77 ! [M,N] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) 7.68/7.77 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))) ) ). 7.68/7.77 7.68/7.77 fof(fact_38_card__image__le,axiom, 7.68/7.77 ! [F,A_1] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(F,A_1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))) 7.68/7.77 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_13_finite__imageI,axiom, 7.68/7.77 ! [H,F_1] : 7.68/7.77 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(H,F_1))) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___018,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_nat_fun_a_bool(Q,R)) ). 7.68/7.77 7.68/7.77 fof(fact_510_order__trans,axiom, 7.68/7.77 ! [Z_1,X_3,Y_2] : 7.68/7.77 ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Z_1)) 7.68/7.77 <= hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1)) ) 7.68/7.77 <= hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_011,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_p61793385e_bool(P,hAPP_f1128469712_pname(Q,R)) = hAPP_f1794073134e_bool(cOMBB_1693087065a_bool(P,Q),R) ). 7.68/7.77 7.68/7.77 fof(fact_305_imageI,axiom, 7.68/7.77 ! [F,X_3,A_1] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(F,X_3)),image_nat_pname(F,A_1))) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_694_Suc__not__Zero,axiom, 7.68/7.77 ! [M] : zero_zero_nat != hAPP_nat_nat(suc,M) ). 7.68/7.77 7.68/7.77 fof(fact_641_nat__less__le,axiom, 7.68/7.77 ! [M_1,Na] : 7.68/7.77 ( ( Na != M_1 7.68/7.77 & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) 7.68/7.77 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ). 7.68/7.77 7.68/7.77 fof(fact_237_insert__compr,axiom, 7.68/7.77 ! [A_3,B_6] : collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B_6))) = insert_pname(A_3,B_6) ). 7.68/7.77 7.68/7.77 fof(fact_290_Collect__def,axiom, 7.68/7.77 ! [Pa] : 7.68/7.77 ( is_fun_a_bool(Pa) 7.68/7.77 => collect_a(Pa) = Pa ) ). 7.68/7.77 7.68/7.77 fof(fact_380_le__funE,axiom, 7.68/7.77 ! [X_3,F,G_1] : 7.68/7.77 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_3)),hAPP_pname_bool(G_1,X_3))) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_373_assms_I3_J,axiom, 7.68/7.77 ! [G,C_1] : 7.68/7.77 ( hBOOL(wt(C_1)) 7.68/7.77 => ( hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(mgt(C_1),bot_bot_fun_a_bool))) 7.68/7.77 <= ! [X_1] : 7.68/7.77 ( is_pname(X_1) 7.68/7.77 => ( hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(hAPP_pname_a(mgt_call,X_1),bot_bot_fun_a_bool))) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),u)) ) ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_182_lift__Suc__mono__le,axiom, 7.68/7.77 ! [Na,N_3,F] : 7.68/7.77 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) 7.68/7.77 => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Na)),hAPP_nat_bool(F,N_3))) ) 7.68/7.77 <= ! [N_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,N_2)),hAPP_nat_bool(F,hAPP_nat_nat(suc,N_2)))) ) ). 7.68/7.77 7.68/7.77 fof(fact_179_finite__subset__image,axiom, 7.68/7.77 ! [F,A_1,B_6] : 7.68/7.77 ( is_fun_pname_bool(B_6) 7.68/7.77 => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) 7.68/7.77 => ( ? [C_7] : 7.68/7.77 ( B_6 = image_nat_pname(F,C_7) 7.68/7.77 & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) 7.68/7.77 & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_nat_pname(F,A_1))) ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_530_xt1_I3_J,axiom, 7.68/7.77 ! [C_1,B_1,A_3] : 7.68/7.77 ( ( hBOOL(A_3) 7.68/7.77 <=> hBOOL(B_1) ) 7.68/7.77 => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),B_1)) 7.68/7.77 => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),A_3)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_154_finite__surj,axiom, 7.68/7.77 ! [B_6,F,A_1] : 7.68/7.77 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1))) 7.68/7.77 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_250_insert__commute,axiom, 7.68/7.77 ! [X_3,Y_2,A_1] : insert_a(Y_2,insert_a(X_3,A_1)) = insert_a(X_3,insert_a(Y_2,A_1)) ). 7.68/7.77 7.68/7.77 fof(fact_235_insert__compr,axiom, 7.68/7.77 ! [A_3,B_6] : collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),B_6))) = insert_fun_a_bool(A_3,B_6) ). 7.68/7.77 7.68/7.77 fof(fact_385_emptyE,axiom, 7.68/7.77 ! [A_3] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),bot_bot_fun_a_bool)) ). 7.68/7.77 7.68/7.77 fof(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___001,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( is_fun949378684l_bool(B_2_1) 7.68/7.77 => is_fun949378684l_bool(hAPP_f2117159681l_bool(B_1_1,B_2_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_517_order__antisym,axiom, 7.68/7.77 ! [X_3,Y_2] : 7.68/7.77 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) 7.68/7.77 => ( X_3 = Y_2 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3)) ) ) 7.68/7.77 <= ( is_fun_pname_bool(Y_2) 7.68/7.77 & is_fun_pname_bool(X_3) ) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(P,R),Q) ). 7.68/7.77 7.68/7.77 fof(help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U,axiom, 7.68/7.77 ! [P,Q] : 7.68/7.77 ( is_a(P) 7.68/7.77 => P = hAPP_pname_a(cOMBK_a_pname(P),Q) ) ). 7.68/7.77 7.68/7.77 fof(fact_426_bot__fun__def,axiom, 7.68/7.77 ! [X_1] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1)) 7.68/7.77 <=> hBOOL(bot_bot_bool) ) ). 7.68/7.77 7.68/7.77 fof(fact_638_le__neq__implies__less,axiom, 7.68/7.77 ! [M,N] : 7.68/7.77 ( ( N != M 7.68/7.77 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ). 7.68/7.77 7.68/7.77 fof(fact_685_diff__is__0__eq,axiom, 7.68/7.77 ! [M_1,Na] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) 7.68/7.77 <=> zero_zero_nat = hAPP_nat_nat(minus_minus_nat(M_1),Na) ) ). 7.68/7.77 7.68/7.77 fof(fact_593_add__leD1,axiom, 7.68/7.77 ! [M,K,N] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N)) 7.68/7.77 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ). 7.68/7.77 7.68/7.77 fof(fact_645_less__not__refl,axiom, 7.68/7.77 ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(P,R),Q) ). 7.68/7.77 7.68/7.77 fof(fact_189_pigeonhole__infinite,axiom, 7.68/7.77 ! [F,A_1] : 7.68/7.77 ( ( ? [X_1] : 7.68/7.77 ( is_pname(X_1) 7.68/7.77 & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.77 & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,F)),hAPP_pname_pname(F,X_1)))))) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(F,A_1))) ) 7.68/7.77 <= ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_381_le__funE,axiom, 7.68/7.77 ! [X_3,F,G_1] : 7.68/7.77 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_3)),hAPP_nat_bool(G_1,X_3))) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) ) ). 7.68/7.77 7.68/7.77 fof(conj_5,hypothesis, 7.68/7.77 ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)) ). 7.68/7.77 7.68/7.77 fof(fact_460_insert__not__empty,axiom, 7.68/7.77 ! [A_3,A_1] : insert_a(A_3,A_1) != bot_bot_fun_a_bool ). 7.68/7.77 7.68/7.77 fof(fact_573_add__Suc__shift,axiom, 7.68/7.77 ! [M,N] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N)) ). 7.68/7.77 7.68/7.77 fof(fact_412_empty__Collect__eq,axiom, 7.68/7.77 ! [Pa] : 7.68/7.77 ( collect_nat(Pa) = bot_bot_fun_nat_bool 7.68/7.77 <=> ! [X_1] : ~ hBOOL(hAPP_nat_bool(Pa,X_1)) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_a_fun_a_bool(cOMBB_a_fun_a_bool_a(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_a_a(Q,R)) ). 7.68/7.77 7.68/7.77 fof(fact_669_less__diff__iff,axiom, 7.68/7.77 ! [Na,K_2,M_1] : 7.68/7.77 ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_2)),hAPP_nat_nat(minus_minus_nat(Na),K_2))) 7.68/7.77 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) ) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_578_nat__add__commute,axiom, 7.68/7.77 ! [M,N] : hAPP_nat_nat(plus_plus_nat(N),M) = hAPP_nat_nat(plus_plus_nat(M),N) ). 7.68/7.77 7.68/7.77 fof(fact_95_finite__Collect__disjI,axiom, 7.68/7.77 ! [Pa,Q_1] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_1)))) 7.68/7.77 <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1))) 7.68/7.77 & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_130_diff__le__self,axiom, 7.68/7.77 ! [M,N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),N)),M)) ). 7.68/7.77 7.68/7.77 fof(fact_12_finite__imageI,axiom, 7.68/7.77 ! [H,F_1] : 7.68/7.77 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(H,F_1))) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(P,R),Q) ). 7.68/7.77 7.68/7.77 fof(fact_409_empty__Collect__eq,axiom, 7.68/7.77 ! [Pa] : 7.68/7.77 ( collec1974731493e_bool(Pa) = bot_bo1649642514l_bool 7.68/7.77 <=> ! [X_1] : 7.68/7.77 ( is_fun_pname_bool(X_1) 7.68/7.77 => ~ hBOOL(hAPP_f1664156314l_bool(Pa,X_1)) ) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom, 7.68/7.77 ! [P,Q] : 7.68/7.77 ( is_bool(P) 7.68/7.77 => hAPP_nat_bool(cOMBK_bool_nat(P),Q) = P ) ). 7.68/7.77 7.68/7.77 fof(fact_55_card__insert__le,axiom, 7.68/7.77 ! [X_3,A_1] : 7.68/7.77 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) 7.68/7.77 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)))) ) ). 7.68/7.77 7.68/7.77 fof(help_fequal_2_1_fequal_000t__a_T,axiom, 7.68/7.77 ! [X,Y] : 7.68/7.77 ( X != Y 7.68/7.77 | hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X),Y)) ) ). 7.68/7.77 7.68/7.77 fof(fact_430_bot__apply,axiom, 7.68/7.77 ! [X_3] : 7.68/7.77 ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_3)) 7.68/7.77 <=> hBOOL(bot_bot_bool) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : is_pname(hAPP_f1291551745_pname(B_1_1,B_2_1)) ). 7.68/7.77 7.68/7.77 fof(fact_153_finite__surj,axiom, 7.68/7.77 ! [B_6,F,A_1] : 7.68/7.77 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) 7.68/7.77 => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_fun_a_bool_nat(F,A_1))) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_93_finite__Collect__disjI,axiom, 7.68/7.77 ! [Pa,Q_1] : 7.68/7.77 ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) 7.68/7.77 & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1))) ) 7.68/7.77 <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_1)))) ) ). 7.68/7.77 7.68/7.77 fof(fact_212_image__eqI,axiom, 7.68/7.77 ! [A_1,B_1,F,X_3] : 7.68/7.77 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) 7.68/7.77 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1))) ) 7.68/7.77 <= B_1 = hAPP_a_nat(F,X_3) ) ). 7.68/7.77 7.68/7.77 fof(fact_457_singleton__iff,axiom, 7.68/7.77 ! [B_1,A_3] : 7.68/7.77 ( ( is_a(B_1) 7.68/7.77 & is_a(A_3) ) 7.68/7.77 => ( B_1 = A_3 7.68/7.77 <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),insert_a(A_3,bot_bot_fun_a_bool))) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_440_bot__unique,axiom, 7.68/7.77 ! [A_3] : 7.68/7.77 ( bot_bot_nat = A_3 7.68/7.77 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_3),bot_bot_nat)) ) ). 7.68/7.77 7.68/7.77 fof(fact_280_in__mono,axiom, 7.68/7.77 ! [X_3,A_1,B_6] : 7.68/7.77 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) 7.68/7.77 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) ) 7.68/7.77 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ). 7.68/7.77 7.68/7.77 fof(help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,axiom, 7.68/7.77 ! [X,Y] : 7.68/7.77 ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X),Y)) 7.68/7.77 | Y = X ) 7.68/7.77 <= ( is_fun_a_bool(X) 7.68/7.77 & is_fun_a_bool(Y) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_164_finite__subset__image,axiom, 7.68/7.77 ! [F,A_1,B_6] : 7.68/7.77 ( ( ( ? [C_7] : 7.68/7.77 ( B_6 = image_1283814551_pname(F,C_7) 7.68/7.77 & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7)) 7.68/7.77 & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1)) 7.68/7.77 & is_fun1661590463l_bool(C_7) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1283814551_pname(F,A_1))) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) 7.68/7.77 <= is_fun_pname_bool(B_6) ) ). 7.68/7.77 7.68/7.77 fof(help_fdisj_3_1_U,axiom, 7.68/7.77 ! [P,Q] : 7.68/7.77 ( hBOOL(P) 7.68/7.77 | hBOOL(Q) 7.68/7.77 | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ). 7.68/7.77 7.68/7.77 fof(fact_504_xt1_I6_J,axiom, 7.68/7.77 ! [Z_1,Y_2,X_3] : 7.68/7.77 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3)) 7.68/7.77 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_1),X_3)) 7.68/7.77 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_1),Y_2)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_271_set__eq__subset,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( ( is_fun_a_bool(B_6) 7.68/7.77 & is_fun_a_bool(A_1) ) 7.68/7.77 => ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) 7.68/7.77 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1)) ) 7.68/7.77 <=> B_6 = A_1 ) ) ). 7.68/7.77 7.68/7.77 fof(fact_529_ord__le__eq__trans,axiom, 7.68/7.77 ! [C_1,A_3,B_1] : 7.68/7.77 ( ( C_1 = B_1 7.68/7.77 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),C_1)) ) 7.68/7.77 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),B_1)) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : is_fun_a_bool(hAPP_f1549043526a_bool(B_1_1,B_2_1)) ). 7.68/7.77 7.68/7.77 fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( is_fun949378684l_bool(hAPP_p1824510254l_bool(B_1_1,B_2_1)) 7.68/7.77 <= is_pname(B_2_1) ) ). 7.68/7.77 7.68/7.77 fof(fact_358_subsetI,axiom, 7.68/7.77 ! [B_6,A_1] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.77 <= ! [X_1] : 7.68/7.77 ( is_pname(X_1) 7.68/7.77 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.77 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B_6)) ) ) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_pname_bool(hAPP_n1025906991e_bool(P,R),Q) = hAPP_nat_bool(hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(P),Q),R) ). 7.68/7.77 7.68/7.77 fof(fact_454_doubleton__eq__iff,axiom, 7.68/7.77 ! [A_3,B_1,C_1,D] : 7.68/7.77 ( ( is_a(D) 7.68/7.77 & is_a(C_1) 7.68/7.77 & is_a(B_1) 7.68/7.77 & is_a(A_3) ) 7.68/7.77 => ( insert_a(C_1,insert_a(D,bot_bot_fun_a_bool)) = insert_a(A_3,insert_a(B_1,bot_bot_fun_a_bool)) 7.68/7.77 <=> ( ( C_1 = B_1 7.68/7.77 & A_3 = D ) 7.68/7.77 | ( A_3 = C_1 7.68/7.77 & D = B_1 ) ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_105_finite__subset,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6)) 7.68/7.77 => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) 7.68/7.77 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) ) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_013,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f54304608l_bool(Q,R)) ). 7.68/7.77 7.68/7.77 fof(fact_7_finite__imageI,axiom, 7.68/7.77 ! [H,F_1] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) 7.68/7.77 => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(H,F_1))) ) ). 7.68/7.77 7.68/7.77 fof(fact_298_subset__trans,axiom, 7.68/7.77 ! [C_6,A_1,B_6] : 7.68/7.77 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),C_6)) 7.68/7.77 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),C_6)) ) 7.68/7.77 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ). 7.68/7.77 7.68/7.77 fof(fact_100_finite__insert,axiom, 7.68/7.77 ! [A_3,A_1] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.77 <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_3,A_1))) ) ). 7.68/7.77 7.68/7.77 fof(fact_594_add__leE,axiom, 7.68/7.77 ! [M,K,N] : 7.68/7.77 ( ~ ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N)) ) ). 7.68/7.77 7.68/7.77 fof(fact_233_insert__compr,axiom, 7.68/7.77 ! [A_3,B_6] : insert_fun_nat_bool(A_3,B_6) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),B_6))) ). 7.68/7.77 7.68/7.77 fof(fact_421_empty__def,axiom, 7.68/7.77 bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)) ). 7.68/7.77 7.68/7.77 fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__009,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_n1699378549t_bool(P,hAPP_fun_a_bool_nat(Q,R)) = hAPP_f282463732t_bool(cOMBB_164527437a_bool(P,Q),R) ). 7.68/7.77 7.68/7.77 fof(fact_414_ex__in__conv,axiom, 7.68/7.77 ! [A_1] : 7.68/7.77 ( is_fun_pname_bool(A_1) 7.68/7.77 => ( bot_bo844097828e_bool != A_1 7.68/7.77 <=> ? [X_1] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.77 & is_pname(X_1) ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_615_termination__basic__simps_I1_J,axiom, 7.68/7.77 ! [Z,X,Y] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) 7.68/7.77 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_p338031245l_bool(cOMBC_1004116266e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f759274231e_bool(P,R),Q) ). 7.68/7.77 7.68/7.77 fof(fact_107_finite__subset,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ) ). 7.68/7.77 7.68/7.77 fof(fact_96_finite__Collect__disjI,axiom, 7.68/7.77 ! [Pa,Q_1] : 7.68/7.77 ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1))) 7.68/7.77 & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) ) 7.68/7.77 <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_1)))) ) ). 7.68/7.77 7.68/7.77 fof(fact_329_subset__insertI2,axiom, 7.68/7.77 ! [B_1,A_1,B_6] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.68/7.77 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(B_1,B_6))) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : 7.68/7.77 ( is_fun949378684l_bool(cOMBS_1035972772l_bool(B_1_1,B_2_1)) 7.68/7.77 <= is_fun949378684l_bool(B_2_1) ) ). 7.68/7.77 7.68/7.77 fof(fact_516_order__antisym,axiom, 7.68/7.77 ! [X_3,Y_2] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) 7.68/7.77 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) 7.68/7.77 => Y_2 = X_3 ) ) ). 7.68/7.77 7.68/7.77 fof(fact_681_add__is__1,axiom, 7.68/7.77 ! [M_1,Na] : 7.68/7.77 ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(M_1),Na) 7.68/7.77 <=> ( ( hAPP_nat_nat(suc,zero_zero_nat) = Na 7.68/7.77 & zero_zero_nat = M_1 ) 7.68/7.77 | ( Na = zero_zero_nat 7.68/7.77 & M_1 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_9_finite__imageI,axiom, 7.68/7.77 ! [H,F_1] : 7.68/7.77 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(H,F_1))) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(P,R),Q) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(cOMBC_385542954t_bool(P),Q),R) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_p130839763l_bool(P,R),Q) = hAPP_pname_bool(hAPP_f654413245e_bool(cOMBC_267053842l_bool(P),Q),R) ). 7.68/7.77 7.68/7.77 fof(fact_27_finite_OinsertI,axiom, 7.68/7.77 ! [A_3,A_1] : 7.68/7.77 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.77 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_3,A_1))) ) ). 7.68/7.77 7.68/7.77 fof(fact_276_equalityD2,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( B_6 = A_1 7.68/7.77 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_217_equalityI,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1)) 7.68/7.77 => B_6 = A_1 ) 7.68/7.77 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ) ). 7.68/7.77 7.68/7.77 fof(fact_42_card__mono,axiom, 7.68/7.77 ! [A_1,B_6] : 7.68/7.77 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) 7.68/7.77 => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6)) 7.68/7.77 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)),hAPP_f696928925ol_nat(finite346522414t_bool,B_6))) ) ) ). 7.68/7.77 7.68/7.77 fof(help_fimplies_3_1_U,axiom, 7.68/7.77 ! [P,Q] : 7.68/7.77 ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) 7.68/7.77 | ~ hBOOL(P) 7.68/7.77 | hBOOL(Q) ) ). 7.68/7.77 7.68/7.77 fof(fact_535_ord__eq__le__trans,axiom, 7.68/7.77 ! [C_1,B_1,A_3] : 7.68/7.77 ( ( hBOOL(A_3) 7.68/7.77 <=> hBOOL(B_1) ) 7.68/7.77 => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),C_1)) 7.68/7.77 <= hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),C_1)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_461_empty__not__insert,axiom, 7.68/7.77 ! [A_3,A_1] : insert_pname(A_3,A_1) != bot_bo844097828e_bool ). 7.68/7.77 7.68/7.77 fof(help_fimplies_1_1_U,axiom, 7.68/7.77 ! [Q,P] : 7.68/7.77 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) 7.68/7.77 | hBOOL(P) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_pname_bool(hAPP_f1794073134e_bool(P,R),Q) = hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(P),Q),R) ). 7.68/7.77 7.68/7.77 fof(fact_532_xt1_I3_J,axiom, 7.68/7.77 ! [C_1,A_3,B_1] : 7.68/7.77 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),B_1)) 7.68/7.77 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_3)) ) 7.68/7.77 <= A_3 = B_1 ) ). 7.68/7.77 7.68/7.77 fof(fact_420_empty__def,axiom, 7.68/7.77 collect_fun_nat_bool(cOMBK_1994329625t_bool(fFalse)) = bot_bo1701429464l_bool ). 7.68/7.77 7.68/7.77 fof(fact_147_finite__surj,axiom, 7.68/7.77 ! [B_6,F,A_1] : 7.68/7.77 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1921560913_pname(F,A_1))) 7.68/7.77 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) 7.68/7.77 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ) ). 7.68/7.77 7.68/7.77 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O,axiom, 7.68/7.77 ! [P,Q,R] : hAPP_nat_bool(hAPP_f1066163005t_bool(P,R),Q) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(cOMBC_1666426608t_bool(P),Q),R) ). 7.68/7.77 7.68/7.77 fof(fact_559_finite__subset__induct,axiom, 7.68/7.77 ! [Pa,A_1,F_1] : 7.68/7.77 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) 7.68/7.77 => ( ( ( ! [A_2,F_2] : 7.68/7.77 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_2)) 7.68/7.77 => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,A_2),A_1)) 7.68/7.77 => ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,A_2),F_2)) 7.68/7.77 => ( hBOOL(hAPP_f1637334154l_bool(Pa,insert_fun_nat_bool(A_2,F_2))) 7.68/7.77 <= hBOOL(hAPP_f1637334154l_bool(Pa,F_2)) ) ) ) ) 7.68/7.77 => hBOOL(hAPP_f1637334154l_bool(Pa,F_1)) ) 7.68/7.77 <= hBOOL(hAPP_f1637334154l_bool(Pa,bot_bo1701429464l_bool)) ) 7.68/7.77 <= hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,F_1),A_1)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_132_finite__surj,axiom, 7.68/7.77 ! [B_6,F,A_1] : 7.68/7.77 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) 7.68/7.77 => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) 7.68/7.77 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_nat_bool_a(F,A_1))) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_18_finite__imageI,axiom, 7.68/7.77 ! [H,F_1] : 7.68/7.77 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) 7.68/7.77 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(H,F_1))) ) ). 7.68/7.77 7.68/7.77 fof(fact_239_insert__Collect,axiom, 7.68/7.77 ! [A_3,Pa] : insert_pname(A_3,collect_pname(Pa)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3))),Pa)) ). 7.68/7.77 7.68/7.77 fof(fact_165_finite__subset__image,axiom, 7.68/7.77 ! [F,A_1,B_6] : 7.68/7.77 ( ( ( ? [C_7] : 7.68/7.77 ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1)) 7.68/7.77 & image_1854862208_pname(F,C_7) = B_6 7.68/7.77 & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7)) 7.68/7.77 & is_fun949378684l_bool(C_7) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1854862208_pname(F,A_1))) ) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) 7.68/7.77 <= is_fun_pname_bool(B_6) ) ). 7.68/7.77 7.68/7.77 fof(fact_684_diff__is__0__eq_H,axiom, 7.68/7.77 ! [M,N] : 7.68/7.77 ( zero_zero_nat = hAPP_nat_nat(minus_minus_nat(M),N) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ). 7.68/7.77 7.68/7.77 fof(fact_333_insert__mono,axiom, 7.68/7.77 ! [A_3,C_6,D_1] : 7.68/7.77 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),D_1)) 7.68/7.77 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_3,C_6)),insert_a(A_3,D_1))) ) ). 7.68/7.77 7.68/7.77 fof(fact_343_insert__image,axiom, 7.68/7.77 ! [F,X_3,A_1] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.77 => insert_a(hAPP_pname_a(F,X_3),image_pname_a(F,A_1)) = image_pname_a(F,A_1) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom, 7.68/7.77 is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))) ). 7.68/7.77 7.68/7.77 fof(fact_371_order__refl,axiom, 7.68/7.77 ! [X_10] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),X_10)) ). 7.68/7.77 7.68/7.77 fof(fact_84_n__not__Suc__n,axiom, 7.68/7.77 ! [N] : hAPP_nat_nat(suc,N) != N ). 7.68/7.77 7.68/7.77 fof(gsy_c_HOL_Oundefined_000tc__Com__Opname,axiom, 7.68/7.77 is_pname(undefined_pname(pname)) ). 7.68/7.77 7.68/7.77 fof(fact_491_singleton__conv2,axiom, 7.68/7.77 ! [A_3] : collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool) ). 7.68/7.77 7.68/7.77 fof(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom, 7.68/7.77 ! [X,Y] : 7.68/7.77 ( Y != X 7.68/7.77 | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) ) ). 7.68/7.77 7.68/7.77 fof(fact_600_le__diff__conv2,axiom, 7.68/7.77 ! [I_1,K_2,J_1] : 7.68/7.77 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1)) 7.68/7.77 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_2))) 7.68/7.77 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_2)),J_1)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_370_order__refl,axiom, 7.68/7.77 ! [X_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),X_3)) ). 7.68/7.77 7.68/7.77 fof(fact_628_less__SucE,axiom, 7.68/7.77 ! [M,N] : 7.68/7.77 ( ( N = M 7.68/7.77 <= ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) ) ). 7.68/7.77 7.68/7.77 fof(fact_296_subset__trans,axiom, 7.68/7.77 ! [C_6,A_1,B_6] : 7.68/7.77 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.77 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),C_6)) 7.68/7.77 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_6)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_629_less__trans__Suc,axiom, 7.68/7.77 ! [K,I,J_2] : 7.68/7.77 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K)) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K)) ) 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ) ). 7.68/7.77 7.68/7.77 fof(fact_338_insert__image,axiom, 7.68/7.77 ! [F,X_3,A_1] : 7.68/7.77 ( image_pname_pname(F,A_1) = insert_pname(hAPP_pname_pname(F,X_3),image_pname_pname(F,A_1)) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_334_image__insert,axiom, 7.68/7.77 ! [F,A_3,B_6] : insert_pname(hAPP_a_pname(F,A_3),image_a_pname(F,B_6)) = image_a_pname(F,insert_a(A_3,B_6)) ). 7.68/7.77 7.68/7.77 fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U,axiom, 7.68/7.77 ! [P,Q] : 7.68/7.77 ( hAPP_pname_bool(cOMBK_bool_pname(P),Q) = P 7.68/7.77 <= is_bool(P) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname,axiom, 7.68/7.77 ! [B_1_1,B_2_1] : is_pname(hAPP_nat_pname(B_1_1,B_2_1)) ). 7.68/7.77 7.68/7.77 fof(fact_401_Collect__empty__eq,axiom, 7.68/7.77 ! [Pa] : 7.68/7.77 ( ! [X_1] : 7.68/7.77 ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,X_1)) 7.68/7.77 <= is_fun_a_bool(X_1) ) 7.68/7.77 <=> bot_bo1389914601l_bool = collect_fun_a_bool(Pa) ) ). 7.68/7.77 7.68/7.77 fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,axiom, 7.68/7.77 is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))) ). 7.68/7.77 7.68/7.77 fof(fact_452_doubleton__eq__iff,axiom, 7.68/7.77 ! [A_3,B_1,C_1,D] : 7.68/7.77 ( ( insert_pname(C_1,insert_pname(D,bot_bo844097828e_bool)) = insert_pname(A_3,insert_pname(B_1,bot_bo844097828e_bool)) 7.68/7.77 <=> ( ( A_3 = D 7.68/7.77 & B_1 = C_1 ) 7.68/7.77 | ( A_3 = C_1 7.68/7.77 & D = B_1 ) ) ) 7.68/7.77 <= ( is_pname(A_3) 7.68/7.77 & is_pname(B_1) 7.68/7.77 & is_pname(C_1) 7.68/7.77 & is_pname(D) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_448_singleton__inject,axiom, 7.68/7.77 ! [A_3,B_1] : 7.68/7.77 ( ( is_a(A_3) 7.68/7.77 & is_a(B_1) ) 7.68/7.77 => ( B_1 = A_3 7.68/7.77 <= insert_a(B_1,bot_bot_fun_a_bool) = insert_a(A_3,bot_bot_fun_a_bool) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_151_finite__surj,axiom, 7.68/7.77 ! [B_6,F,A_1] : 7.68/7.77 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_496248727ol_nat(F,A_1))) 7.68/7.77 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) 7.68/7.77 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ) ). 7.68/7.77 7.68/7.77 fof(fact_580_diff__add__inverse,axiom, 7.68/7.77 ! [N,M] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),N) = M ). 7.68/7.77 7.68/7.77 fof(fact_474_Collect__conv__if,axiom, 7.68/7.77 ! [Pa,A_3] : 7.68/7.77 ( ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),Pa)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool) 7.68/7.77 <= hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) ) 7.68/7.77 & ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),Pa)) = bot_bo1649642514l_bool 7.68/7.77 <= ~ hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) ) ) ). 7.68/7.77 7.68/7.77 fof(fact_650_less__not__refl3,axiom, 7.68/7.77 ! [S,T] : 7.68/7.77 ( S != T 7.68/7.77 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) ) ). 7.68/7.77 7.68/7.77 fof(fact_494_subset__singletonD,axiom, 7.68/7.77 ! [A_1,X_3] : 7.68/7.77 ( ( bot_bot_fun_nat_bool = A_1 7.68/7.78 | insert_nat(X_3,bot_bot_fun_nat_bool) = A_1 ) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(X_3,bot_bot_fun_nat_bool))) ) ). 7.68/7.78 7.68/7.78 fof(fact_505_xt1_I5_J,axiom, 7.68/7.78 ! [Y_2,X_3] : 7.68/7.78 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) 7.68/7.78 => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) 7.68/7.78 => ( hBOOL(Y_2) 7.68/7.78 <=> hBOOL(X_3) ) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_300_equalityE,axiom, 7.68/7.78 ! [A_1,B_6] : 7.68/7.78 ( B_6 = A_1 7.68/7.78 => ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.68/7.78 => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_609_diff__Suc__diff__eq1,axiom, 7.68/7.78 ! [M,K,J_2] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) 7.68/7.78 => hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J_2),K))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K)),hAPP_nat_nat(suc,J_2)) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : is_fun_pname_bool(image_nat_pname(B_1_1,B_2_1)) ). 7.68/7.78 7.68/7.78 fof(gsy_c_Set_OCollect_000t__a,axiom, 7.68/7.78 ! [B_1_1] : 7.68/7.78 ( is_fun_a_bool(B_1_1) 7.68/7.78 => is_fun_a_bool(collect_a(B_1_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_283_set__rev__mp,axiom, 7.68/7.78 ! [B_6,X_3,A_1] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) 7.68/7.78 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_611_termination__basic__simps_I4_J,axiom, 7.68/7.78 ! [Y,X,Z] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z)) ) ). 7.68/7.78 7.68/7.78 fof(fact_379_le__funD,axiom, 7.68/7.78 ! [X_3,F,G_1] : 7.68/7.78 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_3)),hAPP_a_bool(G_1,X_3))) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_528_ord__le__eq__trans,axiom, 7.68/7.78 ! [C_4,A_6,B_4] : 7.68/7.78 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),C_4)) 7.68/7.78 <= C_4 = B_4 ) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),B_4)) ) ). 7.68/7.78 7.68/7.78 fof(fact_618_less__add__eq__less,axiom, 7.68/7.78 ! [M,N,K,L] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L)) 7.68/7.78 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) 7.68/7.78 <= hAPP_nat_nat(plus_plus_nat(M),L) = hAPP_nat_nat(plus_plus_nat(K),N) ) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_a_bool(hAPP_p1534023578a_bool(cOMBC_a_pname_bool(P),Q),R) = hAPP_pname_bool(hAPP_a93125764e_bool(P,R),Q) ). 7.68/7.78 7.68/7.78 fof(fact_251_insert__iff,axiom, 7.68/7.78 ! [A_3,B_1,A_1] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,A_1))) 7.68/7.78 <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1)) 7.68/7.78 | B_1 = A_3 ) ) ). 7.68/7.78 7.68/7.78 fof(fact_315_insert__compr__raw,axiom, 7.68/7.78 ! [X_1,Xa] : collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),Xa))) = insert_fun_a_bool(X_1,Xa) ). 7.68/7.78 7.68/7.78 fof(fact_623_nat__add__left__cancel__less,axiom, 7.68/7.78 ! [K_2,M_1,Na] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) 7.68/7.78 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K_2),M_1)),hAPP_nat_nat(plus_plus_nat(K_2),Na))) ) ). 7.68/7.78 7.68/7.78 fof(fact_268_subset__refl,axiom, 7.68/7.78 ! [A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),A_1)) ). 7.68/7.78 7.68/7.78 fof(fact_288_mem__def,axiom, 7.68/7.78 ! [X_3,A_1] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.78 <=> hBOOL(hAPP_pname_bool(A_1,X_3)) ) ). 7.68/7.78 7.68/7.78 fof(fact_634_Suc__less__eq,axiom, 7.68/7.78 ! [M_1,Na] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,Na))) 7.68/7.78 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ). 7.68/7.78 7.68/7.78 fof(fact_87_eq__imp__le,axiom, 7.68/7.78 ! [M,N] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) 7.68/7.78 <= N = M ) ). 7.68/7.78 7.68/7.78 fof(fact_546_order__eq__refl,axiom, 7.68/7.78 ! [X_3,Y_2] : 7.68/7.78 ( X_3 = Y_2 7.68/7.78 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) ) ). 7.68/7.78 7.68/7.78 fof(help_fFalse_1_1_U,axiom, 7.68/7.78 ~ hBOOL(fFalse) ). 7.68/7.78 7.68/7.78 fof(fact_592_add__leD2,axiom, 7.68/7.78 ! [M,K,N] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N)) ) ). 7.68/7.78 7.68/7.78 fof(fact_597_diff__add__assoc,axiom, 7.68/7.78 ! [I,K,J_2] : 7.68/7.78 ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),J_2)),K) = hAPP_nat_nat(plus_plus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ) ). 7.68/7.78 7.68/7.78 fof(fact_463_empty__not__insert,axiom, 7.68/7.78 ! [A_3,A_1] : bot_bot_fun_a_bool != insert_a(A_3,A_1) ). 7.68/7.78 7.68/7.78 fof(fact_156_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) 7.68/7.78 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_876012084bool_a(F,A_1))) 7.68/7.78 => ? [C_7] : 7.68/7.78 ( is_fun1661590463l_bool(C_7) 7.68/7.78 & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1)) 7.68/7.78 & B_6 = image_876012084bool_a(F,C_7) 7.68/7.78 & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7)) ) ) ) 7.68/7.78 <= is_fun_a_bool(B_6) ) ). 7.68/7.78 7.68/7.78 fof(fact_466_subset__empty,axiom, 7.68/7.78 ! [A_1] : 7.68/7.78 ( is_fun_a_bool(A_1) 7.68/7.78 => ( bot_bot_fun_a_bool = A_1 7.68/7.78 <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),bot_bot_fun_a_bool)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_162_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( ( ( ? [C_7] : 7.68/7.78 ( is_fun_a_bool(C_7) 7.68/7.78 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) 7.68/7.78 & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) 7.68/7.78 & B_6 = image_a_pname(F,C_7) ) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1))) ) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) 7.68/7.78 <= is_fun_pname_bool(B_6) ) ). 7.68/7.78 7.68/7.78 fof(fact_207_pigeonhole__infinite,axiom, 7.68/7.78 ! [F,A_1] : 7.68/7.78 ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) 7.68/7.78 => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(F,A_1))) 7.68/7.78 => ? [X_1] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) 7.68/7.78 & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,F)),hAPP_a_fun_nat_bool(F,X_1)))))) 7.68/7.78 & is_a(X_1) ) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_218_equalityI,axiom, 7.68/7.78 ! [A_1,B_6] : 7.68/7.78 ( ( is_fun_a_bool(A_1) 7.68/7.78 & is_fun_a_bool(B_6) ) 7.68/7.78 => ( ( A_1 = B_6 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1)) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ) ). 7.68/7.78 7.68/7.78 fof(help_fNot_2_1_U,axiom, 7.68/7.78 ! [P] : 7.68/7.78 ( hBOOL(hAPP_bool_bool(fNot,P)) 7.68/7.78 | hBOOL(P) ) ). 7.68/7.78 7.68/7.78 fof(fact_389_finite_OemptyI,axiom, 7.68/7.78 hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)) ). 7.68/7.78 7.68/7.78 fof(help_fdisj_1_1_U,axiom, 7.68/7.78 ! [Q,P] : 7.68/7.78 ( ~ hBOOL(P) 7.68/7.78 | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ). 7.68/7.78 7.68/7.78 fof(fact_423_empty__def,axiom, 7.68/7.78 collect_a(cOMBK_bool_a(fFalse)) = bot_bot_fun_a_bool ). 7.68/7.78 7.68/7.78 fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(P,R),Q) ). 7.68/7.78 7.68/7.78 fof(fact_442_bot__least,axiom, 7.68/7.78 ! [A_3] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_3)) ). 7.68/7.78 7.68/7.78 fof(fact_306_imageI,axiom, 7.68/7.78 ! [F,X_3,A_1] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(F,X_3)),image_nat_a(F,A_1))) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_585_le__add1,axiom, 7.68/7.78 ! [N,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(N),M))) ). 7.68/7.78 7.68/7.78 fof(fact_141_finite__surj,axiom, 7.68/7.78 ! [B_6,F,A_1] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.78 => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) 7.68/7.78 <= hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_26036933t_bool(F,A_1))) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_211_image__eqI,axiom, 7.68/7.78 ! [A_1,B_1,F,X_3] : 7.68/7.78 ( hAPP_pname_nat(F,X_3) = B_1 7.68/7.78 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.78 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1))) ) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_p61793385e_bool(P,hAPP_a_pname(Q,R)) = hAPP_a93125764e_bool(cOMBB_610033911bool_a(P,Q),R) ). 7.68/7.78 7.68/7.78 fof(fact_231_insertI1,axiom, 7.68/7.78 ! [A_3,B_6] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(A_3,B_6))) ). 7.68/7.78 7.68/7.78 fof(fact_301_equalityE,axiom, 7.68/7.78 ! [A_1,B_6] : 7.68/7.78 ( ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1)) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) 7.68/7.78 <= B_6 = A_1 ) ). 7.68/7.78 7.68/7.78 fof(fact_77_finite__Collect__conjI,axiom, 7.68/7.78 ! [Q_1,Pa] : 7.68/7.78 ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1))) 7.68/7.78 | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) ) 7.68/7.78 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),Q_1)))) ) ). 7.68/7.78 7.68/7.78 fof(fact_265_insert__absorb,axiom, 7.68/7.78 ! [A_3,A_1] : 7.68/7.78 ( is_fun_a_bool(A_1) 7.68/7.78 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) 7.68/7.78 => A_1 = insert_a(A_3,A_1) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_526_ord__le__eq__trans,axiom, 7.68/7.78 ! [C_1,A_3,B_1] : 7.68/7.78 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),C_1)) 7.68/7.78 <= B_1 = C_1 ) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),B_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_219_subsetD,axiom, 7.68/7.78 ! [C_1,A_1,B_6] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) 7.68/7.78 => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B_6)) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A_1)) ) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__H,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun_pname_bool(B_2_1) 7.68/7.78 => is_fun_a_bool(hAPP_f1051908748a_bool(B_1_1,B_2_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_549_order__eq__refl,axiom, 7.68/7.78 ! [X_3,Y_2] : 7.68/7.78 ( Y_2 = X_3 7.68/7.78 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) ) ). 7.68/7.78 7.68/7.78 fof(fact_595_diff__add__assoc2,axiom, 7.68/7.78 ! [I,K,J_2] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) 7.68/7.78 => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_2),I)),K) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_2),K)),I) ) ). 7.68/7.78 7.68/7.78 fof(fact_550_order__eq__iff,axiom, 7.68/7.78 ! [Y_2,X_3] : 7.68/7.78 ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) 7.68/7.78 & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) ) 7.68/7.78 <=> ( hBOOL(X_3) 7.68/7.78 <=> hBOOL(Y_2) ) ) ). 7.68/7.78 7.68/7.78 fof(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom, 7.68/7.78 ! [X,Y] : 7.68/7.78 ( X != Y 7.68/7.78 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)) ). 7.68/7.78 7.68/7.78 fof(fact_266_subset__refl,axiom, 7.68/7.78 ! [A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A_1)) ). 7.68/7.78 7.68/7.78 fof(fact_81_Suc__inject,axiom, 7.68/7.78 ! [X,Y] : 7.68/7.78 ( hAPP_nat_nat(suc,Y) = hAPP_nat_nat(suc,X) 7.68/7.78 => Y = X ) ). 7.68/7.78 7.68/7.78 fof(fact_488_singleton__conv2,axiom, 7.68/7.78 ! [A_3] : insert_nat(A_3,bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(fequal_nat,A_3)) ). 7.68/7.78 7.68/7.78 fof(fact_664_Suc__le__lessD,axiom, 7.68/7.78 ! [M,N] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) ) ). 7.68/7.78 7.68/7.78 fof(fact_171_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) 7.68/7.78 => ( ? [C_7] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) 7.68/7.78 & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) 7.68/7.78 & B_6 = image_47868345e_bool(F,C_7) 7.68/7.78 & is_fun_pname_bool(C_7) ) 7.68/7.78 <= hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_47868345e_bool(F,A_1))) ) ) 7.68/7.78 <= is_fun1661590463l_bool(B_6) ) ). 7.68/7.78 7.68/7.78 fof(fact_522_xt1_I4_J,axiom, 7.68/7.78 ! [C_1,B_1,A_3] : 7.68/7.78 ( ( C_1 = B_1 7.68/7.78 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_3)) ) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A_3)) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1)) 7.68/7.78 <= is_pname(B_2_1) ) ). 7.68/7.78 7.68/7.78 fof(gsy_v_P,axiom, 7.68/7.78 ! [B_1_1] : 7.68/7.78 ( is_fun949378684l_bool(p(B_1_1)) 7.68/7.78 <= is_fun_a_bool(B_1_1) ) ). 7.68/7.78 7.68/7.78 fof(fact_113_rev__finite__subset,axiom, 7.68/7.78 ! [A_1,B_6] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) 7.68/7.78 => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ) ) ). 7.68/7.78 7.68/7.78 fof(gsy_v_U,hypothesis, 7.68/7.78 is_fun_pname_bool(u) ). 7.68/7.78 7.68/7.78 fof(fact_422_empty__def,axiom, 7.68/7.78 collect_fun_a_bool(cOMBK_324466864a_bool(fFalse)) = bot_bo1389914601l_bool ). 7.68/7.78 7.68/7.78 fof(fact_472_Collect__conv__if,axiom, 7.68/7.78 ! [Pa,A_3] : 7.68/7.78 ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),Pa)) = bot_bot_fun_a_bool 7.68/7.78 <= ~ hBOOL(hAPP_a_bool(Pa,A_3)) ) 7.68/7.78 & ( insert_a(A_3,bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),Pa)) 7.68/7.78 <= hBOOL(hAPP_a_bool(Pa,A_3)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_140_finite__surj,axiom, 7.68/7.78 ! [B_6,F,A_1] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) 7.68/7.78 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1))) 7.68/7.78 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_415_ex__in__conv,axiom, 7.68/7.78 ! [A_1] : 7.68/7.78 ( ( ? [X_1] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) 7.68/7.78 & is_a(X_1) ) 7.68/7.78 <=> A_1 != bot_bot_fun_a_bool ) 7.68/7.78 <= is_fun_a_bool(A_1) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun_a_bool(B_2_1) 7.68/7.78 => is_fun949378684l_bool(image_a_fun_a_bool(B_1_1,B_2_1)) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_a(B_2_1) 7.68/7.78 => is_fun_a_bool(hAPP_a_fun_a_bool(B_1_1,B_2_1)) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2_1)) 7.68/7.78 <= is_fun_pname_bool(B_2_1) ) ). 7.68/7.78 7.68/7.78 fof(fact_149_finite__surj,axiom, 7.68/7.78 ! [B_6,F,A_1] : 7.68/7.78 ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1854862208_pname(F,A_1))) ) 7.68/7.78 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : is_bool(hAPP_f292226953l_bool(B_1_1,B_2_1)) ). 7.68/7.78 7.68/7.78 fof(help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_a_bool(hAPP_a_fun_a_bool(P,R),Q) = hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(P),Q),R) ). 7.68/7.78 7.68/7.78 fof(fact_138_finite__surj,axiom, 7.68/7.78 ! [B_6,F,A_1] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.78 => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_pname_pname(F,A_1))) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_489_singleton__conv2,axiom, 7.68/7.78 ! [A_3] : collect_pname(hAPP_p61793385e_bool(fequal_pname,A_3)) = insert_pname(A_3,bot_bo844097828e_bool) ). 7.68/7.78 7.68/7.78 fof(fact_75_finite__Collect__conjI,axiom, 7.68/7.78 ! [Q_1,Pa] : 7.68/7.78 ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1))) 7.68/7.78 | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) ) 7.68/7.78 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,Pa),Q_1)))) ) ). 7.68/7.78 7.68/7.78 fof(fact_668_diff__less__mono,axiom, 7.68/7.78 ! [C,A,B] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B)) 7.68/7.78 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A)) 7.68/7.78 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(A),C)),hAPP_nat_nat(minus_minus_nat(B),C))) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_361_image__subsetI,axiom, 7.68/7.78 ! [F,B_6,A_1] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(F,A_1)),B_6)) 7.68/7.78 <= ! [X_1] : 7.68/7.78 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.78 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(F,X_1)),B_6)) ) 7.68/7.78 <= is_pname(X_1) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_70_card__insert__disjoint,axiom, 7.68/7.78 ! [X_3,A_1] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.78 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) 7.68/7.78 => hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A_1)) = hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) ) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_pname_a(Q,R)) ). 7.68/7.78 7.68/7.78 fof(fact_382_le__funE,axiom, 7.68/7.78 ! [X_3,F,G_1] : 7.68/7.78 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_3)),hAPP_a_bool(G_1,X_3))) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) ) ). 7.68/7.78 7.68/7.78 fof(help_fimplies_2_1_U,axiom, 7.68/7.78 ! [P,Q] : 7.68/7.78 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) 7.68/7.78 | ~ hBOOL(Q) ) ). 7.68/7.78 7.68/7.78 fof(fact_173_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) 7.68/7.78 => ( ? [C_7] : 7.68/7.78 ( is_fun_pname_bool(C_7) 7.68/7.78 & B_6 = image_pname_pname(F,C_7) 7.68/7.78 & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) 7.68/7.78 & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) ) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_pname_pname(F,A_1))) ) ) 7.68/7.78 <= is_fun_pname_bool(B_6) ) ). 7.68/7.78 7.68/7.78 fof(fact_308_rev__image__eqI,axiom, 7.68/7.78 ! [B_1,F,X_3,A_1] : 7.68/7.78 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1))) 7.68/7.78 <= B_1 = hAPP_pname_nat(F,X_3) ) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_407_empty__Collect__eq,axiom, 7.68/7.78 ! [Pa] : 7.68/7.78 ( bot_bo844097828e_bool = collect_pname(Pa) 7.68/7.78 <=> ! [X_1] : 7.68/7.78 ( is_pname(X_1) 7.68/7.78 => ~ hBOOL(hAPP_pname_bool(Pa,X_1)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_214_image__eqI,axiom, 7.68/7.78 ! [A_1,B_1,F,X_3] : 7.68/7.78 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1))) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ) 7.68/7.78 <= hAPP_nat_a(F,X_3) = B_1 ) ). 7.68/7.78 7.68/7.78 fof(fact_248_insert__commute,axiom, 7.68/7.78 ! [X_3,Y_2,A_1] : insert_pname(Y_2,insert_pname(X_3,A_1)) = insert_pname(X_3,insert_pname(Y_2,A_1)) ). 7.68/7.78 7.68/7.78 fof(fact_314_insert__compr__raw,axiom, 7.68/7.78 ! [X_1,Xa] : collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),Xa))) = insert1325755072e_bool(X_1,Xa) ). 7.68/7.78 7.68/7.78 fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_bool(hAPP_f1664156314l_bool(B_1_1,B_2_1)) 7.68/7.78 <= ( is_fun1661590463l_bool(B_1_1) 7.68/7.78 & is_fun_pname_bool(B_2_1) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_264_insert__absorb,axiom, 7.68/7.78 ! [A_3,A_1] : 7.68/7.78 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)) 7.68/7.78 => A_1 = insert_pname(A_3,A_1) ) 7.68/7.78 <= is_fun_pname_bool(A_1) ) ). 7.68/7.78 7.68/7.78 fof(fact_177_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) 7.68/7.78 => ( ? [C_7] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) 7.68/7.78 & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) 7.68/7.78 & image_1655916159e_bool(F,C_7) = B_6 ) 7.68/7.78 <= hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_1655916159e_bool(F,A_1))) ) ) 7.68/7.78 <= is_fun1661590463l_bool(B_6) ) ). 7.68/7.78 7.68/7.78 fof(fact_34_card__image__le,axiom, 7.68/7.78 ! [F,A_1] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1))) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_558_finite__subset__induct,axiom, 7.68/7.78 ! [Pa,A_1,F_1] : 7.68/7.78 ( ( ( ( ! [A_2,F_2] : 7.68/7.78 ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2)) 7.68/7.78 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A_1)) 7.68/7.78 => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),F_2)) 7.68/7.78 => ( hBOOL(hAPP_fun_a_bool_bool(Pa,insert_a(A_2,F_2))) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(Pa,F_2)) ) ) ) ) 7.68/7.78 <= ( is_fun_a_bool(F_2) 7.68/7.78 & is_a(A_2) ) ) 7.68/7.78 => hBOOL(hAPP_fun_a_bool_bool(Pa,F_1)) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool)) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F_1),A_1)) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_655_less__add__Suc1,axiom, 7.68/7.78 ! [I,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(I),M)))) ). 7.68/7.78 7.68/7.78 fof(fact_552_order__eq__iff,axiom, 7.68/7.78 ! [X_3,Y_2] : 7.68/7.78 ( ( Y_2 = X_3 7.68/7.78 <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3)) 7.68/7.78 & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) ) ) 7.68/7.78 <= ( is_fun_pname_bool(X_3) 7.68/7.78 & is_fun_pname_bool(Y_2) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_39_card__image__le,axiom, 7.68/7.78 ! [F,A_1] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) 7.68/7.78 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1))) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__003,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R)) = hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(P,Q),R) ). 7.68/7.78 7.68/7.78 fof(fact_115_Suc__leD,axiom, 7.68/7.78 ! [M,N] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) 7.68/7.78 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ). 7.68/7.78 7.68/7.78 fof(fact_21_finite__imageI,axiom, 7.68/7.78 ! [H,F_1] : 7.68/7.78 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) 7.68/7.78 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(H,F_1))) ) ). 7.68/7.78 7.68/7.78 fof(fact_484_singleton__conv,axiom, 7.68/7.78 ! [A_3] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)) = insert_a(A_3,bot_bot_fun_a_bool) ). 7.68/7.78 7.68/7.78 fof(fact_344_subset__image__iff,axiom, 7.68/7.78 ! [B_6,F,A_1] : 7.68/7.78 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1))) 7.68/7.78 <=> ? [AA] : 7.68/7.78 ( B_6 = image_nat_a(F,AA) 7.68/7.78 & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A_1)) ) ) 7.68/7.78 <= is_fun_a_bool(B_6) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun_pname_bool(B_2_1) 7.68/7.78 => is_fun1661590463l_bool(image_47868345e_bool(B_1_1,B_2_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_519_order__antisym,axiom, 7.68/7.78 ! [X_3,Y_2] : 7.68/7.78 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) 7.68/7.78 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3)) 7.68/7.78 => X_3 = Y_2 ) ) 7.68/7.78 <= ( is_fun_a_bool(X_3) 7.68/7.78 & is_fun_a_bool(Y_2) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_642_diff__less__mono2,axiom, 7.68/7.78 ! [L,M,N] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) 7.68/7.78 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M))) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_102_finite__insert,axiom, 7.68/7.78 ! [A_3,A_1] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_3,A_1))) 7.68/7.78 <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_122_Suc__diff__diff,axiom, 7.68/7.78 ! [M,N,K] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),K) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N)),hAPP_nat_nat(suc,K)) ). 7.68/7.78 7.68/7.78 fof(fact_180_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( ( ? [C_7] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) 7.68/7.78 & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) 7.68/7.78 & B_6 = image_nat_nat(F,C_7) ) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_nat_nat(F,A_1))) ) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ). 7.68/7.78 7.68/7.78 fof(fact_287_mem__def,axiom, 7.68/7.78 ! [X_3,A_1] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) 7.68/7.78 <=> hBOOL(hAPP_nat_bool(A_1,X_3)) ) ). 7.68/7.78 7.68/7.78 fof(fact_612_lessI,axiom, 7.68/7.78 ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N))) ). 7.68/7.78 7.68/7.78 fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_023,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_n1025906991e_bool(Q,R)) ). 7.68/7.78 7.68/7.78 fof(fact_44_card__mono,axiom, 7.68/7.78 ! [A_1,B_6] : 7.68/7.78 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,B_6))) 7.68/7.78 <= hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6)) ) 7.68/7.78 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) ) ). 7.68/7.78 7.68/7.78 fof(fact_657_less__iff__Suc__add,axiom, 7.68/7.78 ! [M_1,Na] : 7.68/7.78 ( ? [K_1] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M_1),K_1)) 7.68/7.78 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ). 7.68/7.78 7.68/7.78 fof(gsy_v_pn,hypothesis, 7.68/7.78 is_pname(pn) ). 7.68/7.78 7.68/7.78 fof(fact_506_xt1_I5_J,axiom, 7.68/7.78 ! [Y_2,X_3] : 7.68/7.78 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) 7.68/7.78 => X_3 = Y_2 ) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) ) ). 7.68/7.78 7.68/7.78 fof(fact_500_xt1_I6_J,axiom, 7.68/7.78 ! [Z_1,Y_2,X_3] : 7.68/7.78 ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) 7.68/7.78 => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),X_3)) 7.68/7.78 <= hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_210_pigeonhole__infinite,axiom, 7.68/7.78 ! [F,A_1] : 7.68/7.78 ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(F,A_1))) 7.68/7.78 => ? [X_1] : 7.68/7.78 ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,F)),hAPP_pname_a(F,X_1)))))) 7.68/7.78 & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) 7.68/7.78 & is_pname(X_1) ) ) 7.68/7.78 <= ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL,hypothesis, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun_a_bool(B_2_1) 7.68/7.78 => is_fun949378684l_bool(hAPP_f1631501043l_bool(B_1_1,B_2_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_502_xt1_I6_J,axiom, 7.68/7.78 ! [Z_1,Y_2,X_3] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3)) 7.68/7.78 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z_1),Y_2)) 7.68/7.78 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z_1),X_3)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_438_bot__unique,axiom, 7.68/7.78 ! [A_3] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),bot_bot_fun_nat_bool)) 7.68/7.78 <=> A_3 = bot_bot_fun_nat_bool ) ). 7.68/7.78 7.68/7.78 fof(fact_73_finite__Collect__conjI,axiom, 7.68/7.78 ! [Q_1,Pa] : 7.68/7.78 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,Pa),Q_1)))) 7.68/7.78 <= ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) 7.68/7.78 | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1))) ) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun1661590463l_bool(hAPP_a217006258l_bool(B_1_1,B_2_1)) 7.68/7.78 <= is_a(B_2_1) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q) ). 7.68/7.78 7.68/7.78 fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun_pname_bool(B_2_1) 7.68/7.78 => is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_678_less__zeroE,axiom, 7.68/7.78 ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)) ). 7.68/7.78 7.68/7.78 fof(fact_387_finite_OemptyI,axiom, 7.68/7.78 hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)) ). 7.68/7.78 7.68/7.78 fof(fact_648_less__irrefl__nat,axiom, 7.68/7.78 ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)) ). 7.68/7.78 7.68/7.78 fof(fact_631_less__SucI,axiom, 7.68/7.78 ! [M,N] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) 7.68/7.78 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_COMBK_000tc__HOL__Obool_000t__a,axiom, 7.68/7.78 ! [B_1_1] : 7.68/7.78 ( is_fun_a_bool(cOMBK_bool_a(B_1_1)) 7.68/7.78 <= is_bool(B_1_1) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun_a_bool(B_2_1) 7.68/7.78 => is_fun_a_bool(cOMBB_bool_bool_a(B_1_1,B_2_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_372_finite__nat__set__iff__bounded__le,axiom, 7.68/7.78 ! [N_1] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1)) 7.68/7.78 <=> ? [M_2] : 7.68/7.78 ! [X_1] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M_2)) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) ) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_Finite__Set_Ofinite_000t__a,axiom, 7.68/7.78 is_fun949378684l_bool(finite_finite_a) ). 7.68/7.78 7.68/7.78 fof(fact_397_equals0D,axiom, 7.68/7.78 ! [A_3,A_1] : 7.68/7.78 ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) 7.68/7.78 <= A_1 = bot_bot_fun_a_bool ) ). 7.68/7.78 7.68/7.78 fof(fact_238_insert__compr,axiom, 7.68/7.78 ! [A_3,B_6] : insert_a(A_3,B_6) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B_6))) ). 7.68/7.78 7.68/7.78 fof(fact_157_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( is_fun_a_bool(B_6) 7.68/7.78 => ( ( ? [C_7] : 7.68/7.78 ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1)) 7.68/7.78 & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7)) 7.68/7.78 & image_fun_a_bool_a(F,C_7) = B_6 7.68/7.78 & is_fun949378684l_bool(C_7) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_a_bool_a(F,A_1))) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_nat_fun_a_bool(cOMBB_1885489796ol_nat(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_nat_a(Q,R)) ). 7.68/7.78 7.68/7.78 fof(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom, 7.68/7.78 ! [X,Y] : 7.68/7.78 ( ( Y = X 7.68/7.78 | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) ) 7.68/7.78 <= ( is_fun_pname_bool(Y) 7.68/7.78 & is_fun_pname_bool(X) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_542_order__antisym__conv,axiom, 7.68/7.78 ! [Y_2,X_3] : 7.68/7.78 ( ( is_fun_pname_bool(Y_2) 7.68/7.78 & is_fun_pname_bool(X_3) ) 7.68/7.78 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3)) 7.68/7.78 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) 7.68/7.78 <=> Y_2 = X_3 ) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_20_finite__imageI,axiom, 7.68/7.78 ! [H,F_1] : 7.68/7.78 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) 7.68/7.78 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(H,F_1))) ) ). 7.68/7.78 7.68/7.78 fof(fact_586_le__iff__add,axiom, 7.68/7.78 ! [M_1,Na] : 7.68/7.78 ( ? [K_1] : hAPP_nat_nat(plus_plus_nat(M_1),K_1) = Na 7.68/7.78 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ). 7.68/7.78 7.68/7.78 fof(fact_161_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) 7.68/7.78 => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_a_fun_a_bool(F,A_1))) 7.68/7.78 => ? [C_7] : 7.68/7.78 ( is_fun_a_bool(C_7) 7.68/7.78 & B_6 = image_a_fun_a_bool(F,C_7) 7.68/7.78 & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) 7.68/7.78 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) ) ) ) 7.68/7.78 <= is_fun949378684l_bool(B_6) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_024,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q) ). 7.68/7.78 7.68/7.78 fof(fact_68_card__insert__disjoint,axiom, 7.68/7.78 ! [X_3,A_1] : 7.68/7.78 ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1)) 7.68/7.78 => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)) ) 7.68/7.78 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_71_card__insert__disjoint,axiom, 7.68/7.78 ! [X_3,A_1] : 7.68/7.78 ( ( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A_1)) = hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) 7.68/7.78 <= ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : is_fun_a_bool(hAPP_nat_fun_a_bool(B_1_1,B_2_1)) ). 7.68/7.78 7.68/7.78 fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(P,R),Q) ). 7.68/7.78 7.68/7.78 fof(fact_158_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_a_a(F,A_1))) 7.68/7.78 => ? [C_7] : 7.68/7.78 ( is_fun_a_bool(C_7) 7.68/7.78 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) 7.68/7.78 & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) 7.68/7.78 & B_6 = image_a_a(F,C_7) ) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) 7.68/7.78 <= is_fun_a_bool(B_6) ) ). 7.68/7.78 7.68/7.78 fof(fact_83_Suc__n__not__n,axiom, 7.68/7.78 ! [N] : N != hAPP_nat_nat(suc,N) ). 7.68/7.78 7.68/7.78 fof(fact_403_Collect__empty__eq,axiom, 7.68/7.78 ! [Pa] : 7.68/7.78 ( collect_nat(Pa) = bot_bot_fun_nat_bool 7.68/7.78 <=> ! [X_1] : ~ hBOOL(hAPP_nat_bool(Pa,X_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_643_less__imp__diff__less,axiom, 7.68/7.78 ! [N,J_2,K] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(J_2),N)),K)) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K)) ) ). 7.68/7.78 7.68/7.78 fof(fact_483_singleton__conv,axiom, 7.68/7.78 ! [A_3] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)) = insert_pname(A_3,bot_bo844097828e_bool) ). 7.68/7.78 7.68/7.78 fof(fact_183_lift__Suc__mono__le,axiom, 7.68/7.78 ! [Na,N_3,F] : 7.68/7.78 ( ! [N_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,N_2)),hAPP_n1025906991e_bool(F,hAPP_nat_nat(suc,N_2)))) 7.68/7.78 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) 7.68/7.78 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,Na)),hAPP_n1025906991e_bool(F,N_3))) ) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_fFalse,axiom, 7.68/7.78 is_bool(fFalse) ). 7.68/7.78 7.68/7.78 fof(fact_518_order__antisym,axiom, 7.68/7.78 ! [X_5,Y_4] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_5),Y_4)) 7.68/7.78 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_4),X_5)) 7.68/7.78 => Y_4 = X_5 ) ) ). 7.68/7.78 7.68/7.78 fof(fact_178_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( is_fun949378684l_bool(B_6) 7.68/7.78 => ( ( ? [C_7] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) 7.68/7.78 & image_nat_fun_a_bool(F,C_7) = B_6 7.68/7.78 & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) ) 7.68/7.78 <= hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_nat_fun_a_bool(F,A_1))) ) 7.68/7.78 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_353_imageE,axiom, 7.68/7.78 ! [B_1,F,A_1] : 7.68/7.78 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1))) 7.68/7.78 => ~ ! [X_1] : 7.68/7.78 ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) 7.68/7.78 <= B_1 = hAPP_nat_a(F,X_1) ) ) 7.68/7.78 <= is_a(B_1) ) ). 7.68/7.78 7.68/7.78 fof(fact_3_finite__Collect__subsets,axiom, 7.68/7.78 ! [A_1] : 7.68/7.78 ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),A_1)))) 7.68/7.78 <= hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_348_image__mono,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(F,A_1)),image_a_pname(F,B_6))) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ). 7.68/7.78 7.68/7.78 fof(fact_596_add__diff__assoc2,axiom, 7.68/7.78 ! [I,K,J_2] : 7.68/7.78 ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_2),K)),I) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_2),I)),K) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ) ). 7.68/7.78 7.68/7.78 fof(fact_575_nat__add__left__cancel,axiom, 7.68/7.78 ! [K_2,M_1,Na] : 7.68/7.78 ( hAPP_nat_nat(plus_plus_nat(K_2),Na) = hAPP_nat_nat(plus_plus_nat(K_2),M_1) 7.68/7.78 <=> Na = M_1 ) ). 7.68/7.78 7.68/7.78 fof(fact_94_finite__Collect__disjI,axiom, 7.68/7.78 ! [Pa,Q_1] : 7.68/7.78 ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1))) 7.68/7.78 & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) ) 7.68/7.78 <=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_1)))) ) ). 7.68/7.78 7.68/7.78 fof(fact_537_ord__eq__le__trans,axiom, 7.68/7.78 ! [C_1,A_3,B_1] : 7.68/7.78 ( B_1 = A_3 7.68/7.78 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),C_1)) 7.68/7.78 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),C_1)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_352_imageE,axiom, 7.68/7.78 ! [B_1,F,A_1] : 7.68/7.78 ( is_pname(B_1) 7.68/7.78 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1))) 7.68/7.78 => ~ ! [X_1] : 7.68/7.78 ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) 7.68/7.78 <= hAPP_nat_pname(F,X_1) = B_1 ) ) ) ). 7.68/7.78 7.68/7.78 fof(help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,axiom, 7.68/7.78 ! [X,Y] : 7.68/7.78 ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)) 7.68/7.78 | Y = X ) ). 7.68/7.78 7.68/7.78 fof(fact_327_subset__insert,axiom, 7.68/7.78 ! [B_6,X_3,A_1] : 7.68/7.78 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) 7.68/7.78 <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(X_3,B_6))) ) 7.68/7.78 <= ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_293_Collect__def,axiom, 7.68/7.78 ! [Pa] : 7.68/7.78 ( is_fun1661590463l_bool(Pa) 7.68/7.78 => collec1974731493e_bool(Pa) = Pa ) ). 7.68/7.78 7.68/7.78 fof(fact_136_finite__surj,axiom, 7.68/7.78 ! [B_6,F,A_1] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) 7.68/7.78 => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) 7.68/7.78 <= hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_47868345e_bool(F,A_1))) ) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_p130839763l_bool(cOMBC_615407716e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f654413245e_bool(P,R),Q) ). 7.68/7.78 7.68/7.78 fof(fact_450_singletonE,axiom, 7.68/7.78 ! [B_1,A_3] : 7.68/7.78 ( ( is_pname(B_1) 7.68/7.78 & is_pname(A_3) ) 7.68/7.78 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_3,bot_bo844097828e_bool))) 7.68/7.78 => B_1 = A_3 ) ) ). 7.68/7.78 7.68/7.78 fof(fact_274_equalityD1,axiom, 7.68/7.78 ! [A_1,B_6] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) 7.68/7.78 <= B_6 = A_1 ) ). 7.68/7.78 7.68/7.78 fof(fact_232_insertI1,axiom, 7.68/7.78 ! [A_3,B_6] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(A_3,B_6))) ). 7.68/7.78 7.68/7.78 fof(fact_88_nat__le__linear,axiom, 7.68/7.78 ! [M,N] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) 7.68/7.78 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ). 7.68/7.78 7.68/7.78 fof(fact_328_subset__insertI2,axiom, 7.68/7.78 ! [B_1,A_1,B_6] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.78 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(B_1,B_6))) ) ). 7.68/7.78 7.68/7.78 fof(fact_636_not__less__eq,axiom, 7.68/7.78 ! [M_1,Na] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) 7.68/7.78 <=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ). 7.68/7.78 7.68/7.78 fof(fact_126_eq__diff__iff,axiom, 7.68/7.78 ! [Na,K_2,M_1] : 7.68/7.78 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) 7.68/7.78 => ( hAPP_nat_nat(minus_minus_nat(M_1),K_2) = hAPP_nat_nat(minus_minus_nat(Na),K_2) 7.68/7.78 <=> M_1 = Na ) ) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_579_diff__add__inverse2,axiom, 7.68/7.78 ! [M,N] : M = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),N) ). 7.68/7.78 7.68/7.78 fof(fact_695_nat_Osimps_I2_J,axiom, 7.68/7.78 ! [Nat] : zero_zero_nat != hAPP_nat_nat(suc,Nat) ). 7.68/7.78 7.68/7.78 fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_nat_bool(hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(P),Q),R) = hAPP_a_bool(hAPP_nat_fun_a_bool(P,R),Q) ). 7.68/7.78 7.68/7.78 fof(fact_181_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( is_fun_a_bool(B_6) 7.68/7.78 => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) 7.68/7.78 => ( ? [C_7] : 7.68/7.78 ( is_fun_pname_bool(C_7) 7.68/7.78 & B_6 = image_pname_a(F,C_7) 7.68/7.78 & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) 7.68/7.78 & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1))) ) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_216_equalityI,axiom, 7.68/7.78 ! [A_1,B_6] : 7.68/7.78 ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1)) 7.68/7.78 => A_1 = B_6 ) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ) 7.68/7.78 <= ( is_fun_pname_bool(B_6) 7.68/7.78 & is_fun_pname_bool(A_1) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_551_order__eq__iff,axiom, 7.68/7.78 ! [X_3,Y_2] : 7.68/7.78 ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) 7.68/7.78 & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) ) 7.68/7.78 <=> X_3 = Y_2 ) ). 7.68/7.78 7.68/7.78 fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__014,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_n1699378549t_bool(P,hAPP_f921600141ol_nat(Q,R)) = hAPP_f1066163005t_bool(cOMBB_1896684278e_bool(P,Q),R) ). 7.68/7.78 7.68/7.78 fof(gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun1661590463l_bool(image_819518260e_bool(B_1_1,B_2_1)) 7.68/7.78 <= is_fun_a_bool(B_2_1) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_bool_bool(hAPP_f1748468828l_bool(P,R),hAPP_f54304608l_bool(Q,R)) = hAPP_f54304608l_bool(cOMBS_1187019125l_bool(P,Q),R) ). 7.68/7.78 7.68/7.78 fof(fact_462_empty__not__insert,axiom, 7.68/7.78 ! [A_3,A_1] : bot_bot_fun_nat_bool != insert_nat(A_3,A_1) ). 7.68/7.78 7.68/7.78 fof(fact_150_finite__surj,axiom, 7.68/7.78 ! [B_6,F,A_1] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) 7.68/7.78 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1))) 7.68/7.78 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_a217006258l_bool(cOMBB_1137537805bool_a(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_a93125764e_bool(Q,R)) ). 7.68/7.78 7.68/7.78 fof(fact_632_less__antisym,axiom, 7.68/7.78 ! [N,M] : 7.68/7.78 ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) 7.68/7.78 => ( M = N 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))) ) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___019,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_p1824510254l_bool(cOMBB_392435466_pname(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_p1534023578a_bool(Q,R)) ). 7.68/7.78 7.68/7.78 fof(fact_362_image__subsetI,axiom, 7.68/7.78 ! [F,B_6,A_1] : 7.68/7.78 ( ! [X_1] : 7.68/7.78 ( is_a(X_1) 7.68/7.78 => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(F,X_1)),B_6)) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) ) ) 7.68/7.78 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(F,A_1)),B_6)) ) ). 7.68/7.78 7.68/7.78 fof(fact_170_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) 7.68/7.78 => ( ? [C_7] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) 7.68/7.78 & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) 7.68/7.78 & image_2129980159t_bool(F,C_7) = B_6 7.68/7.78 & is_fun_pname_bool(C_7) ) 7.68/7.78 <= hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_2129980159t_bool(F,A_1))) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_408_empty__Collect__eq,axiom, 7.68/7.78 ! [Pa] : 7.68/7.78 ( ! [X_1] : ~ hBOOL(hAPP_f54304608l_bool(Pa,X_1)) 7.68/7.78 <=> bot_bo1701429464l_bool = collect_fun_nat_bool(Pa) ) ). 7.68/7.78 7.68/7.78 fof(fact_53_card__seteq,axiom, 7.68/7.78 ! [A_1,B_6] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) 7.68/7.78 => ( ( A_1 = B_6 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B_6)),hAPP_f22106695ol_nat(finite_card_nat,A_1))) ) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_40_card__image__le,axiom, 7.68/7.78 ! [F,A_1] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(F,A_1))),hAPP_f22106695ol_nat(finite_card_nat,A_1))) 7.68/7.78 <= hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_622_trans__less__add1,axiom, 7.68/7.78 ! [M,I,J_2] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) 7.68/7.78 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(plus_plus_nat(J_2),M))) ) ). 7.68/7.78 7.68/7.78 fof(fact_4_finite__Collect__subsets,axiom, 7.68/7.78 ! [A_1] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) 7.68/7.78 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),A_1)))) ) ). 7.68/7.78 7.68/7.78 fof(fact_449_singletonE,axiom, 7.68/7.78 ! [B_1,A_3] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),insert_nat(A_3,bot_bot_fun_nat_bool))) 7.68/7.78 => B_1 = A_3 ) ). 7.68/7.78 7.68/7.78 fof(fact_402_Collect__empty__eq,axiom, 7.68/7.78 ! [Pa] : 7.68/7.78 ( ! [X_1] : 7.68/7.78 ( is_a(X_1) 7.68/7.78 => ~ hBOOL(hAPP_a_bool(Pa,X_1)) ) 7.68/7.78 <=> bot_bot_fun_a_bool = collect_a(Pa) ) ). 7.68/7.78 7.68/7.78 fof(fact_555_linorder__linear,axiom, 7.68/7.78 ! [X_2,Y_1] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_2)) 7.68/7.78 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_355_imageE,axiom, 7.68/7.78 ! [B_1,F,A_1] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1))) 7.68/7.78 => ~ ! [X_1] : 7.68/7.78 ( is_a(X_1) 7.68/7.78 => ( B_1 = hAPP_a_nat(F,X_1) 7.68/7.78 => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) ) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_562_assms_I2_J,axiom, 7.68/7.78 ! [Pn,G] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(hAPP_pname_a(mgt_call,Pn),bot_bot_fun_a_bool))) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(p(insert_a(hAPP_pname_a(mgt_call,Pn),G)),insert_a(mgt(the_com(body(Pn))),bot_bot_fun_a_bool))) ) ). 7.68/7.78 7.68/7.78 fof(fact_269_set__eq__subset,axiom, 7.68/7.78 ! [A_1,B_6] : 7.68/7.78 ( ( B_6 = A_1 7.68/7.78 <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) 7.68/7.78 & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1)) ) ) 7.68/7.78 <= ( is_fun_pname_bool(A_1) 7.68/7.78 & is_fun_pname_bool(B_6) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_674_bounded__nat__set__is__finite,axiom, 7.68/7.78 ! [Na,N_1] : 7.68/7.78 ( ! [X_1] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) 7.68/7.78 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Na)) ) 7.68/7.78 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_359_subsetI,axiom, 7.68/7.78 ! [B_6,A_1] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) 7.68/7.78 <= ! [X_1] : 7.68/7.78 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) ) 7.68/7.78 <= is_a(X_1) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_671_mono__nat__linear__lb,axiom, 7.68/7.78 ! [M_1,K_2,F] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(F,M_1)),K_2)),hAPP_nat_nat(F,hAPP_nat_nat(plus_plus_nat(M_1),K_2)))) 7.68/7.78 <= ! [M_2,N_2] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_2)),hAPP_nat_nat(F,N_2))) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_46_card__mono,axiom, 7.68/7.78 ! [A_1,B_6] : 7.68/7.78 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A_1)),hAPP_fun_a_bool_nat(finite_card_a,B_6))) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ). 7.68/7.78 7.68/7.78 fof(fact_363_image__subsetI,axiom, 7.68/7.78 ! [F,B_6,A_1] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(F,A_1)),B_6)) 7.68/7.78 <= ! [X_1] : 7.68/7.78 ( is_a(X_1) 7.68/7.78 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(F,X_1)),B_6)) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) ) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_199_pigeonhole__infinite,axiom, 7.68/7.78 ! [F,A_1] : 7.68/7.78 ( ( ? [X_1] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) 7.68/7.78 & ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A_1)),hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,F)),hAPP_nat_a(F,X_1)))))) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(F,A_1))) ) 7.68/7.78 <= ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_0_assms_I1_J,axiom, 7.68/7.78 ! [Ts,G] : 7.68/7.78 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Ts),G)) 7.68/7.78 => hBOOL(hAPP_fun_a_bool_bool(p(G),Ts)) ) ). 7.68/7.78 7.68/7.78 fof(fact_367_order__refl,axiom, 7.68/7.78 ! [X_3] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),X_3)) ). 7.68/7.78 7.68/7.78 fof(fact_176_finite__subset__image,axiom, 7.68/7.78 ! [F,A_1,B_6] : 7.68/7.78 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) 7.68/7.78 => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_26036933t_bool(F,A_1))) 7.68/7.78 => ? [C_7] : 7.68/7.78 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) 7.68/7.78 & image_26036933t_bool(F,C_7) = B_6 7.68/7.78 & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) ) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_473_Collect__conv__if,axiom, 7.68/7.78 ! [Pa,A_3] : 7.68/7.78 ( ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),Pa)) = bot_bo1701429464l_bool 7.68/7.78 <= ~ hBOOL(hAPP_f54304608l_bool(Pa,A_3)) ) 7.68/7.78 & ( hBOOL(hAPP_f54304608l_bool(Pa,A_3)) 7.68/7.78 => insert_fun_nat_bool(A_3,bot_bo1701429464l_bool) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),Pa)) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_41_card__image__le,axiom, 7.68/7.78 ! [F,A_1] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1))) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_243_insert__Collect,axiom, 7.68/7.78 ! [A_3,Pa] : insert_nat(A_3,collect_nat(Pa)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3))),Pa)) ). 7.68/7.78 7.68/7.78 fof(fact_691_Suc__neq__Zero,axiom, 7.68/7.78 ! [M] : hAPP_nat_nat(suc,M) != zero_zero_nat ). 7.68/7.78 7.68/7.78 fof(fact_320_subset__insertI,axiom, 7.68/7.78 ! [B_6,A_3] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),insert_nat(A_3,B_6))) ). 7.68/7.78 7.68/7.78 fof(fact_366_image__subsetI,axiom, 7.68/7.78 ! [F,B_6,A_1] : 7.68/7.78 ( ! [X_1] : 7.68/7.78 ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_1)),B_6)) 7.68/7.78 <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) ) 7.68/7.78 <= is_pname(X_1) ) 7.68/7.78 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A_1)),B_6)) ) ). 7.68/7.78 7.68/7.78 fof(fact_533_xt1_I3_J,axiom, 7.68/7.78 ! [C_3,A_5,B_3] : 7.68/7.78 ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),B_3)) 7.68/7.78 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),A_5)) ) 7.68/7.78 <= A_5 = B_3 ) ). 7.68/7.78 7.68/7.78 fof(fact_639_less__imp__le__nat,axiom, 7.68/7.78 ! [M,N] : 7.68/7.78 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ). 7.68/7.78 7.68/7.78 fof(fact_134_finite__surj,axiom, 7.68/7.78 ! [B_6,F,A_1] : 7.68/7.78 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) 7.68/7.78 => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_a_bool_a(F,A_1))) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_36_card__image__le,axiom, 7.68/7.78 ! [F,A_1] : 7.68/7.78 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) 7.68/7.78 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(F,A_1))),hAPP_f696928925ol_nat(finite346522414t_bool,A_1))) ) ). 7.68/7.78 7.68/7.78 fof(fact_76_finite__Collect__conjI,axiom, 7.68/7.78 ! [Q_1,Pa] : 7.68/7.78 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,Pa),Q_1)))) 7.68/7.78 <= ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) 7.68/7.78 | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1))) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_453_doubleton__eq__iff,axiom, 7.68/7.78 ! [A_3,B_1,C_1,D] : 7.68/7.78 ( insert_nat(C_1,insert_nat(D,bot_bot_fun_nat_bool)) = insert_nat(A_3,insert_nat(B_1,bot_bot_fun_nat_bool)) 7.68/7.78 <=> ( ( C_1 = A_3 7.68/7.78 & D = B_1 ) 7.68/7.78 | ( B_1 = C_1 7.68/7.78 & D = A_3 ) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_23_finite_OinsertI,axiom, 7.68/7.78 ! [A_3,A_1] : 7.68/7.78 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_3,A_1))) 7.68/7.78 <= hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ) ). 7.68/7.78 7.68/7.78 fof(fact_599_le__add__diff__inverse2,axiom, 7.68/7.78 ! [N,M] : 7.68/7.78 ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),N) = M 7.68/7.78 <= hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) ) ). 7.68/7.78 7.68/7.78 fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_008,axiom, 7.68/7.78 ! [P,Q,R] : hAPP_p61793385e_bool(cOMBB_542850580_pname(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_pname_pname(Q,R)) ). 7.68/7.78 7.68/7.78 fof(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_bool(hAPP_pname_bool(B_1_1,B_2_1)) 7.68/7.78 <= ( is_pname(B_2_1) 7.68/7.78 & is_fun_pname_bool(B_1_1) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_254_insert__code,axiom, 7.68/7.78 ! [Y_2,A_1,X_3] : 7.68/7.78 ( ( ( hBOOL(hAPP_pname_bool(A_1,X_3)) 7.68/7.78 | Y_2 = X_3 ) 7.68/7.78 <=> hBOOL(hAPP_pname_bool(insert_pname(Y_2,A_1),X_3)) ) 7.68/7.78 <= ( is_pname(X_3) 7.68/7.78 & is_pname(Y_2) ) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom, 7.68/7.78 is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))) ). 7.68/7.78 7.68/7.78 fof(fact_544_order__antisym__conv,axiom, 7.68/7.78 ! [Y_2,X_3] : 7.68/7.78 ( ( is_fun_a_bool(X_3) 7.68/7.78 & is_fun_a_bool(Y_2) ) 7.68/7.78 => ( ( Y_2 = X_3 7.68/7.78 <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) ) 7.68/7.78 <= hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3)) ) ) ). 7.68/7.78 7.68/7.78 fof(gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool,axiom, 7.68/7.78 ! [B_1_1,B_2_1] : 7.68/7.78 ( is_fun_a_bool(cOMBS_a_bool_bool(B_1_1,B_2_1)) 7.68/7.78 <= is_fun_a_bool(B_2_1) ) ). 7.68/7.78 7.68/7.78 fof(fact_456_singleton__iff,axiom, 7.68/7.78 ! [B_1,A_3] : 7.68/7.78 ( ( A_3 = B_1 7.68/7.78 <=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_3,bot_bo844097828e_bool))) ) 7.68/7.78 <= ( is_pname(A_3) 7.68/7.78 & is_pname(B_1) ) ) ). 7.68/7.78 7.68/7.78 fof(fact_431_le__bot,axiom, 7.68/7.78 ! [A_3] : 7.68/7.78 ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),bot_bo844097828e_bool)) 7.68/7.78 => A_3 = bot_bo844097828e_bool ) 7.68/7.78 <= is_fun_pname_bool(A_3) ) ). 7.68/7.78 7.68/7.78 %------------------------------------------- 7.68/7.78 % Proof found 7.68/7.78 % SZS status Theorem for theBenchmark 7.68/7.78 % SZS output start Proof 7.68/7.78 %ClaNum:1995(EqnAxiom:682) 7.68/7.78 %VarNum:5837(SingletonVarNum:2467) 7.68/7.78 %MaxLitNum:7 7.68/7.78 %MaxfuncDepth:7 7.68/7.78 %SharedTerms:187 7.68/7.78 %goalClause: 937 7.68/7.78 %singleGoalClaCount:1 7.68/7.78 [683]E(a1,a11) 7.68/7.78 [686]P1(a4) 7.68/7.78 [687]P1(a236) 7.68/7.78 [688]P2(a260) 7.68/7.78 [689]P2(a7) 7.68/7.78 [690]P6(a8) 7.68/7.78 [691]P6(a262) 7.68/7.78 [692]P7(a264) 7.68/7.78 [693]P7(a9) 7.68/7.78 [694]P8(a265) 7.68/7.78 [695]P3(a10) 7.68/7.78 [696]P3(a12) 7.68/7.78 [697]P3(a237) 7.68/7.78 [909]~P5(a12) 7.68/7.78 [684]E(f13(a12),a2) 7.68/7.78 [685]E(f14(a12),a3) 7.68/7.78 [702]P4(f397(a396)) 7.68/7.78 [703]P8(f401(a393)) 7.68/7.78 [706]E(f267(a394,a11),a377) 7.68/7.78 [711]P5(f268(a261,a2)) 7.68/7.78 [712]P5(f269(a260,a264)) 7.68/7.78 [713]P5(f269(a260,a9)) 7.68/7.78 [714]P5(f311(a236,a8)) 7.68/7.78 [715]P5(f270(a239,a3)) 7.68/7.78 [716]P5(f312(a253,a4)) 7.68/7.78 [717]P5(f295(a255,a7)) 7.68/7.78 [698]E(f89(f88(a12)),a9) 7.68/7.78 [699]E(f90(f15(a12)),a7) 7.68/7.78 [700]E(f99(f85(a12)),a8) 7.68/7.78 [701]E(f101(f86(a12)),a4) 7.68/7.78 [744]P6(f402(f263(a396,a5))) 7.68/7.78 [745]P7(f398(f263(a393,a5))) 7.68/7.78 [749]P5(f269(f336(a369,a265),a264)) 7.68/7.78 [851]P5(f311(f294(a386,a262),f332(a379,a264))) 7.68/7.78 [867]E(f267(f378(f324(a257,f332(a379,a264))),f267(a394,a380)),f324(a257,a262)) 7.68/7.78 [937]~P5(f311(f294(a386,f99(f96(f31(a240,f282(f77(a244),f344(a379,a265))),f305(f60(a372),a262)))),f332(a379,a264))) 7.68/7.78 [857]P1(f399(f263(f263(a396,a5),a5))) 7.68/7.78 [858]P2(f400(f263(f263(a393,a5),a5))) 7.68/7.78 [875]P5(f331(f327(a384,f267(a394,a380)),f324(a257,f332(a379,a264)))) 7.68/7.78 [927]~P5(f311(f277(a372,f344(a379,a265)),a262)) 7.68/7.78 [704]P4(f266(x7041)) 7.68/7.78 [705]P3(f403(x7051)) 7.68/7.78 [707]E(f332(x7071,a9),a8) 7.68/7.78 [915]~E(f267(a394,x9151),a11) 7.68/7.78 [917]~E(f267(a394,x9171),x9171) 7.68/7.78 [708]E(f267(f378(a11),x7081),a11) 7.68/7.78 [709]E(f267(f378(x7091),a11),x7091) 7.68/7.78 [710]E(f267(f378(x7101),x7101),a11) 7.68/7.78 [718]E(f267(f382(a377),x7181),f267(a394,x7181)) 7.68/7.78 [740]E(f267(f382(x7401),a377),f267(a394,x7401)) 7.68/7.78 [743]E(f327(a384,f267(a394,x7431)),f327(a383,x7431)) 7.68/7.78 [751]P5(f268(f273(a385,a2),x7511)) 7.68/7.78 [753]P5(f269(f309(a389,a9),x7531)) 7.68/7.78 [755]P5(f331(f327(a384,a11),x7551)) 7.68/7.78 [756]P5(f331(f327(a384,a1),x7561)) 7.68/7.78 [757]P5(f286(f274(a390,a10),x7571)) 7.68/7.78 [759]P5(f311(f294(a386,a8),x7591)) 7.68/7.78 [761]P5(f268(f273(a385,x7611),x7611)) 7.68/7.78 [763]P5(f269(f309(a389,x7631),x7631)) 7.68/7.78 [765]P5(f331(f327(a384,x7651),x7651)) 7.68/7.78 [766]P5(f286(f274(a390,x7661),x7661)) 7.68/7.78 [768]P5(f311(f294(a386,x7681),x7681)) 7.68/7.78 [852]P5(f331(f327(a383,a11),f267(a394,x8521))) 7.68/7.78 [855]P5(f331(f327(a383,x8551),f267(a394,x8551))) 7.68/7.78 [919]~P5(f268(f328(a376,x9191),a2)) 7.68/7.78 [921]~P5(f269(f336(a369,x9211),a9)) 7.68/7.78 [922]~P5(f331(f327(a383,x9221),a11)) 7.68/7.78 [924]~P5(f311(f277(a372,x9241),a8)) 7.68/7.78 [926]~P5(f331(f327(a383,x9261),x9261)) 7.68/7.78 [742]E(f301(a256,f327(f16(a383),x7421)),x7421) 7.68/7.78 [746]E(f301(a256,f327(f16(a384),x7461)),f267(a394,x7461)) 7.68/7.78 [748]E(f267(f378(f267(a394,x7481)),a377),x7481) 7.68/7.78 [805]P5(f268(a261,f327(f16(a384),x8051))) 7.68/7.78 [806]P5(f268(a261,f327(f16(a383),x8061))) 7.68/7.78 [859]E(f93(f45(a240,f273(f53(a242),x8591)),f290(f58(a370),a3)),f273(a242,x8591)) 7.68/7.78 [860]E(f93(f45(a240,f273(f53(a242),x8601)),f290(f58(a370),a3)),f273(f53(a242),x8601)) 7.68/7.78 [928]~P5(f331(f327(a384,f267(a394,x9281)),x9281)) 7.68/7.78 [876]E(f89(f95(f41(a240,f341(f55(a248),x8761)),f320(f57(a369),a9))),f89(f341(a248,x8761))) 7.68/7.78 [877]E(f101(f92(f39(a240,f294(f63(a243),x8771)),f304(f64(a371),a4))),f101(f294(a243,x8771))) 7.68/7.78 [878]E(f99(f96(f31(a240,f282(f77(a244),x8781)),f305(f60(a372),a8))),f99(f282(a244,x8781))) 7.68/7.78 [879]E(f90(f91(f36(a240,f309(f54(a245),x8791)),f313(f66(a373),a7))),f90(f309(a245,x8791))) 7.68/7.78 [880]E(f99(f96(f31(a240,f282(f77(a244),x8801)),f305(f60(a372),a8))),f99(f282(f77(a244),x8801))) 7.68/7.78 [881]E(f89(f95(f41(a240,f341(f55(a248),x8811)),f320(f57(a369),a9))),f89(f341(f55(a248),x8811))) 7.68/7.78 [882]E(f101(f92(f39(a240,f294(f63(a243),x8821)),f304(f64(a371),a4))),f101(f294(f63(a243),x8821))) 7.68/7.78 [883]E(f90(f91(f36(a240,f309(f54(a245),x8831)),f313(f66(a373),a7))),f90(f309(f54(a245),x8831))) 7.68/7.78 [869]E(f94(f21(a246,f52(a238,f327(f16(a247),x8691))),a2),f327(a247,x8691)) 7.68/7.78 [870]E(f94(f21(a246,f52(a238,f327(f16(a247),x8701))),a2),f327(f16(a247),x8701)) 7.68/7.78 [719]P1(f322(x7191,x7192)) 7.68/7.78 [720]P1(f333(x7201,x7202)) 7.68/7.78 [721]P2(f334(x7211,x7212)) 7.68/7.78 [722]P2(f326(x7221,x7222)) 7.68/7.78 [723]P6(f350(x7231,x7232)) 7.68/7.78 [724]P6(f329(x7241,x7242)) 7.68/7.78 [725]P6(f351(x7251,x7252)) 7.68/7.78 [726]P6(f271(x7261,x7262)) 7.68/7.78 [727]P4(f330(x7271,x7272)) 7.68/7.78 [728]P7(f316(x7281,x7282)) 7.68/7.78 [729]P7(f323(x7291,x7292)) 7.68/7.78 [730]P7(f367(x7301,x7302)) 7.68/7.78 [731]P7(f352(x7311,x7312)) 7.68/7.78 [732]P8(f335(x7321,x7322)) 7.68/7.78 [733]P8(f272(x7331,x7332)) 7.68/7.78 [734]P3(f268(x7341,x7342)) 7.68/7.78 [735]P3(f331(x7351,x7352)) 7.68/7.78 [736]P3(f270(x7361,x7362)) 7.68/7.78 [737]P3(f317(x7371,x7372)) 7.68/7.78 [738]P3(f299(x7381,x7382)) 7.68/7.78 [739]P3(f300(x7391,x7392)) 7.68/7.78 [741]E(f267(f382(x7411),x7412),f267(f382(x7412),x7411)) 7.68/7.78 [849]E(f267(f378(f267(a394,x8491)),f267(a394,x8492)),f267(f378(x8491),x8492)) 7.68/7.78 [874]P5(f331(f327(a383,f267(f378(x8741),x8742)),f267(a394,x8741))) 7.68/7.78 [747]E(f267(f378(x7471),f267(f382(x7471),x7472)),a11) 7.68/7.78 [840]E(f267(f382(x8401),f267(a394,x8402)),f267(a394,f267(f382(x8401),x8402))) 7.68/7.78 [850]E(f267(f382(f267(a394,x8501)),x8502),f267(f382(x8501),f267(a394,x8502))) 7.68/7.78 [853]E(f267(f382(f267(a394,x8531)),x8532),f267(a394,f267(f382(x8531),x8532))) 7.68/7.78 [861]P5(f331(f327(a384,x8611),f267(f382(x8612),x8611))) 7.68/7.78 [862]P5(f331(f327(a384,x8621),f267(f382(x8621),x8622))) 7.68/7.78 [841]E(f267(f378(f267(f382(x8411),x8412)),x8412),x8411) 7.68/7.78 [842]E(f267(f378(f267(f382(x8421),x8422)),x8421),x8422) 7.68/7.78 [856]E(f267(f378(f267(f378(x8561),a377)),x8562),f267(f378(x8561),f267(a394,x8562))) 7.68/7.78 [871]P5(f331(f327(a384,f267(f378(x8711),x8712)),x8711)) 7.68/7.78 [872]P5(f331(f327(a383,x8721),f267(a394,f267(f382(x8722),x8721)))) 7.68/7.78 [873]P5(f331(f327(a383,x8731),f267(a394,f267(f382(x8731),x8732)))) 7.68/7.78 [884]P5(f268(a261,f94(f21(a241,x8841),f327(f16(a383),x8842)))) 7.68/7.78 [931]~P5(f331(f327(a383,f267(f382(x9311),x9312)),x9312)) 7.68/7.78 [932]~P5(f331(f327(a383,f267(f382(x9321),x9322)),x9321)) 7.68/7.78 [935]~E(f99(f96(f31(a240,f282(f77(a244),x9351)),f305(f60(a372),x9352))),a8) 7.68/7.78 [936]~E(f89(f95(f41(a240,f341(f55(a248),x9361)),f320(f57(a369),x9362))),a9) 7.68/7.78 [886]E(f94(f21(a240,f327(f16(a247),x8861)),f319(f61(a376),x8862)),f94(f21(a246,f52(a238,f327(f16(a247),x8861))),x8862)) 7.68/7.78 [887]E(f93(f45(a240,f273(f53(a242),x8871)),f290(f58(a370),x8872)),f93(f45(a246,f30(a238,f273(f53(a242),x8871))),x8872)) 7.68/7.78 [900]P5(f269(f309(a389,x9001),f89(f95(f41(a240,f341(f55(a248),x9002)),f320(f57(a369),x9001))))) 7.68/7.78 [901]P5(f269(f336(a369,x9011),f89(f95(f41(a240,f341(f55(a248),x9011)),f320(f57(a369),x9012))))) 7.68/7.78 [902]P5(f311(f294(a386,x9021),f99(f96(f31(a240,f282(f77(a244),x9022)),f305(f60(a372),x9021))))) 7.68/7.78 [903]P5(f311(f277(a372,x9031),f99(f96(f31(a240,f282(f77(a244),x9031)),f305(f60(a372),x9032))))) 7.68/7.78 [930]~E(f94(f21(a246,f52(a238,f327(f16(a247),x9301))),x9302),a2) 7.68/7.78 [889]E(f99(f96(f31(a240,f282(f77(a244),x8891)),f305(f60(a372),f99(x8892)))),f99(f96(f31(a246,f50(a238,f282(f77(a244),x8891))),x8892))) 7.68/7.78 [890]E(f89(f95(f41(a240,f341(f55(a248),x8901)),f320(f57(a369),f89(x8902)))),f89(f95(f41(a246,f48(a238,f341(f55(a248),x8901))),x8902))) 7.68/7.78 [891]E(f90(f91(f36(a240,f309(f54(a245),x8911)),f313(f66(a373),f90(x8912)))),f90(f91(f36(a246,f38(a238,f309(f54(a245),x8911))),x8912))) 7.68/7.78 [892]E(f101(f92(f39(a240,f294(f63(a243),x8921)),f304(f64(a371),f101(x8922)))),f101(f92(f39(a246,f34(a238,f294(f63(a243),x8921))),x8922))) 7.68/7.78 [893]E(f94(f21(a246,f52(a238,f327(f16(a247),x8931))),f94(f21(a246,f52(a238,f327(f16(a247),x8931))),x8932)),f94(f21(a246,f52(a238,f327(f16(a247),x8931))),x8932)) 7.68/7.78 [894]P5(f268(f273(a385,x8941),f94(f21(a246,f52(a238,f327(f16(a247),x8942))),x8941))) 7.68/7.78 [895]P5(f268(f328(a376,x8951),f94(f21(a246,f52(a238,f327(f16(a247),x8951))),x8952))) 7.68/7.78 [905]E(f89(f95(f41(a240,f341(f55(a248),x9051)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x9051)),f320(f57(a369),x9052)))))),f89(f95(f41(a240,f341(f55(a248),x9051)),f320(f57(a369),x9052)))) 7.68/7.78 [906]E(f99(f96(f31(a240,f282(f77(a244),x9061)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x9061)),f305(f60(a372),x9062)))))),f99(f96(f31(a240,f282(f77(a244),x9061)),f305(f60(a372),x9062)))) 7.68/7.78 [769]E(f337(f17(x7691,x7692),x7693),f273(x7691,f338(x7692,x7693))) 7.68/7.78 [770]E(f327(f18(x7701,x7702),x7703),f327(x7701,f267(x7702,x7703))) 7.68/7.78 [771]E(f287(f19(x7711,x7712),x7713),f327(x7711,f318(x7712,x7713))) 7.68/7.78 [772]E(f307(f20(x7721,x7722),x7723),f327(x7721,f324(x7722,x7723))) 7.68/7.78 [773]E(f286(x7731,f268(x7732,x7733)),f268(f30(x7731,x7732),x7733)) 7.68/7.78 [774]E(f275(f50(x7741,x7742),x7743),f286(x7741,f275(x7742,x7743))) 7.68/7.78 [775]E(f336(f37(x7751,x7752),x7753),f309(x7751,f341(x7752,x7753))) 7.68/7.78 [776]E(f325(f21(x7761,x7762),x7763),f274(x7761,f331(x7762,x7763))) 7.68/7.78 [777]E(f342(f41(x7771,x7772),x7773),f274(x7771,f343(x7772,x7773))) 7.68/7.78 [778]E(f281(f31(x7781,x7782),x7783),f274(x7781,f275(x7782,x7783))) 7.68/7.78 [779]E(f276(f42(x7791,x7792),x7793),f341(x7791,f283(x7792,x7793))) 7.68/7.78 [780]E(f341(x7801,f272(x7802,x7803)),f316(f22(x7801,x7802),x7803)) 7.68/7.78 [781]E(f296(f27(x7811,x7812),x7813),f341(x7811,f289(x7812,x7813))) 7.68/7.78 [782]E(f328(f33(x7821,x7822),x7823),f273(x7821,f327(x7822,x7823))) 7.68/7.78 [783]E(f286(x7831,f269(x7832,x7833)),f269(f38(x7831,x7832),x7833)) 7.68/7.78 [784]E(f286(x7841,f331(x7842,x7843)),f331(f52(x7841,x7842),x7843)) 7.68/7.78 [785]E(f286(x7851,f311(x7852,x7853)),f311(f34(x7851,x7852),x7853)) 7.68/7.78 [786]E(f343(f48(x7861,x7862),x7863),f286(x7861,f343(x7862,x7863))) 7.68/7.78 [787]E(f341(f43(x7871,x7872),x7873),f341(x7871,f345(x7872,x7873))) 7.68/7.78 [788]E(f282(x7881,f344(x7882,x7883)),f339(f32(x7881,x7882),x7883)) 7.68/7.78 [789]E(f282(f51(x7891,x7892),x7893),f282(x7891,f280(x7892,x7893))) 7.68/7.78 [790]E(f277(f44(x7901,x7902),x7903),f294(x7901,f282(x7902,x7903))) 7.68/7.78 [791]E(f319(f23(x7911,x7912),x7913),f327(x7911,f301(x7912,x7913))) 7.68/7.78 [792]E(f338(f46(x7921,x7922),x7923),f327(x7921,f346(x7922,x7923))) 7.68/7.78 [793]E(f302(f39(x7931,x7932),x7933),f274(x7931,f311(x7932,x7933))) 7.68/7.78 [794]E(f284(f26(x7941,x7942),x7943),f327(x7941,f285(x7942,x7943))) 7.68/7.78 [795]E(f282(x7951,f330(x7952,x7953)),f329(f28(x7951,x7952),x7953)) 7.68/7.78 [796]E(f341(x7961,f335(x7962,x7963)),f323(f24(x7961,x7962),x7963)) 7.68/7.78 [797]E(f278(f25(x7971,x7972),x7973),f309(x7971,f276(x7972,x7973))) 7.68/7.78 [798]E(f294(x7981,f329(x7982,x7983)),f322(f29(x7981,x7982),x7983)) 7.68/7.78 [799]E(f320(f47(x7991,x7992),x7993),f341(x7991,f291(x7992,x7993))) 7.68/7.78 [800]E(f279(f49(x8001,x8002),x8003),f273(x8001,f284(x8002,x8003))) 7.68/7.78 [801]E(f309(x8011,f323(x8012,x8013)),f326(f35(x8011,x8012),x8013)) 7.68/7.78 [802]E(f292(f36(x8021,x8022),x8023),f274(x8021,f269(x8022,x8023))) 7.68/7.78 [803]E(f340(f40(x8031,x8032),x8033),f294(x8031,f339(x8032,x8033))) 7.68/7.78 [804]E(f297(f45(x8041,x8042),x8043),f274(x8041,f268(x8042,x8043))) 7.68/7.78 [843]E(f286(f292(x8431,x8432),f269(x8433,x8432)),f269(f91(x8431,x8433),x8432)) 7.68/7.78 [844]E(f286(f325(x8441,x8442),f331(x8443,x8442)),f331(f94(x8441,x8443),x8442)) 7.68/7.78 [845]E(f286(f342(x8451,x8452),f343(x8453,x8452)),f343(f95(x8451,x8453),x8452)) 7.68/7.78 [846]E(f286(f281(x8461,x8462),f275(x8463,x8462)),f275(f96(x8461,x8463),x8462)) 7.68/7.78 [847]E(f286(f302(x8471,x8472),f311(x8473,x8472)),f311(f92(x8471,x8473),x8472)) 7.68/7.78 [848]E(f286(f297(x8481,x8482),f268(x8483,x8482)),f268(f93(x8481,x8483),x8482)) 7.68/7.78 [807]E(f268(f273(f53(x8071),x8072),x8073),f268(f273(x8071,x8073),x8072)) 7.68/7.78 [808]E(f331(f319(f61(x8081),x8082),x8083),f268(f328(x8081,x8083),x8082)) 7.68/7.78 [809]E(f343(f316(f68(x8091),x8092),x8093),f268(f337(x8091,x8093),x8092)) 7.68/7.78 [810]E(f269(f309(f54(x8101),x8102),x8103),f269(f309(x8101,x8103),x8102)) 7.68/7.78 [811]E(f268(f328(f69(x8111),x8112),x8113),f331(f319(x8111,x8113),x8112)) 7.68/7.78 [812]E(f343(f323(f82(x8121),x8122),x8123),f331(f338(x8121,x8123),x8122)) 7.68/7.78 [813]E(f275(f329(f71(x8131),x8132),x8133),f331(f284(x8131,x8133),x8132)) 7.68/7.78 [814]E(f311(f322(f72(x8141),x8142),x8143),f331(f307(x8141,x8143),x8142)) 7.68/7.78 [815]E(f269(f326(f59(x8151),x8152),x8153),f331(f287(x8151,x8153),x8152)) 7.68/7.78 [816]E(f343(f296(f73(x8161),x8162),x8163),f311(f340(x8161,x8163),x8162)) 7.68/7.78 [817]E(f343(f341(f55(x8171),x8172),x8173),f343(f341(x8171,x8173),x8172)) 7.68/7.78 [818]E(f331(f338(f83(x8181),x8182),x8183),f343(f323(x8181,x8183),x8182)) 7.68/7.78 [819]E(f311(f340(f62(x8191),x8192),x8193),f343(f296(x8191,x8193),x8192)) 7.68/7.78 [820]E(f311(f304(f64(x8201),x8202),x8203),f312(f308(x8201,x8203),x8202)) 7.68/7.78 [821]E(f275(f282(f77(x8211),x8212),x8213),f275(f282(x8211,x8213),x8212)) 7.68/7.78 [822]E(f268(f337(f75(x8221),x8222),x8223),f343(f316(x8221,x8223),x8222)) 7.68/7.78 [823]E(f268(f290(f58(x8231),x8232),x8233),f270(f303(x8231,x8233),x8232)) 7.68/7.78 [824]E(f269(f313(f66(x8241),x8242),x8243),f295(f314(x8241,x8243),x8242)) 7.68/7.78 [825]E(f269(f336(f56(x8251),x8252),x8253),f343(f320(x8251,x8253),x8252)) 7.68/7.78 [826]E(f331(f327(f16(x8261),x8262),x8263),f331(f327(x8261,x8263),x8262)) 7.68/7.78 [827]E(f331(f284(f80(x8271),x8272),x8273),f275(f329(x8271,x8273),x8272)) 7.68/7.78 [828]E(f331(f307(f67(x8281),x8282),x8283),f311(f322(x8281,x8283),x8282)) 7.68/7.78 [829]E(f331(f287(f74(x8291),x8292),x8293),f269(f326(x8291,x8293),x8292)) 7.68/7.78 [830]E(f311(f294(f63(x8301),x8302),x8303),f311(f294(x8301,x8303),x8302)) 7.68/7.78 [831]E(f343(f276(f84(x8311),x8312),x8313),f275(f339(x8311,x8313),x8312)) 7.68/7.78 [832]E(f343(f320(f57(x8321),x8322),x8323),f269(f336(x8321,x8323),x8322)) 7.68/7.78 [833]E(f270(f298(f76(x8331),x8332),x8333),f270(f298(x8331,x8333),x8332)) 7.68/7.78 [834]E(f312(f293(f70(x8341),x8342),x8343),f312(f293(x8341,x8343),x8342)) 7.68/7.78 [835]E(f275(f339(f81(x8351),x8352),x8353),f343(f276(x8351,x8353),x8352)) 7.68/7.78 [836]E(f275(f305(f60(x8361),x8362),x8363),f311(f277(x8361,x8363),x8362)) 7.68/7.78 [837]E(f275(f288(f65(x8371),x8372),x8373),f269(f278(x8371,x8373),x8372)) 7.68/7.78 [838]E(f275(f271(f78(x8381),x8382),x8383),f268(f279(x8381,x8383),x8382)) 7.68/7.78 [839]E(f295(f310(f79(x8391),x8392),x8393),f295(f310(x8391,x8393),x8392)) 7.68/7.78 [854]E(f267(f382(x8541),f267(f382(x8542),x8543)),f267(f382(x8542),f267(f382(x8541),x8543))) 7.68/7.78 [863]E(f267(f378(f267(f382(x8631),x8632)),f267(f382(x8633),x8632)),f267(f378(x8631),x8633)) 7.68/7.78 [866]E(f267(f378(f267(f382(x8661),x8662)),f267(f382(x8661),x8663)),f267(f378(x8662),x8663)) 7.68/7.78 [864]E(f267(f378(f267(f378(x8641),x8642)),x8643),f267(f378(x8641),f267(f382(x8642),x8643))) 7.68/7.78 [865]E(f267(f382(f267(f382(x8651),x8652)),x8653),f267(f382(x8651),f267(f382(x8652),x8653))) 7.68/7.78 [868]E(f267(f378(f267(f378(x8681),x8682)),x8683),f267(f378(f267(f378(x8681),x8683)),x8682)) 7.68/7.78 [888]E(f267(f378(f267(f378(f267(a394,x8881)),x8882)),f267(a394,x8883)),f267(f378(f267(f378(x8881),x8882)),x8883)) 7.68/7.78 [896]E(f94(f21(a246,f52(a238,f327(f16(a247),f285(x8961,x8962)))),f354(x8961,x8963)),f354(x8961,f99(f96(f31(a240,f282(f77(a244),x8962)),f305(f60(a372),x8963))))) 7.68/7.78 [898]E(f99(f96(f31(a240,f282(f77(a244),f344(x8981,x8982))),f305(f60(a372),f332(x8981,x8983)))),f332(x8981,f89(f95(f41(a240,f341(f55(a248),x8982)),f320(f57(a369),x8983))))) 7.68/7.78 [899]E(f89(f95(f41(a240,f341(f55(a248),f283(x8991,x8992))),f320(f57(a369),f364(x8991,x8993)))),f364(x8991,f99(f96(f31(a240,f282(f77(a244),x8992)),f305(f60(a372),x8993))))) 7.68/7.78 [897]E(f99(f96(f31(a240,f282(f77(a244),f330(x8971,x8972))),f305(f60(a372),f350(x8971,x8973)))),f350(x8971,f94(f21(a246,f52(a238,f327(f16(a247),x8972))),x8973))) 7.68/7.78 [904]E(f94(f21(a246,f52(a238,f327(f16(a247),x9041))),f94(f21(a246,f52(a238,f327(f16(a247),x9042))),x9043)),f94(f21(a246,f52(a238,f327(f16(a247),x9042))),f94(f21(a246,f52(a238,f327(f16(a247),x9041))),x9043))) 7.68/7.78 [907]E(f99(f96(f31(a240,f282(f77(a244),x9071)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x9072)),f305(f60(a372),x9073)))))),f99(f96(f31(a240,f282(f77(a244),x9072)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x9071)),f305(f60(a372),x9073))))))) 7.68/7.78 [908]E(f89(f95(f41(a240,f341(f55(a248),x9081)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x9082)),f320(f57(a369),x9083)))))),f89(f95(f41(a240,f341(f55(a248),x9082)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x9081)),f320(f57(a369),x9083))))))) 7.68/7.78 [939]~P7(x9391)+E(f89(x9391),x9391) 7.68/7.78 [940]~P6(x9401)+E(f99(x9401),x9401) 7.68/7.78 [941]~P2(x9411)+E(f90(x9411),x9411) 7.68/7.78 [942]~P1(x9421)+E(f101(x9421),x9421) 7.68/7.78 [943]P6(f102(x9431))+E(f101(x9431),a4) 7.68/7.78 [944]P4(f103(x9441))+E(f99(x9441),a8) 7.68/7.78 [945]P4(f104(x9451))+E(f99(x9451),a8) 7.68/7.78 [946]P8(f132(x9461))+E(f89(x9461),a9) 7.68/7.78 [947]P8(f105(x9471))+E(f89(x9471),a9) 7.68/7.78 [948]P7(f155(x9481))+E(f90(x9481),a7) 7.68/7.78 [949]P7(f193(x9491))+E(f90(x9491),a7) 7.68/7.78 [950]P6(f194(x9501))+E(f101(x9501),a4) 7.68/7.78 [951]~P1(x9511)+P1(f101(x9511)) 7.68/7.78 [952]~P3(x9521)+P1(f86(x9521)) 7.68/7.78 [953]~P6(x9531)+P1(f392(x9531)) 7.68/7.78 [954]~P2(x9541)+P2(f90(x9541)) 7.68/7.78 [955]~P3(x9551)+P2(f15(x9551)) 7.68/7.78 [956]~P6(x9561)+P6(f99(x9561)) 7.68/7.78 [957]~P3(x9571)+P6(f85(x9571)) 7.68/7.78 [958]~P7(x9581)+P7(f89(x9581)) 7.68/7.78 [959]~P3(x9591)+P7(f88(x9591)) 7.68/7.78 [976]P5(x9761)+P5(f286(a238,x9761)) 7.68/7.78 [978]~P5(a10)+P5(f331(a2,x9781)) 7.68/7.78 [980]~P5(a10)+P5(f343(a9,x9801)) 7.68/7.78 [982]~P5(a10)+P5(f275(a8,x9821)) 7.68/7.78 [1039]P5(a10)+~P5(f331(a2,x10391)) 7.68/7.78 [1041]P5(a10)+~P5(f343(a9,x10411)) 7.68/7.78 [1043]P5(a10)+~P5(f275(a8,x10431)) 7.68/7.78 [1056]~P5(x10561)+~P5(f286(a238,x10561)) 7.68/7.78 [1030]E(x10301,a2)+P5(f331(x10301,f212(x10301))) 7.68/7.78 [1031]E(x10311,a2)+P5(f331(x10311,f108(x10311))) 7.68/7.78 [1032]E(a3,x10321)+P5(f268(x10321,f195(x10321))) 7.68/7.78 [1033]E(a3,x10331)+P5(f268(x10331,f123(x10331))) 7.68/7.78 [1044]E(f101(x10441),a4)+P5(f311(x10441,f102(x10441))) 7.68/7.78 [1045]E(f99(x10451),a8)+P5(f275(x10451,f103(x10451))) 7.68/7.78 [1046]E(f99(x10461),a8)+P5(f275(x10461,f104(x10461))) 7.68/7.78 [1047]E(f89(x10471),a9)+P5(f343(x10471,f132(x10471))) 7.68/7.78 [1048]E(f89(x10481),a9)+P5(f343(x10481,f105(x10481))) 7.68/7.78 [1049]E(f90(x10491),a7)+P5(f269(x10491,f155(x10491))) 7.68/7.78 [1050]E(f90(x10501),a7)+P5(f269(x10501,f193(x10501))) 7.68/7.78 [1051]E(f101(x10511),a4)+P5(f311(x10511,f194(x10511))) 7.68/7.78 [1156]E(x11561,a2)+~P5(f268(f273(a385,x11561),a2)) 7.68/7.78 [1157]E(x11571,a1)+~P5(f331(f327(a384,x11571),a1)) 7.68/7.78 [1158]E(a11,x11581)+~P5(f331(f327(a384,x11581),a11)) 7.68/7.78 [1159]E(a1,x11591)+~P5(f331(f327(a384,x11591),a1)) 7.68/7.78 [1140]E(a2,x11401)+P5(f268(f328(a376,f224(x11401)),x11401)) 7.68/7.78 [1141]E(a2,x11411)+P5(f268(f328(a376,f109(x11411)),x11411)) 7.68/7.78 [1208]~P5(f268(a261,x12081))+P5(f270(a239,f273(f53(a385),x12081))) 7.68/7.78 [1234]~P5(f269(f336(a369,x12341),a264))+P5(f403(f395(f6(x12341)))) 7.68/7.78 [1303]~P5(f311(a236,x13031))+P5(f312(a253,f101(f294(f63(a386),x13031)))) 7.68/7.78 [1304]~P5(f269(a260,x13041))+P5(f295(a255,f90(f309(f54(a389),x13041)))) 7.68/7.78 [1305]~P5(f270(a239,x13051))+P5(f317(a249,f97(f298(f76(a387),x13051)))) 7.68/7.78 [1306]~P5(f295(a255,x13061))+P5(f299(a258,f98(f310(f79(a391),x13061)))) 7.68/7.78 [1307]~P5(f312(a253,x13071))+P5(f300(a250,f100(f293(f70(a388),x13071)))) 7.68/7.78 [983]~P6(x9832)+P1(f294(x9831,x9832)) 7.68/7.78 [984]~P6(x9842)+P1(f355(x9841,x9842)) 7.68/7.78 [985]~P4(x9852)+P1(f277(x9851,x9852)) 7.68/7.78 [986]~P7(x9862)+P1(f347(x9861,x9862)) 7.68/7.78 [987]~P1(x9872)+P1(f92(x9871,x9872)) 7.68/7.78 [988]~P1(x9882)+P1(f34(x9881,x9882)) 7.68/7.78 [989]~P1(x9892)+P1(f304(x9891,x9892)) 7.68/7.78 [990]~P8(x9902)+P1(f340(x9901,x9902)) 7.68/7.78 [991]~P2(x9912)+P2(f313(x9911,x9912)) 7.68/7.78 [992]~P7(x9922)+P2(f309(x9921,x9922)) 7.68/7.78 [993]~P8(x9932)+P2(f336(x9931,x9932)) 7.68/7.78 [994]~P6(x9942)+P2(f356(x9941,x9942)) 7.68/7.78 [995]~P2(x9952)+P2(f91(x9951,x9952)) 7.68/7.78 [996]~P2(x9962)+P2(f38(x9961,x9962)) 7.68/7.78 [997]~P4(x9972)+P2(f278(x9971,x9972)) 7.68/7.78 [998]~P7(x9982)+P2(f357(x9981,x9982)) 7.68/7.78 [999]~P7(x9992)+P6(f332(x9991,x9992)) 7.68/7.78 [1000]~P8(x10002)+P6(f339(x10001,x10002)) 7.68/7.78 [1001]~P6(x10012)+P6(f305(x10011,x10012)) 7.68/7.78 [1002]~P4(x10022)+P6(f282(x10021,x10022)) 7.68/7.78 [1003]~P6(x10032)+P6(f96(x10031,x10032)) 7.68/7.78 [1004]~P1(x10042)+P6(f365(x10041,x10042)) 7.68/7.78 [1005]~P7(x10052)+P6(f288(x10051,x10052)) 7.68/7.78 [1006]~P6(x10062)+P6(f361(x10061,x10062)) 7.68/7.78 [1007]~P6(x10072)+P6(f50(x10071,x10072)) 7.68/7.78 [1008]~P2(x10082)+P6(f362(x10081,x10082)) 7.68/7.78 [1009]~P4(x10092)+P4(f280(x10091,x10092)) 7.68/7.78 [1010]~P8(x10102)+P4(f344(x10101,x10102)) 7.68/7.78 [1011]~P8(x10112)+P7(f341(x10111,x10112)) 7.68/7.78 [1012]~P7(x10122)+P7(f374(x10121,x10122)) 7.68/7.78 [1013]~P7(x10132)+P7(f95(x10131,x10132)) 7.68/7.78 [1014]~P1(x10142)+P7(f353(x10141,x10142)) 7.68/7.78 [1015]~P4(x10152)+P7(f276(x10151,x10152)) 7.68/7.78 [1016]~P6(x10162)+P7(f364(x10161,x10162)) 7.68/7.78 [1017]~P7(x10172)+P7(f320(x10171,x10172)) 7.68/7.78 [1018]~P6(x10182)+P7(f296(x10181,x10182)) 7.68/7.78 [1019]~P2(x10192)+P7(f348(x10191,x10192)) 7.68/7.78 [1020]~P7(x10202)+P7(f48(x10201,x10202)) 7.68/7.78 [1021]~P4(x10212)+P8(f283(x10211,x10212)) 7.68/7.78 [1022]~P8(x10222)+P8(f345(x10221,x10222)) 7.68/7.78 [1023]~P7(x10232)+P8(f291(x10231,x10232)) 7.68/7.78 [1024]~P6(x10242)+P8(f289(x10241,x10242)) 7.68/7.78 [1025]~P3(x10252)+P3(f286(x10251,x10252)) 7.68/7.78 [1026]~P1(x10262)+P3(f312(x10261,x10262)) 7.68/7.78 [1027]~P2(x10272)+P3(f295(x10271,x10272)) 7.68/7.78 [1029]E(x10291,x10292)+~E(f267(a394,x10291),f267(a394,x10292)) 7.68/7.78 [1053]~E(x10531,a2)+~P5(f331(x10531,x10532)) 7.68/7.78 [1055]~E(a3,x10551)+~P5(f268(x10551,x10552)) 7.68/7.78 [966]~P3(x9661)+E(f311(f86(x9661),x9662),x9661) 7.68/7.78 [967]~P4(x9671)+E(f344(f87(x9671),x9672),x9671) 7.68/7.78 [968]~P3(x9681)+E(f268(f14(x9681),x9682),x9681) 7.68/7.78 [969]~P3(x9691)+E(f269(f15(x9691),x9692),x9691) 7.68/7.78 [970]~P3(x9701)+E(f331(f13(x9701),x9702),x9701) 7.68/7.78 [971]~P3(x9711)+E(f343(f88(x9711),x9712),x9711) 7.68/7.78 [972]~P3(x9721)+E(f275(f85(x9721),x9722),x9721) 7.68/7.78 [1084]~E(x10842,x10841)+P5(f268(f273(a385,x10841),x10842)) 7.68/7.78 [1092]~E(x10921,x10922)+P5(f268(f273(a385,x10921),x10922)) 7.68/7.78 [1093]~E(x10932,x10931)+P5(f268(f273(a242,x10931),x10932)) 7.68/7.78 [1095]~E(x10952,x10951)+P5(f269(f309(a389,x10951),x10952)) 7.68/7.78 [1098]~E(x10981,x10982)+P5(f269(f309(a389,x10981),x10982)) 7.68/7.78 [1099]~E(x10992,x10991)+P5(f269(f309(a245,x10991),x10992)) 7.68/7.78 [1102]~E(x11022,x11021)+P5(f331(f327(a384,x11021),x11022)) 7.68/7.78 [1105]~E(x11051,x11052)+P5(f331(f327(a384,x11051),x11052)) 7.68/7.78 [1106]~E(x11061,x11062)+P5(f331(f327(a247,x11061),x11062)) 7.68/7.78 [1109]~E(x11092,x11091)+P5(f311(f294(a386,x11091),x11092)) 7.68/7.78 [1111]~E(x11111,x11112)+P5(f311(f294(a386,x11111),x11112)) 7.68/7.78 [1112]~E(x11121,x11122)+P5(f311(f294(a243,x11121),x11122)) 7.68/7.78 [1113]~E(x11132,x11131)+P5(f343(f341(a248,x11131),x11132)) 7.68/7.79 [1114]~E(x11141,x11142)+P5(f275(f282(a244,x11141),x11142)) 7.68/7.79 [1115]P5(x11151)+P5(f286(f274(a246,x11151),x11152)) 7.68/7.79 [1121]~P5(x11212)+P5(f286(f274(a246,x11211),x11212)) 7.68/7.79 [1122]~P5(x11222)+P5(f286(f274(a240,x11221),x11222)) 7.68/7.79 [1123]~P5(x11231)+P5(f286(f274(a240,x11231),x11232)) 7.68/7.79 [1142]P4(f213(x11421,x11422))+P5(f311(f294(a386,x11421),x11422)) 7.68/7.79 [1143]P4(f133(x11431,x11432))+P5(f311(f294(a386,x11432),x11431)) 7.68/7.79 [1144]P8(f167(x11441,x11442))+P5(f269(f309(a389,x11441),x11442)) 7.68/7.79 [1145]P8(f225(x11451,x11452))+P5(f269(f309(a389,x11452),x11451)) 7.68/7.79 [1146]~E(f267(f378(x11461),x11462),a11)+P5(f331(f327(a384,x11461),x11462)) 7.68/7.79 [1160]E(x11601,x11602)+~P5(f268(f273(a242,x11601),x11602)) 7.68/7.79 [1161]E(x11611,x11612)+~P5(f331(f327(a247,x11611),x11612)) 7.68/7.79 [1162]~E(x11621,a8)+~P5(f311(f277(a372,x11622),x11621)) 7.68/7.79 [1163]~E(x11631,a9)+~P5(f269(f336(a369,x11632),x11631)) 7.68/7.79 [1166]~E(a2,x11661)+~P5(f268(f328(a376,x11662),x11661)) 7.68/7.79 [1167]~P5(f311(a236,x11672))+P5(f268(a261,f354(x11671,x11672))) 7.68/7.79 [1168]~P5(f312(a253,x11682))+P5(f268(a261,f366(x11681,x11682))) 7.68/7.79 [1169]~P5(f295(a255,x11692))+P5(f268(a261,f349(x11691,x11692))) 7.68/7.79 [1170]~P5(f270(a239,x11702))+P5(f268(a261,f360(x11701,x11702))) 7.68/7.79 [1171]~P5(f312(a253,x11712))+P5(f269(a260,f353(x11711,x11712))) 7.68/7.79 [1172]~P5(f311(a236,x11722))+P5(f269(a260,f364(x11721,x11722))) 7.68/7.79 [1173]~P5(f270(a239,x11732))+P5(f269(a260,f352(x11731,x11732))) 7.68/7.79 [1174]~P5(f295(a255,x11742))+P5(f269(a260,f348(x11741,x11742))) 7.68/7.79 [1175]~P5(f269(a260,x11752))+P5(f311(a236,f332(x11751,x11752))) 7.68/7.79 [1176]~P5(f268(a261,x11762))+P5(f311(a236,f350(x11761,x11762))) 7.68/7.79 [1177]~P5(f268(a261,x11772))+P5(f270(a239,f358(x11771,x11772))) 7.68/7.79 [1178]~P5(f269(a260,x11782))+P5(f270(a239,f359(x11781,x11782))) 7.68/7.79 [1179]~P5(f269(a260,x11792))+P5(f312(a253,f347(x11791,x11792))) 7.68/7.79 [1180]~P5(f268(a261,x11802))+P5(f312(a253,f333(x11801,x11802))) 7.68/7.79 [1181]~P5(f268(a261,x11812))+P5(f295(a255,f334(x11811,x11812))) 7.68/7.79 [1182]~P5(f269(a260,x11822))+P5(f295(a255,f357(x11821,x11822))) 7.68/7.79 [1183]~E(x11831,x11832)+~P5(f331(f327(a383,x11832),x11831)) 7.68/7.79 [1187]~E(x11871,x11872)+~P5(f331(f327(a383,x11871),x11872)) 7.68/7.79 [1194]~P5(f331(x11942,x11941))+P5(f268(f328(a376,x11941),x11942)) 7.68/7.79 [1195]~P5(f343(x11952,x11951))+P5(f269(f336(a369,x11951),x11952)) 7.68/7.79 [1196]~P5(f275(x11962,x11961))+P5(f311(f277(a372,x11961),x11962)) 7.68/7.79 [1197]P5(x11971)+~P5(f286(f274(a241,x11972),x11971)) 7.68/7.79 [1198]P5(x11981)+~P5(f286(f274(a241,x11981),x11982)) 7.68/7.79 [1203]~E(x12031,x12032)+P5(f331(f327(a383,x12031),f267(a394,x12032))) 7.68/7.79 [1219]E(f267(f378(x12191),x12192),a11)+~P5(f331(f327(a384,x12191),x12192)) 7.68/7.79 [1225]P5(f331(x12251,x12252))+~P5(f268(f328(a376,x12252),x12251)) 7.68/7.79 [1226]P5(f343(x12261,x12262))+~P5(f269(f336(a369,x12262),x12261)) 7.68/7.79 [1227]P5(f275(x12271,x12272))+~P5(f311(f277(a372,x12272),x12271)) 7.68/7.79 [1230]P5(f331(f327(a384,x12302),x12301))+P5(f331(f327(a384,x12301),x12302)) 7.68/7.79 [1235]P5(f311(f392(x12351),x12352))+~P5(f311(f294(a386,x12352),x12351)) 7.68/7.79 [1236]E(f267(f382(x12361),f117(x12361,x12362)),x12362)+~P5(f331(f327(a384,x12361),x12362)) 7.68/7.79 [1274]~P5(f331(f327(a383,x12741),x12742))+P5(f331(f327(a384,x12741),x12742)) 7.68/7.79 [1282]P5(f331(f327(a383,x12821),x12822))+P5(f331(f327(a383,x12822),f267(a394,x12821))) 7.68/7.79 [1322]~P5(f331(f327(a384,x13221),x13222))+P5(f331(f327(a384,x13221),f267(a394,x13222))) 7.68/7.79 [1324]~P5(f331(f327(a384,x13241),x13242))+P5(f331(f327(a383,x13241),f267(a394,x13242))) 7.68/7.79 [1326]~P5(f331(f327(a383,x13261),x13262))+P5(f331(f327(a383,x13261),f267(a394,x13262))) 7.68/7.79 [1370]P5(f331(f327(a384,x13701),x13702))+~P5(f331(f327(a383,x13701),f267(a394,x13702))) 7.68/7.79 [1448]~P5(f331(f327(a383,x14481),x14482))+~P5(f331(f327(a383,x14482),f267(a394,x14481))) 7.68/7.79 [1520]~P5(f331(f327(a384,x15201),x15202))+P5(f331(f327(a384,f267(a394,x15201)),f267(a394,x15202))) 7.68/7.79 [1522]~P5(f331(f327(a383,x15221),x15222))+P5(f331(f327(a383,f267(a394,x15221)),f267(a394,x15222))) 7.68/7.79 [1627]P5(f331(f327(a384,x16271),x16272))+~P5(f331(f327(a384,f267(a394,x16271)),f267(a394,x16272))) 7.68/7.79 [1629]P5(f331(f327(a383,x16291),x16292))+~P5(f331(f327(a383,f267(a394,x16291)),f267(a394,x16292))) 7.68/7.79 [1651]~P5(f269(a260,x16512))+P5(f331(f327(a384,f318(a259,f374(x16511,x16512))),f318(a259,x16512))) 7.68/7.79 [1652]~P5(f311(a236,x16522))+P5(f331(f327(a384,f318(a259,f364(x16521,x16522))),f324(a257,x16522))) 7.68/7.79 [1653]~P5(f268(a261,x16532))+P5(f331(f327(a384,f318(a259,f367(x16531,x16532))),f301(a256,x16532))) 7.68/7.79 [1654]~P5(f269(a260,x16542))+P5(f331(f327(a384,f324(a257,f332(x16541,x16542))),f318(a259,x16542))) 7.68/7.79 [1655]~P5(f312(a253,x16552))+P5(f331(f327(a384,f324(a257,f365(x16551,x16552))),f306(a251,x16552))) 7.68/7.79 [1656]~P5(f311(a236,x16562))+P5(f331(f327(a384,f324(a257,f361(x16561,x16562))),f324(a257,x16562))) 7.68/7.79 [1657]~P5(f270(a239,x16572))+P5(f331(f327(a384,f324(a257,f351(x16571,x16572))),f321(a254,x16572))) 7.68/7.79 [1658]~P5(f295(a255,x16582))+P5(f331(f327(a384,f324(a257,f362(x16581,x16582))),f315(a252,x16582))) 7.68/7.79 [1659]~P5(f269(a260,x16592))+P5(f331(f327(a384,f301(a256,f375(x16591,x16592))),f318(a259,x16592))) 7.68/7.79 [1660]~P5(f311(a236,x16602))+P5(f331(f327(a384,f301(a256,f354(x16601,x16602))),f324(a257,x16602))) 7.68/7.79 [1661]~P5(f312(a253,x16612))+P5(f331(f327(a384,f301(a256,f366(x16611,x16612))),f306(a251,x16612))) 7.68/7.79 [1662]~P5(f295(a255,x16622))+P5(f331(f327(a384,f301(a256,f349(x16621,x16622))),f315(a252,x16622))) 7.68/7.79 [1663]~P5(f270(a239,x16632))+P5(f331(f327(a384,f301(a256,f360(x16631,x16632))),f321(a254,x16632))) 7.68/7.79 [1152]P5(f268(x11522,x11521))+E(f93(f45(a241,f273(a242,x11521)),x11522),a3) 7.68/7.79 [1153]P5(f331(x11532,x11531))+E(f94(f21(a241,f327(a247,x11531)),x11532),a2) 7.68/7.79 [1209]E(f267(f382(x12091),f267(f378(x12092),x12091)),x12092)+P5(f331(f327(a383,x12092),x12091)) 7.68/7.79 [1240]E(f267(f382(x12401),f267(f378(x12402),x12401)),x12402)+~P5(f331(f327(a384,x12401),x12402)) 7.68/7.79 [1241]E(f267(f378(x12411),f267(f378(x12411),x12412)),x12412)+~P5(f331(f327(a384,x12412),x12411)) 7.68/7.79 [1295]P5(f268(a261,x12951))+P5(f268(f328(a376,f134(x12952,x12951)),x12951)) 7.68/7.79 [1296]P5(f268(a261,x12961))+P5(f268(f328(a376,f170(x12961,x12962)),x12961)) 7.68/7.79 [1297]P5(f268(a261,x12971))+P5(f268(f328(a376,f118(x12971,x12972)),x12971)) 7.68/7.79 [1308]~P5(f268(a261,x13082))+P5(f268(a261,f94(f21(a241,x13081),x13082))) 7.68/7.79 [1309]~P5(f268(a261,x13091))+P5(f268(a261,f94(f21(a241,x13091),x13092))) 7.68/7.79 [1310]~P5(f270(a239,x13102))+P5(f270(a239,f93(f45(a241,x13101),x13102))) 7.68/7.79 [1311]~P5(f270(a239,x13111))+P5(f270(a239,f93(f45(a241,x13111),x13112))) 7.68/7.79 [1313]E(f267(a394,f267(f382(x13131),f159(x13131,x13132))),x13132)+~P5(f331(f327(a383,x13131),x13132)) 7.68/7.79 [1314]E(f267(a394,f267(f382(x13141),f111(x13141,x13142))),x13142)+~P5(f331(f327(a383,x13141),x13142)) 7.68/7.79 [1319]E(f267(f378(f267(a394,x13191)),x13192),f267(a394,f267(f378(x13191),x13192)))+~P5(f331(f327(a384,x13192),x13191)) 7.68/7.79 [1338]P5(f331(f327(a384,x13381),x13382))+P5(f331(f327(a384,f267(a394,x13382)),x13381)) 7.68/7.79 [1350]P5(f268(f273(a385,x13501),x13502))+P5(f268(f328(a376,f196(x13502,x13501)),x13501)) 7.68/7.79 [1351]P5(f269(f309(a389,x13511),x13512))+P5(f269(f336(a369,f225(x13512,x13511)),x13511)) 7.68/7.79 [1352]P5(f311(f294(a386,x13521),x13522))+P5(f311(f277(a372,f133(x13522,x13521)),x13521)) 7.68/7.79 [1368]~P5(f268(x13682,x13681))+E(f93(f45(a241,f273(a242,x13681)),x13682),f93(f45(a240,f273(f53(a242),x13681)),f290(f58(a370),a3))) 7.68/7.79 [1430]~P5(f331(f327(a383,x14301),x14302))+P5(f331(f327(a384,f267(a394,x14301)),x14302)) 7.68/7.79 [1437]P5(f268(a261,x14371))+~P5(f268(a261,f94(f21(a240,x14372),x14371))) 7.68/7.79 [1438]P5(f268(a261,x14381))+~P5(f268(a261,f94(f21(a240,x14381),x14382))) 7.68/7.79 [1439]P5(f270(a239,x14391))+~P5(f270(a239,f93(f45(a240,x14392),x14391))) 7.68/7.79 [1440]P5(f270(a239,x14401))+~P5(f270(a239,f93(f45(a240,x14401),x14402))) 7.68/7.79 [1442]E(f267(a394,f202(x14421,x14422)),x14422)+~P5(f331(f327(a384,f267(a394,x14421)),x14422)) 7.68/7.79 [1443]E(f267(a394,f184(x14431,x14432)),x14432)+~P5(f331(f327(a383,f267(a394,x14431)),x14432)) 7.68/7.79 [1445]P5(f268(a261,x14451))+~P5(f331(f327(a383,f134(x14452,x14451)),x14452)) 7.68/7.79 [1446]P5(f268(a261,x14461))+~P5(f331(f327(a384,f118(x14461,x14462)),x14462)) 7.68/7.79 [1447]P5(f268(a261,x14471))+~P5(f331(f327(a383,f170(x14471,x14472)),x14472)) 7.68/7.79 [1523]P5(f331(f327(a384,x15231),x15232))+~P5(f331(f327(a384,f267(a394,x15231)),x15232)) 7.68/7.79 [1526]P5(f331(f327(a383,x15261),x15262))+~P5(f331(f327(a384,f267(a394,x15261)),x15262)) 7.68/7.79 [1527]P5(f331(f327(a383,x15271),x15272))+~P5(f331(f327(a383,f267(a394,x15271)),x15272)) 7.68/7.79 [1564]P5(f268(f273(a385,x15641),x15642))+~P5(f268(f328(a376,f196(x15642,x15641)),x15642)) 7.68/7.79 [1565]P5(f269(f309(a389,x15651),x15652))+~P5(f269(f336(a369,f225(x15652,x15651)),x15652)) 7.68/7.79 [1566]P5(f311(f294(a386,x15661),x15662))+~P5(f311(f277(a372,f133(x15662,x15661)),x15662)) 7.68/7.79 [1612]~P5(f331(f327(a384,x16121),x16122))+~P5(f331(f327(a384,f267(a394,x16122)),x16121)) 7.68/7.79 [1621]P5(f331(f327(a383,x16211),f184(x16211,x16212)))+~P5(f331(f327(a383,f267(a394,x16211)),x16212)) 7.68/7.79 [1638]~P5(f331(f381(a12,f327(a384,x16381)),x16382))+P5(f331(f327(a384,f267(a394,x16381)),x16382)) 7.68/7.79 [1639]~P5(f331(f327(a384,f267(a394,x16391)),x16392))+P5(f331(f381(a12,f327(a384,x16391)),x16392)) 7.68/7.79 [1840]P5(f268(f273(a385,x18401),x18402))+~P5(f286(f274(a390,f331(x18401,f207(x18401,x18402))),f331(x18402,f207(x18401,x18402)))) 7.68/7.79 [1841]P5(f269(f309(a389,x18411),x18412))+~P5(f286(f274(a390,f343(x18411,f167(x18411,x18412))),f343(x18412,f167(x18411,x18412)))) 7.68/7.79 [1842]P5(f311(f294(a386,x18421),x18422))+~P5(f286(f274(a390,f275(x18421,f213(x18421,x18422))),f275(x18422,f213(x18421,x18422)))) 7.68/7.79 [1206]P5(f331(x12062,x12061))+E(f94(f21(a241,f327(f16(a247),x12061)),x12062),a2) 7.68/7.79 [1207]P5(f268(x12072,x12071))+E(f93(f45(a241,f273(f53(a242),x12071)),x12072),a3) 7.68/7.79 [1278]P5(f311(x12782,x12781))+E(f101(f92(f39(a241,f294(a243,x12781)),x12782)),a4) 7.68/7.79 [1279]P5(f269(x12792,x12791))+E(f90(f91(f36(a241,f309(a245,x12791)),x12792)),a7) 7.68/7.79 [1280]P5(f275(x12802,x12801))+E(f99(f96(f31(a241,f282(a244,x12801)),x12802)),a8) 7.68/7.79 [1281]P5(f343(x12812,x12811))+E(f89(f95(f41(a241,f341(a248,x12811)),x12812)),a9) 7.68/7.79 [1312]E(f267(f382(f267(f378(x13121),x13122)),x13122),x13121)+~P5(f331(f327(a384,x13122),x13121)) 7.68/7.79 [1420]~P5(f268(x14202,x14201))+E(f93(f45(a240,f273(f53(a242),x14201)),f290(f58(a370),a3)),f93(f45(a241,f273(f53(a242),x14201)),x14202)) 7.68/7.79 [1613]~P5(f269(a260,f89(x16132)))+P5(f269(a260,f89(f95(f41(a241,x16131),x16132)))) 7.68/7.79 [1614]~P5(f269(a260,f89(x16141)))+P5(f269(a260,f89(f95(f41(a241,x16141),x16142)))) 7.68/7.79 [1615]~P5(f311(a236,f99(x16152)))+P5(f311(a236,f99(f96(f31(a241,x16151),x16152)))) 7.68/7.79 [1616]~P5(f311(a236,f99(x16161)))+P5(f311(a236,f99(f96(f31(a241,x16161),x16162)))) 7.68/7.79 [1617]~P5(f312(a253,f101(x16172)))+P5(f312(a253,f101(f92(f39(a241,x16171),x16172)))) 7.68/7.79 [1618]~P5(f312(a253,f101(x16181)))+P5(f312(a253,f101(f92(f39(a241,x16181),x16182)))) 7.68/7.79 [1619]~P5(f295(a255,f90(x16192)))+P5(f295(a255,f90(f91(f36(a241,x16191),x16192)))) 7.68/7.79 [1620]~P5(f295(a255,f90(x16201)))+P5(f295(a255,f90(f91(f36(a241,x16201),x16202)))) 7.68/7.79 [1666]~P5(f275(x16662,x16661))+E(f99(f96(f31(a241,f282(a244,x16661)),x16662)),f99(f96(f31(a240,f282(f77(a244),x16661)),f305(f60(a372),a8)))) 7.68/7.79 [1667]~P5(f343(x16672,x16671))+E(f89(f95(f41(a240,f341(f55(a248),x16671)),f320(f57(a369),a9))),f89(f95(f41(a241,f341(a248,x16671)),x16672))) 7.68/7.79 [1668]~P5(f269(x16682,x16681))+E(f90(f91(f36(a240,f309(f54(a245),x16681)),f313(f66(a373),a7))),f90(f91(f36(a241,f309(a245,x16681)),x16682))) 7.68/7.79 [1669]~P5(f311(x16692,x16691))+E(f101(f92(f39(a240,f294(f63(a243),x16691)),f304(f64(a371),a4))),f101(f92(f39(a241,f294(a243,x16691)),x16692))) 7.68/7.79 [1729]P5(f269(a260,f89(x17291)))+~P5(f269(a260,f89(f95(f41(a240,x17292),x17291)))) 7.68/7.79 [1730]P5(f269(a260,f89(x17301)))+~P5(f269(a260,f89(f95(f41(a240,x17301),x17302)))) 7.68/7.79 [1731]P5(f311(a236,f99(x17311)))+~P5(f311(a236,f99(f96(f31(a240,x17312),x17311)))) 7.68/7.79 [1732]P5(f311(a236,f99(x17321)))+~P5(f311(a236,f99(f96(f31(a240,x17321),x17322)))) 7.68/7.79 [1733]P5(f312(a253,f101(x17331)))+~P5(f312(a253,f101(f92(f39(a240,x17332),x17331)))) 7.68/7.79 [1734]P5(f312(a253,f101(x17341)))+~P5(f312(a253,f101(f92(f39(a240,x17341),x17342)))) 7.68/7.79 [1735]P5(f295(a255,f90(x17351)))+~P5(f295(a255,f90(f91(f36(a240,x17352),x17351)))) 7.68/7.79 [1736]P5(f295(a255,f90(x17361)))+~P5(f295(a255,f90(f91(f36(a240,x17361),x17362)))) 7.68/7.79 [1751]~P5(f270(a239,x17512))+P5(f270(a239,f93(f45(a240,f273(f53(a242),x17511)),f290(f58(a370),x17512)))) 7.68/7.79 [1828]~P5(f331(f327(a384,f180(x18282,x18281)),f267(x18281,f180(x18282,x18281))))+P5(f268(a261,f327(f16(f18(a384,x18281)),x18282))) 7.68/7.79 [1833]P5(f270(a239,x18331))+~P5(f270(a239,f93(f45(a240,f273(f53(a242),x18332)),f290(f58(a370),x18331)))) 7.68/7.79 [1315]P5(f343(x13152,x13151))+E(f89(f95(f41(a241,f341(f55(a248),x13151)),x13152)),a9) 7.68/7.79 [1316]P5(f275(x13162,x13161))+E(f99(f96(f31(a241,f282(f77(a244),x13161)),x13162)),a8) 7.68/7.79 [1317]P5(f269(x13172,x13171))+E(f90(f91(f36(a241,f309(f54(a245),x13171)),x13172)),a7) 7.68/7.79 [1318]P5(f311(x13182,x13181))+E(f101(f92(f39(a241,f294(f63(a243),x13181)),x13182)),a4) 7.68/7.79 [1495]~P5(f268(f328(a376,x14951),x14952))+E(f94(f21(a246,f52(a238,f327(f16(a247),x14951))),x14952),x14952) 7.68/7.79 [1528]~P5(f331(x15282,x15281))+E(f94(f21(a246,f52(a238,f327(f16(a247),x15281))),a2),f94(f21(a241,f327(a247,x15281)),x15282)) 7.68/7.79 [1560]~P5(f331(x15602,x15601))+E(f94(f21(a246,f52(a238,f327(f16(a247),x15601))),a2),f94(f21(a241,f327(f16(a247),x15601)),x15602)) 7.68/7.79 [1716]~P5(f269(x17162,x17161))+E(f90(f91(f36(a241,f309(f54(a245),x17161)),x17162)),f90(f91(f36(a240,f309(f54(a245),x17161)),f313(f66(a373),a7)))) 7.68/7.79 [1717]~P5(f275(x17172,x17171))+E(f99(f96(f31(a240,f282(f77(a244),x17171)),f305(f60(a372),a8))),f99(f96(f31(a241,f282(f77(a244),x17171)),x17172))) 7.68/7.79 [1718]~P5(f343(x17182,x17181))+E(f89(f95(f41(a240,f341(f55(a248),x17181)),f320(f57(a369),a9))),f89(f95(f41(a241,f341(f55(a248),x17181)),x17182))) 7.68/7.79 [1719]~P5(f311(x17192,x17191))+E(f101(f92(f39(a240,f294(f63(a243),x17191)),f304(f64(a371),a4))),f101(f92(f39(a241,f294(f63(a243),x17191)),x17192))) 7.68/7.79 [1755]E(x17551,x17552)+~E(f94(f21(a246,f52(a238,f327(f16(a247),x17551))),a2),f94(f21(a246,f52(a238,f327(f16(a247),x17552))),a2)) 7.68/7.79 [1856]~P5(f269(a260,x18562))+P5(f269(a260,f89(f95(f41(a240,f341(f55(a248),x18561)),f320(f57(a369),x18562))))) 7.68/7.79 [1858]~P5(f311(a236,x18582))+P5(f311(a236,f99(f96(f31(a240,f282(f77(a244),x18581)),f305(f60(a372),x18582))))) 7.68/7.79 [1860]~P5(f312(a253,x18602))+P5(f312(a253,f101(f92(f39(a240,f294(f63(a243),x18601)),f304(f64(a371),x18602))))) 7.68/7.79 [1862]~P5(f295(a255,x18622))+P5(f295(a255,f90(f91(f36(a240,f309(f54(a245),x18621)),f313(f66(a373),x18622))))) 7.68/7.79 [1878]~P5(f270(a239,x18781))+P5(f331(f327(a384,f321(a254,x18781)),f321(a254,f93(f45(a240,f273(f53(a242),x18782)),f290(f58(a370),x18781))))) 7.68/7.79 [1898]P5(f269(a260,x18981))+~P5(f269(a260,f89(f95(f41(a240,f341(f55(a248),x18982)),f320(f57(a369),x18981))))) 7.68/7.79 [1899]P5(f311(a236,x18991))+~P5(f311(a236,f99(f96(f31(a240,f282(f77(a244),x18992)),f305(f60(a372),x18991))))) 7.68/7.79 [1900]P5(f312(a253,x19001))+~P5(f312(a253,f101(f92(f39(a240,f294(f63(a243),x19002)),f304(f64(a371),x19001))))) 7.68/7.79 [1901]P5(f295(a255,x19011))+~P5(f295(a255,f90(f91(f36(a240,f309(f54(a245),x19012)),f313(f66(a373),x19011))))) 7.68/7.79 [1995]P5(f311(f392(x19951),f99(f96(f31(a240,f282(f77(a244),f344(a379,x19952))),f305(f60(a372),a8)))))+~P5(f311(f392(f99(f96(f31(a240,f282(f77(a244),f344(a379,x19952))),f305(f60(a372),x19951)))),f99(f96(f31(a240,f282(f77(a244),f266(f395(f6(x19952))))),f305(f60(a372),a8))))) 7.68/7.79 [1835]~P5(f268(a261,x18352))+P5(f268(a261,f94(f21(a246,f52(a238,f327(f16(a247),x18351))),x18352))) 7.68/7.79 [1888]P5(f268(a261,x18881))+~P5(f268(a261,f94(f21(a246,f52(a238,f327(f16(a247),x18882))),x18881))) 7.68/7.79 [1891]E(x18911,x18912)+~P5(f268(f328(a376,x18911),f94(f21(a246,f52(a238,f327(f16(a247),x18912))),a2))) 7.68/7.79 [1930]~P5(f269(a260,x19301))+P5(f331(f327(a384,f318(a259,x19301)),f318(a259,f89(f95(f41(a240,f341(f55(a248),x19302)),f320(f57(a369),x19301)))))) 7.68/7.79 [1931]~P5(f312(a253,x19311))+P5(f331(f327(a384,f306(a251,x19311)),f306(a251,f101(f92(f39(a240,f294(f63(a243),x19312)),f304(f64(a371),x19311)))))) 7.68/7.79 [1932]~P5(f311(a236,x19321))+P5(f331(f327(a384,f324(a257,x19321)),f324(a257,f99(f96(f31(a240,f282(f77(a244),x19322)),f305(f60(a372),x19321)))))) 7.68/7.79 [1933]~P5(f295(a255,x19331))+P5(f331(f327(a384,f315(a252,x19331)),f315(a252,f90(f91(f36(a240,f309(f54(a245),x19332)),f313(f66(a373),x19331)))))) 7.68/7.79 [1919]~P5(f268(a261,x19191))+P5(f331(f327(a384,f301(a256,x19191)),f301(a256,f94(f21(a246,f52(a238,f327(f16(a247),x19192))),x19191)))) 7.68/7.79 [1075]E(x10751,x10752)+~E(f267(f382(x10753),x10751),f267(f382(x10753),x10752)) 7.68/7.79 [1076]E(x10761,x10762)+~E(f267(f382(x10761),x10763),f267(f382(x10762),x10763)) 7.68/7.79 [1151]~E(f267(f382(x11511),x11513),x11512)+P5(f331(f327(a384,x11511),x11512)) 7.68/7.79 [1449]P6(f189(x14491,x14492,x14493))+~P5(f268(f273(a385,x14491),f354(x14492,x14493))) 7.68/7.79 [1450]P4(f135(x14501,x14502,x14503))+~P5(f268(f328(a376,x14501),f354(x14502,x14503))) 7.68/7.79 [1451]P8(f217(x14511,x14512,x14513))+~P5(f268(f328(a376,x14511),f375(x14512,x14513))) 7.68/7.79 [1485]E(f346(x14851,f217(x14852,x14851,x14853)),x14852)+~P5(f268(f328(a376,x14852),f375(x14851,x14853))) 7.68/7.79 [1486]E(f285(x14861,f135(x14862,x14861,x14863)),x14862)+~P5(f268(f328(a376,x14862),f354(x14861,x14863))) 7.68/7.79 [1487]E(f354(x14871,f189(x14872,x14871,x14873)),x14872)+~P5(f268(f273(a385,x14872),f354(x14871,x14873))) 7.68/7.79 [1538]~P5(f311(f294(a386,x15382),x15383))+P5(f268(f273(a385,f354(x15381,x15382)),f354(x15381,x15383))) 7.68/7.79 [1539]~P5(f269(f336(a369,x15392),x15393))+P5(f268(f328(a376,f346(x15391,x15392)),f375(x15391,x15393))) 7.68/7.79 [1540]~P5(f311(f277(a372,x15402),x15403))+P5(f268(f328(a376,f285(x15401,x15402)),f354(x15401,x15403))) 7.68/7.79 [1541]~P5(f311(f294(a386,x15412),x15413))+P5(f269(f309(a389,f364(x15411,x15412)),f364(x15411,x15413))) 7.68/7.79 [1542]~P5(f268(f328(a376,x15422),x15423))+P5(f269(f336(a369,f335(x15421,x15422)),f367(x15421,x15423))) 7.68/7.79 [1545]~P5(f268(f273(a385,x15451),x15453))+P5(f286(f274(a390,f331(x15451,x15452)),f331(x15453,x15452))) 7.68/7.79 [1547]~P5(f269(f309(a389,x15471),x15473))+P5(f286(f274(a390,f343(x15471,x15472)),f343(x15473,x15472))) 7.68/7.79 [1549]~P5(f311(f294(a386,x15491),x15493))+P5(f286(f274(a390,f275(x15491,x15492)),f275(x15493,x15492))) 7.68/7.79 [1550]~P5(f269(f309(a389,x15502),x15503))+P5(f311(f294(a386,f332(x15501,x15502)),f332(x15501,x15503))) 7.68/7.79 [1551]~P5(f268(f273(a385,x15512),x15513))+P5(f311(f294(a386,f350(x15511,x15512)),f350(x15511,x15513))) 7.68/7.79 [1552]~P5(f269(f336(a369,x15522),x15523))+P5(f311(f277(a372,f344(x15521,x15522)),f332(x15521,x15523))) 7.68/7.79 [1553]~P5(f268(f328(a376,x15532),x15533))+P5(f311(f277(a372,f330(x15531,x15532)),f350(x15531,x15533))) 7.68/7.79 [1744]E(f94(f21(a246,f52(a238,f327(f16(a247),f346(x17441,x17442)))),f375(x17441,x17443)),f375(x17441,x17443))+~P5(f269(f336(a369,x17442),x17443)) 7.68/7.79 [1745]E(f94(f21(a246,f52(a238,f327(f16(a247),f285(x17451,x17452)))),f354(x17451,x17453)),f354(x17451,x17453))+~P5(f311(f277(a372,x17452),x17453)) 7.68/7.79 [1233]~E(x12332,f267(a394,f267(f382(x12331),x12333)))+P5(f331(f327(a383,x12331),x12332)) 7.68/7.79 [1410]~P5(f331(f327(a384,x14101),x14103))+P5(f331(f327(a384,x14101),f267(f382(x14102),x14103))) 7.68/7.79 [1412]~P5(f331(f327(a384,x14121),x14122))+P5(f331(f327(a384,x14121),f267(f382(x14122),x14123))) 7.68/7.79 [1414]~P5(f331(f327(a383,x14141),x14143))+P5(f331(f327(a383,x14141),f267(f382(x14142),x14143))) 7.68/7.79 [1416]~P5(f331(f327(a383,x14161),x14162))+P5(f331(f327(a383,x14161),f267(f382(x14162),x14163))) 7.68/7.79 [1432]P4(f124(x14321,x14322,x14323))+P5(f268(f273(a385,f354(x14321,x14323)),x14322)) 7.68/7.79 [1433]P4(f142(x14331,x14332,x14333))+P5(f269(f309(a389,f364(x14331,x14333)),x14332)) 7.68/7.79 [1434]P8(f176(x14341,x14342,x14343))+P5(f268(f273(a385,f375(x14341,x14343)),x14342)) 7.68/7.79 [1435]P8(f106(x14351,x14352,x14353))+P5(f269(f309(a389,f374(x14351,x14353)),x14352)) 7.68/7.79 [1436]P8(f144(x14361,x14362,x14363))+P5(f311(f294(a386,f332(x14361,x14363)),x14362)) 7.68/7.79 [1630]~P5(f331(f327(a384,x16302),x16303))+P5(f331(f327(a384,f267(f382(x16301),x16302)),f267(f382(x16301),x16303))) 7.68/7.79 [1631]~P5(f331(f327(a384,x16311),x16313))+P5(f331(f327(a384,f267(f382(x16311),x16312)),f267(f382(x16313),x16312))) 7.68/7.79 [1632]~P5(f331(f327(a384,x16323),x16322))+P5(f331(f327(a384,f267(f378(x16321),x16322)),f267(f378(x16321),x16323))) 7.68/7.79 [1633]~P5(f331(f327(a384,x16331),x16333))+P5(f331(f327(a384,f267(f378(x16331),x16332)),f267(f378(x16333),x16332))) 7.68/7.79 [1634]~P5(f331(f327(a383,x16342),x16343))+P5(f331(f327(a383,f267(f382(x16341),x16342)),f267(f382(x16341),x16343))) 7.68/7.79 [1635]~P5(f331(f327(a383,x16351),x16353))+P5(f331(f327(a383,f267(f382(x16351),x16352)),f267(f382(x16353),x16352))) 7.68/7.79 [1741]P5(f331(f327(a384,x17411),x17412))+~P5(f331(f327(a384,f267(f382(x17413),x17411)),f267(f382(x17413),x17412))) 7.68/7.79 [1742]P5(f331(f327(a383,x17421),x17422))+~P5(f331(f327(a383,f267(f382(x17423),x17421)),f267(f382(x17423),x17422))) 7.68/7.79 [1758]P5(f269(f336(a369,f176(x17581,x17583,x17582)),x17582))+P5(f268(f273(a385,f375(x17581,x17582)),x17583)) 7.68/7.79 [1759]P5(f311(f277(a372,f124(x17591,x17593,x17592)),x17592))+P5(f268(f273(a385,f354(x17591,x17592)),x17593)) 7.68/7.79 [1760]P5(f269(f336(a369,f106(x17601,x17603,x17602)),x17602))+P5(f269(f309(a389,f374(x17601,x17602)),x17603)) 7.68/7.79 [1761]P5(f311(f277(a372,f142(x17611,x17613,x17612)),x17612))+P5(f269(f309(a389,f364(x17611,x17612)),x17613)) 7.68/7.79 [1762]P5(f268(f328(a376,f154(x17621,x17623,x17622)),x17622))+P5(f269(f309(a389,f367(x17621,x17622)),x17623)) 7.68/7.79 [1763]P5(f269(f336(a369,f144(x17631,x17633,x17632)),x17632))+P5(f311(f294(a386,f332(x17631,x17632)),x17633)) 7.68/7.79 [1764]P5(f268(f328(a376,f172(x17641,x17643,x17642)),x17642))+P5(f311(f294(a386,f350(x17641,x17642)),x17643)) 7.68/7.79 [1775]~P5(f268(f328(a376,x17751),f375(x17752,x17753)))+P5(f269(f336(a369,f217(x17751,x17752,x17753)),x17753)) 7.68/7.79 [1776]~P5(f268(f273(a385,x17761),f354(x17762,x17763)))+P5(f311(f294(a386,f189(x17761,x17762,x17763)),x17763)) 7.68/7.79 [1777]~P5(f268(f328(a376,x17771),f354(x17772,x17773)))+P5(f311(f277(a372,f135(x17771,x17772,x17773)),x17773)) 7.68/7.79 [1418]E(f267(f378(f267(f382(x14181),x14182)),x14183),f267(f382(x14181),f267(f378(x14182),x14183)))+~P5(f331(f327(a384,x14183),x14182)) 7.68/7.79 [1419]E(f267(f378(f267(f382(x14191),x14192)),x14193),f267(f378(x14191),f267(f378(x14193),x14192)))+~P5(f331(f327(a384,x14192),x14193)) 7.68/7.79 [1453]E(f267(f378(f267(f382(x14531),x14532)),x14533),f267(f382(f267(f378(x14531),x14533)),x14532))+~P5(f331(f327(a384,x14533),x14531)) 7.68/7.79 [1537]~P5(f331(f327(a383,x15371),x15373))+P5(f331(f327(a383,f267(f378(x15371),x15372)),x15373)) 7.68/7.79 [1561]~P5(f331(f327(a384,x15612),x15613))+E(f267(f378(f267(f382(x15611),x15612)),f267(a394,x15613)),f267(f378(x15611),f267(a394,f267(f378(x15613),x15612)))) 7.68/7.79 [1625]E(f332(f87(x16251),x16252),f99(f96(f31(a240,f282(f77(a244),x16251)),f305(f60(a372),a8))))+~P5(f269(f336(a369,x16253),x16252)) 7.68/7.79 [1642]P5(f331(f327(a384,x16421),x16422))+~P5(f331(f327(a384,f267(f382(x16423),x16421)),x16422)) 7.68/7.79 [1643]P5(f331(f327(a384,x16431),x16432))+~P5(f331(f327(a384,f267(f382(x16431),x16433)),x16432)) 7.68/7.79 [1644]P5(f331(f327(a383,x16441),x16442))+~P5(f331(f327(a383,f267(f382(x16441),x16443)),x16442)) 7.68/7.79 [1664]~P5(f331(f327(a384,x16641),f267(f382(x16643),x16642)))+P5(f331(f327(a384,f267(f378(x16641),x16642)),x16643)) 7.68/7.79 [1665]~P5(f331(f327(a383,x16651),f267(f378(x16653),x16652)))+P5(f331(f327(a383,f267(f382(x16651),x16652)),x16653)) 7.68/7.79 [1714]P5(f331(f327(a384,x17141),f267(f382(x17142),x17143)))+~P5(f331(f327(a384,f267(f378(x17141),x17143)),x17142)) 7.68/7.79 [1715]P5(f331(f327(a383,x17151),f267(f378(x17152),x17153)))+~P5(f331(f327(a383,f267(f382(x17151),x17153)),x17152)) 7.68/7.79 [1785]E(f89(f95(f41(a240,f341(f55(a248),f345(x17851,x17852))),f320(f57(a369),f374(x17851,x17853)))),f374(x17851,x17853))+~P5(f269(f336(a369,x17852),x17853)) 7.68/7.79 [1786]E(f99(f96(f31(a240,f282(f77(a244),f330(x17861,x17862))),f305(f60(a372),f350(x17861,x17863)))),f350(x17861,x17863))+~P5(f268(f328(a376,x17862),x17863)) 7.68/7.79 [1787]E(f99(f96(f31(a240,f282(f77(a244),f344(x17871,x17872))),f305(f60(a372),f332(x17871,x17873)))),f332(x17871,x17873))+~P5(f269(f336(a369,x17872),x17873)) 7.68/7.79 [1788]E(f89(f95(f41(a240,f341(f55(a248),f283(x17881,x17882))),f320(f57(a369),f364(x17881,x17883)))),f364(x17881,x17883))+~P5(f311(f277(a372,x17882),x17883)) 7.68/7.79 [1895]P5(f331(f327(a383,f139(x18951,x18952,x18953)),f143(x18951,x18952,x18953)))+P5(f331(f327(a384,f267(f382(f267(x18953,x18951)),x18952)),f267(x18953,f267(f382(x18951),x18952)))) 7.68/7.79 [1908]P5(f268(f273(a385,f375(x19081,x19082)),x19083))+~P5(f268(f328(a376,f346(x19081,f176(x19081,x19083,x19082))),x19083)) 7.68/7.79 [1909]P5(f268(f273(a385,f354(x19091,x19092)),x19093))+~P5(f268(f328(a376,f285(x19091,f124(x19091,x19093,x19092))),x19093)) 7.68/7.79 [1910]P5(f269(f309(a389,f374(x19101,x19102)),x19103))+~P5(f269(f336(a369,f345(x19101,f106(x19101,x19103,x19102))),x19103)) 7.68/7.79 [1911]P5(f269(f309(a389,f364(x19111,x19112)),x19113))+~P5(f269(f336(a369,f283(x19111,f142(x19111,x19113,x19112))),x19113)) 7.68/7.79 [1912]P5(f269(f309(a389,f367(x19121,x19122)),x19123))+~P5(f269(f336(a369,f335(x19121,f154(x19121,x19123,x19122))),x19123)) 7.68/7.79 [1913]P5(f311(f294(a386,f332(x19131,x19132)),x19133))+~P5(f311(f277(a372,f344(x19131,f144(x19131,x19133,x19132))),x19133)) 7.68/7.79 [1914]P5(f311(f294(a386,f350(x19141,x19142)),x19143))+~P5(f311(f277(a372,f330(x19141,f172(x19141,x19143,x19142))),x19143)) 7.68/7.79 [1948]~P5(f331(f327(a383,f267(x19481,f139(x19482,x19483,x19481))),f267(x19481,f143(x19482,x19483,x19481))))+P5(f331(f327(a384,f267(f382(f267(x19481,x19482)),x19483)),f267(x19481,f267(f382(x19482),x19483)))) 7.68/7.79 [1645]~P5(f331(f327(a384,x16452),x16451))+E(f267(f378(f267(a394,f267(f378(x16451),x16452))),x16453),f267(f378(f267(a394,x16451)),f267(f382(x16452),x16453))) 7.68/7.79 [1743]~P5(f331(f327(a384,x17433),x17432))+P5(f331(f327(a384,x17431),f267(f378(f267(f382(x17432),x17431)),x17433))) 7.68/7.79 [1863]~E(x18631,x18632)+P5(f269(f336(a369,x18631),f89(f95(f41(a240,f341(f55(a248),x18632)),f320(f57(a369),x18633))))) 7.68/7.79 [1864]~E(x18641,x18642)+P5(f311(f277(a372,x18641),f99(f96(f31(a240,f282(f77(a244),x18642)),f305(f60(a372),x18643))))) 7.68/7.79 [1870]~P5(f269(f309(a389,x18701),x18703))+P5(f269(f309(a389,x18701),f89(f95(f41(a240,f341(f55(a248),x18702)),f320(f57(a369),x18703))))) 7.68/7.79 [1872]~P5(f269(f336(a369,x18721),x18723))+P5(f269(f336(a369,x18721),f89(f95(f41(a240,f341(f55(a248),x18722)),f320(f57(a369),x18723))))) 7.68/7.79 [1873]~P5(f311(f294(a386,x18731),x18733))+P5(f311(f294(a386,x18731),f99(f96(f31(a240,f282(f77(a244),x18732)),f305(f60(a372),x18733))))) 7.68/7.79 [1875]~P5(f311(f277(a372,x18751),x18753))+P5(f311(f277(a372,x18751),f99(f96(f31(a240,f282(f77(a244),x18752)),f305(f60(a372),x18753))))) 7.68/7.79 [1949]~P5(f269(f309(a389,x19492),x19493))+P5(f269(f309(a389,f89(f95(f41(a240,f341(f55(a248),x19491)),f320(f57(a369),x19492)))),f89(f95(f41(a240,f341(f55(a248),x19491)),f320(f57(a369),x19493))))) 7.68/7.79 [1950]~P5(f311(f294(a386,x19502),x19503))+P5(f311(f294(a386,f99(f96(f31(a240,f282(f77(a244),x19501)),f305(f60(a372),x19502)))),f99(f96(f31(a240,f282(f77(a244),x19501)),f305(f60(a372),x19503))))) 7.68/7.79 [1832]~E(x18323,x18321)+P5(f331(f94(f21(a246,f52(a238,f327(f16(a247),x18321))),x18322),x18323)) 7.68/7.79 [1837]~P5(f331(x18372,x18373))+P5(f331(f94(f21(a246,f52(a238,f327(f16(a247),x18371))),x18372),x18373)) 7.68/7.79 [1838]~E(x18382,x18381)+P5(f268(f328(a376,x18381),f94(f21(a246,f52(a238,f327(f16(a247),x18382))),x18383))) 7.68/7.79 [1839]~E(x18391,x18392)+P5(f268(f328(a376,x18391),f94(f21(a246,f52(a238,f327(f16(a247),x18392))),x18393))) 7.68/7.79 [1845]~P5(f268(f273(a385,x18451),x18453))+P5(f268(f273(a385,x18451),f94(f21(a246,f52(a238,f327(f16(a247),x18452))),x18453))) 7.68/7.79 [1848]~P5(f268(f328(a376,x18481),x18483))+P5(f268(f328(a376,x18481),f94(f21(a246,f52(a238,f327(f16(a247),x18482))),x18483))) 7.68/7.79 [1944]~P5(f268(f273(a385,x19442),x19443))+P5(f268(f273(a385,f94(f21(a246,f52(a238,f327(f16(a247),x19441))),x19442)),f94(f21(a246,f52(a238,f327(f16(a247),x19441))),x19443))) 7.68/7.79 [1956]P5(f269(f309(a389,x19561),x19562))+~P5(f269(f309(a389,f89(f95(f41(a240,f341(f55(a248),x19563)),f320(f57(a369),x19561)))),x19562)) 7.68/7.79 [1957]P5(f269(f336(a369,x19571),x19572))+~P5(f269(f309(a389,f89(f95(f41(a240,f341(f55(a248),x19571)),f320(f57(a369),x19573)))),x19572)) 7.68/7.79 [1958]P5(f311(f294(a386,x19581),x19582))+~P5(f311(f294(a386,f99(f96(f31(a240,f282(f77(a244),x19583)),f305(f60(a372),x19581)))),x19582)) 7.68/7.79 [1959]P5(f311(f277(a372,x19591),x19592))+~P5(f311(f294(a386,f99(f96(f31(a240,f282(f77(a244),x19591)),f305(f60(a372),x19593)))),x19592)) 7.68/7.79 [1946]P5(f268(f273(a385,x19461),x19462))+~P5(f268(f273(a385,f94(f21(a246,f52(a238,f327(f16(a247),x19463))),x19461)),x19462)) 7.68/7.79 [1947]P5(f268(f328(a376,x19471),x19472))+~P5(f268(f273(a385,f94(f21(a246,f52(a238,f327(f16(a247),x19471))),x19473)),x19472)) 7.68/7.79 [938]~P3(x9381)+E(a237,x9381)+E(a12,x9381) 7.68/7.79 [960]~P6(x9601)+E(x9601,a8)+P4(f192(x9601)) 7.68/7.79 [961]~P6(x9611)+E(x9611,a8)+P4(f230(x9611)) 7.68/7.79 [962]~P7(x9621)+E(a9,x9621)+P8(f156(x9621)) 7.68/7.79 [963]~P7(x9631)+E(a9,x9631)+P8(f223(x9631)) 7.68/7.79 [1188]~P6(x11881)+E(x11881,a8)+~P5(f311(f294(a386,x11881),a8)) 7.68/7.79 [1189]~P7(x11891)+E(x11891,a9)+~P5(f269(f309(a389,x11891),a9)) 7.68/7.79 [1191]~P6(x11911)+E(a8,x11911)+~P5(f311(f294(a386,x11911),a8)) 7.68/7.79 [1193]~P7(x11931)+E(a9,x11931)+~P5(f269(f309(a389,x11931),a9)) 7.68/7.79 [1200]P5(x12001)+~P5(a10)+~P5(f286(f274(a390,x12001),a10)) 7.68/7.79 [1202]~P5(x12021)+P5(a10)+~P5(f286(f274(a390,x12021),a10)) 7.68/7.79 [1147]~P6(x11471)+E(x11471,a8)+P5(f311(f277(a372,f192(x11471)),x11471)) 7.68/7.79 [1148]~P6(x11481)+E(x11481,a8)+P5(f311(f277(a372,f230(x11481)),x11481)) 7.68/7.79 [1149]~P7(x11491)+E(a9,x11491)+P5(f269(f336(a369,f156(x11491)),x11491)) 7.68/7.79 [1150]~P7(x11501)+E(a9,x11501)+P5(f269(f336(a369,f223(x11501)),x11501)) 7.68/7.79 [965]~P7(x9652)+~E(a9,x9652)+E(f332(x9651,x9652),a8) 7.68/7.79 [975]~P7(x9751)+E(a9,x9751)+~E(f332(x9752,x9751),a8) 7.68/7.79 [1034]~P2(x10341)+~P7(x10342)+P3(f269(x10341,x10342)) 7.68/7.79 [1035]~P1(x10351)+~P6(x10352)+P3(f311(x10351,x10352)) 7.68/7.79 [1036]~P7(x10361)+~P8(x10362)+P3(f343(x10361,x10362)) 7.68/7.79 [1037]~P6(x10371)+~P4(x10372)+P3(f275(x10371,x10372)) 7.68/7.79 [1065]~P4(x10652)+~P5(f275(x10651,x10652))+~E(f99(x10651),a8) 7.68/7.79 [1067]~P8(x10672)+~P5(f343(x10671,x10672))+~E(f89(x10671),a9) 7.68/7.79 [1069]~P7(x10692)+~P5(f269(x10691,x10692))+~E(f90(x10691),a7) 7.68/7.79 [1070]~P6(x10702)+~P5(f311(x10701,x10702))+~E(f101(x10701),a4) 7.68/7.79 [1057]E(x10571,a11)+E(x10572,a11)+~E(f267(f382(x10572),x10571),f267(a394,a11)) 7.68/7.79 [1058]E(x10581,a11)+E(a11,x10582)+~E(f267(f382(x10582),x10581),f267(a394,a11)) 7.68/7.79 [1060]~E(a11,x10601)+~E(f267(a394,a11),x10602)+E(f267(f382(x10601),x10602),f267(a394,a11)) 7.68/7.79 [1061]~E(x10612,a11)+~E(x10611,f267(a394,a11))+E(f267(f382(x10611),x10612),f267(a394,a11)) 7.68/7.79 [1062]~E(x10621,a11)+~E(x10622,f267(a394,a11))+E(f267(f382(x10621),x10622),f267(a394,a11)) 7.68/7.79 [1071]E(x10711,a11)+E(x10711,f267(a394,a11))+~E(f267(f382(x10712),x10711),f267(a394,a11)) 7.68/7.79 [1072]E(x10721,a11)+E(x10721,f267(a394,a11))+~E(f267(f382(x10721),x10722),f267(a394,a11)) 7.68/7.79 [1073]E(x10731,a11)+E(f267(a394,a11),x10731)+~E(f267(f382(x10732),x10731),f267(a394,a11)) 7.68/7.79 [1074]E(a11,x10741)+E(x10741,f267(a394,a11))+~E(f267(f382(x10741),x10742),f267(a394,a11)) 7.68/7.79 [1077]E(x10771,x10772)+~E(f267(f378(x10771),x10772),a11)+~E(f267(f378(x10772),x10771),a11) 7.68/7.79 [1078]E(x10782,f267(a394,a11))+E(x10781,f267(a394,a11))+~E(f267(f382(x10781),x10782),f267(a394,a11)) 7.68/7.79 [1079]E(f267(a394,a11),x10792)+E(x10791,f267(a394,a11))+~E(f267(f382(x10791),x10792),f267(a394,a11)) 7.68/7.79 [1127]P5(x11271)+P5(x11272)+P5(f286(f274(a390,x11272),x11271)) 7.68/7.79 [1130]~P5(x11302)+~P5(x11301)+P5(f286(f274(a390,x11301),x11302)) 7.68/7.79 [1131]~P5(x11311)+~P5(x11312)+P5(f286(f274(a241,x11311),x11312)) 7.68/7.79 [1204]P5(x12041)+P5(x12042)+~P5(f286(f274(a240,x12042),x12041)) 7.68/7.79 [1205]P5(x12051)+~P5(x12052)+~P5(f286(f274(a246,x12052),x12051)) 7.68/7.79 [1232]E(x12321,x12322)+P5(f331(f327(a383,x12322),x12321))+P5(f331(f327(a383,x12321),x12322)) 7.68/7.79 [1237]E(f267(a394,x12371),x12372)+E(f267(a394,f218(x12371,x12372)),x12372)+~P5(f331(f327(a383,x12371),x12372)) 7.68/7.79 [1242]P6(f138(x12421,x12422))+P5(f312(a253,x12422))+~P5(f268(a261,f366(x12421,x12422))) 7.68/7.79 [1243]P6(f214(x12431,x12432))+P5(f312(a253,x12432))+~P5(f269(a260,f353(x12431,x12432))) 7.68/7.79 [1244]P4(f173(x12441,x12442))+P5(f311(a236,x12442))+~P5(f312(a253,f355(x12441,x12442))) 7.68/7.79 [1245]P4(f140(x12451,x12452))+P5(f311(a236,x12452))+~P5(f311(a236,f361(x12451,x12452))) 7.68/7.79 [1246]P4(f147(x12461,x12462))+P5(f311(a236,x12462))+~P5(f269(a260,f364(x12461,x12462))) 7.68/7.79 [1247]P4(f157(x12471,x12472))+P5(f311(a236,x12472))+~P5(f295(a255,f356(x12471,x12472))) 7.68/7.79 [1248]P4(f174(x12481,x12482))+P5(f311(a236,x12482))+~P5(f268(a261,f354(x12481,x12482))) 7.68/7.79 [1249]P4(f231(x12491,x12492))+P5(f311(a236,x12492))+~P5(f270(a239,f363(x12491,x12492))) 7.68/7.79 [1250]P7(f158(x12501,x12502))+P5(f295(a255,x12502))+~P5(f269(a260,f348(x12501,x12502))) 7.68/7.79 [1251]P7(f197(x12511,x12512))+P5(f295(a255,x12512))+~P5(f268(a261,f349(x12511,x12512))) 7.68/7.79 [1252]P8(f141(x12521,x12522))+P5(f269(a260,x12522))+~P5(f312(a253,f347(x12521,x12522))) 7.68/7.79 [1253]P8(f149(x12531,x12532))+P5(f269(a260,x12532))+~P5(f295(a255,f357(x12531,x12532))) 7.68/7.79 [1254]P8(f175(x12541,x12542))+P5(f269(a260,x12542))+~P5(f270(a239,f359(x12541,x12542))) 7.68/7.79 [1255]P8(f198(x12551,x12552))+P5(f269(a260,x12552))+~P5(f268(a261,f375(x12551,x12552))) 7.68/7.79 [1256]P8(f219(x12561,x12562))+P5(f269(a260,x12562))+~P5(f269(a260,f374(x12561,x12562))) 7.68/7.79 [1257]P8(f110(x12571,x12572))+P5(f269(a260,x12572))+~P5(f311(a236,f332(x12571,x12572))) 7.68/7.79 [1259]P5(f268(a261,x12591))+~P5(f268(a261,x12592))+~P5(f268(f273(a385,x12591),x12592)) 7.68/7.79 [1261]P5(f269(a260,x12611))+~P5(f269(a260,x12612))+~P5(f269(f309(a389,x12611),x12612)) 7.68/7.79 [1263]P5(f311(a236,x12631))+~P5(f311(a236,x12632))+~P5(f311(f294(a386,x12631),x12632)) 7.68/7.79 [1265]P5(f270(a239,x12651))+~P5(f270(a239,x12652))+~P5(f270(f298(a387,x12651),x12652)) 7.68/7.79 [1267]P5(f312(a253,x12671))+~P5(f312(a253,x12672))+~P5(f312(f293(a388,x12671),x12672)) 7.68/7.79 [1269]P5(f295(a255,x12691))+~P5(f295(a255,x12692))+~P5(f295(f310(a391,x12691),x12692)) 7.68/7.79 [1283]E(x12831,x12832)+P5(f331(f327(a383,x12832),x12831))+~P5(f331(f327(a384,x12832),x12831)) 7.68/7.79 [1285]E(x12851,x12852)+P5(f331(f327(a383,x12851),x12852))+~P5(f331(f327(a384,x12851),x12852)) 7.68/7.79 [1289]~E(x12892,x12891)+P5(f331(f327(a383,x12891),x12892))+P5(f331(f327(a383,x12891),f267(a394,x12892))) 7.68/7.79 [1332]E(x13321,x13322)+~P5(f268(f273(a385,x13322),x13321))+~P5(f268(f273(a385,x13321),x13322)) 7.68/7.79 [1337]E(x13371,x13372)+~P5(f331(f327(a384,x13372),x13371))+~P5(f331(f327(a384,x13371),x13372)) 7.68/7.79 [1339]~E(x13392,x13391)+~P5(f331(f327(a384,x13392),x13391))+P5(f331(f327(a383,x13391),f267(a394,x13392))) 7.68/7.79 [1340]~P5(f268(a261,x13402))+~P5(f268(f328(a376,x13401),x13402))+P5(f331(f327(a384,x13401),f119(x13402))) 7.68/7.79 [1341]~P5(f268(a261,x13412))+~P5(f268(f328(a376,x13411),x13412))+P5(f331(f327(a383,x13411),f171(x13412))) 7.68/7.79 [1369]E(f267(a394,x13691),x13692)+~P5(f331(f327(a383,x13691),x13692))+P5(f331(f327(a383,x13691),f218(x13691,x13692))) 7.68/7.79 [1374]E(x13741,x13742)+P5(f331(f327(a383,x13741),x13742))+~P5(f331(f327(a383,x13741),f267(a394,x13742))) 7.68/7.79 [1424]E(x14241,f267(a394,x14242))+P5(f331(f327(a384,x14241),x14242))+~P5(f331(f327(a384,x14241),f267(a394,x14242))) 7.68/7.79 [1454]E(x14541,x14542)+~P5(f331(f327(a384,x14542),x14541))+~P5(f331(f327(a383,x14541),f267(a394,x14542))) 7.68/7.79 [1606]~P5(f270(a239,x16062))+~P5(f270(f298(a387,x16061),x16062))+P5(f331(f327(a384,f321(a254,x16061)),f321(a254,x16062))) 7.68/7.79 [1607]~P5(f269(a260,x16072))+~P5(f269(f309(a389,x16071),x16072))+P5(f331(f327(a384,f318(a259,x16071)),f318(a259,x16072))) 7.68/7.79 [1608]~P5(f312(a253,x16082))+~P5(f312(f293(a388,x16081),x16082))+P5(f331(f327(a384,f306(a251,x16081)),f306(a251,x16082))) 7.68/7.79 [1609]~P5(f311(a236,x16092))+~P5(f311(f294(a386,x16091),x16092))+P5(f331(f327(a384,f324(a257,x16091)),f324(a257,x16092))) 7.68/7.79 [1610]~P5(f268(a261,x16102))+~P5(f268(f273(a385,x16101),x16102))+P5(f331(f327(a384,f301(a256,x16101)),f301(a256,x16102))) 7.68/7.79 [1611]~P5(f295(a255,x16112))+~P5(f295(f310(a391,x16111),x16112))+P5(f331(f327(a384,f315(a252,x16111)),f315(a252,x16112))) 7.68/7.79 [1365]~P5(f268(a261,x13651))+~P5(f268(a261,x13652))+P5(f268(a261,f94(f21(a240,x13651),x13652))) 7.68/7.79 [1366]~P5(f270(a239,x13661))+~P5(f270(a239,x13662))+P5(f270(a239,f93(f45(a240,x13661),x13662))) 7.68/7.79 [1441]E(x14411,f267(a394,x14412))+~P5(f331(f327(a383,x14412),x14411))+P5(f331(f327(a383,f267(a394,x14412)),x14411)) 7.68/7.79 [1496]P5(f268(a261,x14961))+~P5(f269(a260,f367(x14962,x14961)))+P5(f268(f328(a376,f152(x14962,x14961)),x14961)) 7.68/7.79 [1497]P5(f268(a261,x14971))+~P5(f312(a253,f333(x14972,x14971)))+P5(f268(f328(a376,f165(x14972,x14971)),x14971)) 7.68/7.79 [1498]P5(f268(a261,x14981))+~P5(f295(a255,f334(x14982,x14981)))+P5(f268(f328(a376,f185(x14982,x14981)),x14981)) 7.68/7.79 [1499]P5(f268(a261,x14991))+~P5(f270(a239,f358(x14992,x14991)))+P5(f268(f328(a376,f210(x14992,x14991)),x14991)) 7.68/7.79 [1500]P5(f268(a261,x15001))+~P5(f268(a261,f368(x15002,x15001)))+P5(f268(f328(a376,f211(x15002,x15001)),x15001)) 7.68/7.79 [1501]P5(f268(a261,x15011))+~P5(f311(a236,f350(x15012,x15011)))+P5(f268(f328(a376,f145(x15012,x15011)),x15011)) 7.68/7.79 [1502]P5(f269(a260,x15021))+~P5(f312(a253,f347(x15022,x15021)))+P5(f269(f336(a369,f141(x15022,x15021)),x15021)) 7.68/7.79 [1503]P5(f269(a260,x15031))+~P5(f295(a255,f357(x15032,x15031)))+P5(f269(f336(a369,f149(x15032,x15031)),x15031)) 7.68/7.79 [1504]P5(f269(a260,x15041))+~P5(f270(a239,f359(x15042,x15041)))+P5(f269(f336(a369,f175(x15042,x15041)),x15041)) 7.68/7.79 [1505]P5(f269(a260,x15051))+~P5(f268(a261,f375(x15052,x15051)))+P5(f269(f336(a369,f198(x15052,x15051)),x15051)) 7.68/7.79 [1506]P5(f269(a260,x15061))+~P5(f269(a260,f374(x15062,x15061)))+P5(f269(f336(a369,f219(x15062,x15061)),x15061)) 7.68/7.79 [1507]P5(f269(a260,x15071))+~P5(f311(a236,f332(x15072,x15071)))+P5(f269(f336(a369,f110(x15072,x15071)),x15071)) 7.68/7.79 [1508]P5(f311(a236,x15081))+~P5(f312(a253,f355(x15082,x15081)))+P5(f311(f277(a372,f173(x15082,x15081)),x15081)) 7.68/7.79 [1509]P5(f311(a236,x15091))+~P5(f311(a236,f361(x15092,x15091)))+P5(f311(f277(a372,f140(x15092,x15091)),x15091)) 7.68/7.79 [1510]P5(f311(a236,x15101))+~P5(f269(a260,f364(x15102,x15101)))+P5(f311(f277(a372,f147(x15102,x15101)),x15101)) 7.68/7.79 [1511]P5(f311(a236,x15111))+~P5(f295(a255,f356(x15112,x15111)))+P5(f311(f277(a372,f157(x15112,x15111)),x15111)) 7.68/7.79 [1512]P5(f311(a236,x15121))+~P5(f268(a261,f354(x15122,x15121)))+P5(f311(f277(a372,f174(x15122,x15121)),x15121)) 7.68/7.79 [1513]P5(f311(a236,x15131))+~P5(f270(a239,f363(x15132,x15131)))+P5(f311(f277(a372,f231(x15132,x15131)),x15131)) 7.68/7.79 [1514]P5(f270(a239,x15141))+~P5(f268(a261,f360(x15142,x15141)))+P5(f270(f303(a370,f181(x15142,x15141)),x15141)) 7.68/7.79 [1515]P5(f270(a239,x15151))+~P5(f269(a260,f352(x15152,x15151)))+P5(f270(f303(a370,f203(x15152,x15151)),x15151)) 7.68/7.79 [1516]P5(f312(a253,x15161))+~P5(f268(a261,f366(x15162,x15161)))+P5(f312(f308(a371,f138(x15162,x15161)),x15161)) 7.68/7.79 [1517]P5(f312(a253,x15171))+~P5(f269(a260,f353(x15172,x15171)))+P5(f312(f308(a371,f214(x15172,x15171)),x15171)) 7.68/7.79 [1518]P5(f295(a255,x15181))+~P5(f269(a260,f348(x15182,x15181)))+P5(f295(f314(a373,f158(x15182,x15181)),x15181)) 7.68/7.79 [1519]P5(f295(a255,x15191))+~P5(f268(a261,f349(x15192,x15191)))+P5(f295(f314(a373,f197(x15192,x15191)),x15191)) 7.68/7.79 [1431]~P7(x14311)+E(x14311,a9)+E(f99(f96(f31(a240,f282(f77(a244),x14312)),f305(f60(a372),a8))),f332(f87(x14312),x14311)) 7.68/7.79 [1623]~P6(x16232)+E(f99(f96(f31(a240,f282(f77(a244),x16231)),f305(f60(a372),x16232))),x16232)+~P5(f311(f277(a372,x16231),x16232)) 7.68/7.79 [1624]~P7(x16242)+E(f89(f95(f41(a240,f341(f55(a248),x16241)),f320(f57(a369),x16242))),x16242)+~P5(f269(f336(a369,x16241),x16242)) 7.68/7.79 [1637]~P5(f270(a239,x16372))+P5(f270(f303(a370,x16371),x16372))+E(f321(a254,f93(f45(a240,f273(f53(a242),x16371)),f290(f58(a370),x16372))),f267(a394,f321(a254,x16372))) 7.68/7.79 [1646]~P5(f269(a260,f89(x16461)))+~P5(f269(a260,f89(x16462)))+P5(f269(a260,f89(f95(f41(a240,x16461),x16462)))) 7.68/7.79 [1647]~P5(f311(a236,f99(x16471)))+~P5(f311(a236,f99(x16472)))+P5(f311(a236,f99(f96(f31(a240,x16471),x16472)))) 7.68/7.79 [1648]~P5(f312(a253,f101(x16481)))+~P5(f312(a253,f101(x16482)))+P5(f312(a253,f101(f92(f39(a240,x16481),x16482)))) 7.68/7.79 [1649]~P5(f295(a255,f90(x16492)))+~P5(f295(a255,f90(x16491)))+P5(f295(a255,f90(f91(f36(a240,x16491),x16492)))) 7.68/7.79 [1650]~P5(f270(a239,x16502))+~P5(f270(f303(a370,x16501),x16502))+E(f321(a254,f93(f45(a240,f273(f53(a242),x16501)),f290(f58(a370),x16502))),f321(a254,x16502)) 7.68/7.79 [1737]~P1(x17372)+~P6(x17371)+P1(f101(f92(f39(a240,f294(f63(a243),x17371)),f304(f64(a371),x17372)))) 7.68/7.79 [1738]~P2(x17382)+~P7(x17381)+P2(f90(f91(f36(a240,f309(f54(a245),x17381)),f313(f66(a373),x17382)))) 7.68/7.79 [1739]~P6(x17392)+~P4(x17391)+P6(f99(f96(f31(a240,f282(f77(a244),x17391)),f305(f60(a372),x17392)))) 7.68/7.79 [1740]~P7(x17402)+~P8(x17401)+P7(f89(f95(f41(a240,f341(f55(a248),x17401)),f320(f57(a369),x17402)))) 7.68/7.79 [1768]~P5(f269(a260,x17682))+P5(f269(f336(a369,x17681),x17682))+E(f318(a259,f89(f95(f41(a240,f341(f55(a248),x17681)),f320(f57(a369),x17682)))),f267(a394,f318(a259,x17682))) 7.68/7.79 [1769]~P5(f312(a253,x17692))+P5(f312(f308(a371,x17691),x17692))+E(f306(a251,f101(f92(f39(a240,f294(f63(a243),x17691)),f304(f64(a371),x17692)))),f267(a394,f306(a251,x17692))) 7.68/7.79 [1770]~P5(f311(a236,x17702))+P5(f311(f277(a372,x17701),x17702))+E(f324(a257,f99(f96(f31(a240,f282(f77(a244),x17701)),f305(f60(a372),x17702)))),f267(a394,f324(a257,x17702))) 7.68/7.79 [1772]~P5(f295(a255,x17722))+P5(f295(f314(a373,x17721),x17722))+E(f315(a252,f90(f91(f36(a240,f309(f54(a245),x17721)),f313(f66(a373),x17722)))),f267(a394,f315(a252,x17722))) 7.68/7.79 [1789]~P5(f295(a255,x17892))+~P5(f295(f314(a373,x17891),x17892))+E(f315(a252,f90(f91(f36(a240,f309(f54(a245),x17891)),f313(f66(a373),x17892)))),f315(a252,x17892)) 7.68/7.79 [1790]~P5(f269(a260,x17902))+~P5(f269(f336(a369,x17901),x17902))+E(f318(a259,f89(f95(f41(a240,f341(f55(a248),x17901)),f320(f57(a369),x17902)))),f318(a259,x17902)) 7.68/7.79 [1791]~P5(f312(a253,x17912))+~P5(f312(f308(a371,x17911),x17912))+E(f306(a251,f101(f92(f39(a240,f294(f63(a243),x17911)),f304(f64(a371),x17912)))),f306(a251,x17912)) 7.68/7.79 [1792]~P5(f311(a236,x17922))+~P5(f311(f277(a372,x17921),x17922))+E(f324(a257,f99(f96(f31(a240,f282(f77(a244),x17921)),f305(f60(a372),x17922)))),f324(a257,x17922)) 7.68/7.79 [1879]~P5(f403(x18792))+P8(f221(x18791,x18792))+P5(f311(f392(x18791),f99(f96(f31(a240,f282(f77(a244),f266(x18792))),f305(f60(a372),a8))))) 7.68/7.79 [1892]~P5(f403(x18922))+P5(f269(f336(a369,f221(x18921,x18922)),a264))+P5(f311(f392(x18921),f99(f96(f31(a240,f282(f77(a244),f266(x18922))),f305(f60(a372),a8))))) 7.68/7.79 [1936]P5(f268(a261,x19361))+~P5(f268(a261,f368(x19362,x19361)))+~P5(f268(a261,f94(f21(a241,f319(f61(a376),x19361)),f327(f16(f18(a247,x19362)),f267(x19362,f211(x19362,x19361)))))) 7.68/7.79 [1937]P5(f268(a261,x19371))+~P5(f269(a260,f367(x19372,x19371)))+~P5(f268(a261,f94(f21(a241,f319(f61(a376),x19371)),f338(f83(f24(a248,x19372)),f335(x19372,f152(x19372,x19371)))))) 7.68/7.79 [1938]P5(f268(a261,x19381))+~P5(f311(a236,f350(x19382,x19381)))+~P5(f268(a261,f94(f21(a241,f319(f61(a376),x19381)),f284(f80(f28(a244,x19382)),f330(x19382,f145(x19382,x19381)))))) 7.68/7.79 [1939]P5(f268(a261,x19391))+~P5(f270(a239,f358(x19392,x19391)))+~P5(f268(a261,f94(f21(a241,f319(f61(a376),x19391)),f319(f61(f33(a242,x19392)),f327(x19392,f210(x19392,x19391)))))) 7.68/7.79 [1940]P5(f268(a261,x19401))+~P5(f312(a253,f333(x19402,x19401)))+~P5(f268(a261,f94(f21(a241,f319(f61(a376),x19401)),f307(f67(f29(a243,x19402)),f329(x19402,f165(x19402,x19401)))))) 7.68/7.79 [1941]P5(f268(a261,x19411))+~P5(f295(a255,f334(x19412,x19411)))+~P5(f268(a261,f94(f21(a241,f319(f61(a376),x19411)),f287(f74(f35(a245,x19412)),f323(x19412,f185(x19412,x19411)))))) 7.68/7.79 [1942]P5(f270(a239,x19421))+~P5(f268(a261,f360(x19422,x19421)))+~P5(f270(a239,f93(f45(a241,f290(f58(a370),x19421)),f328(f69(f23(a247,x19422)),f301(x19422,f181(x19422,x19421)))))) 7.68/7.79 [1943]P5(f270(a239,x19431))+~P5(f269(a260,f352(x19432,x19431)))+~P5(f270(a239,f93(f45(a241,f290(f58(a370),x19431)),f337(f75(f22(a248,x19432)),f272(x19432,f203(x19432,x19431)))))) 7.68/7.79 [1981]~P5(f403(x19812))+P5(f311(f392(x19811),f99(f96(f31(a240,f282(f77(a244),f266(x19812))),f305(f60(a372),a8)))))+~P5(f311(f392(x19811),f99(f96(f31(a240,f282(f77(a244),f344(a379,f221(x19811,x19812)))),f305(f60(a372),a8))))) 7.68/7.79 [1748]~P5(f268(a261,x17482))+P5(f268(f328(a376,x17481),x17482))+E(f301(a256,f94(f21(a246,f52(a238,f327(f16(a247),x17481))),x17482)),f267(a394,f301(a256,x17482))) 7.68/7.79 [1752]~P5(f268(a261,x17522))+~P5(f268(f328(a376,x17521),x17522))+E(f301(a256,f94(f21(a246,f52(a238,f327(f16(a247),x17521))),x17522)),f301(a256,x17522)) 7.68/7.79 [1897]E(a2,x18971)+E(f94(f21(a246,f52(a238,f327(f16(a247),x18972))),a2),x18971)+~P5(f268(f273(a385,x18971),f94(f21(a246,f52(a238,f327(f16(a247),x18972))),a2))) 7.68/7.79 [1964]P5(f269(a260,x19641))+~P5(f268(a261,f375(x19642,x19641)))+~P5(f269(a260,f89(f95(f41(a241,f320(f57(a369),x19641)),f323(f82(f46(a247,x19642)),f346(x19642,f198(x19642,x19641))))))) 7.68/7.79 [1965]P5(f269(a260,x19651))+~P5(f269(a260,f374(x19652,x19651)))+~P5(f269(a260,f89(f95(f41(a241,f320(f57(a369),x19651)),f341(f55(f43(a248,x19652)),f345(x19652,f219(x19652,x19651))))))) 7.68/7.79 [1966]P5(f269(a260,x19661))+~P5(f311(a236,f332(x19662,x19661)))+~P5(f269(a260,f89(f95(f41(a241,f320(f57(a369),x19661)),f276(f84(f32(a244,x19662)),f344(x19662,f110(x19662,x19661))))))) 7.68/7.79 [1967]P5(f269(a260,x19671))+~P5(f270(a239,f359(x19672,x19671)))+~P5(f269(a260,f89(f95(f41(a241,f320(f57(a369),x19671)),f316(f68(f17(a242,x19672)),f338(x19672,f175(x19672,x19671))))))) 7.68/7.79 [1968]P5(f269(a260,x19681))+~P5(f312(a253,f347(x19682,x19681)))+~P5(f269(a260,f89(f95(f41(a241,f320(f57(a369),x19681)),f296(f73(f40(a243,x19682)),f339(x19682,f141(x19682,x19681))))))) 7.68/7.79 [1969]P5(f269(a260,x19691))+~P5(f295(a255,f357(x19692,x19691)))+~P5(f269(a260,f89(f95(f41(a241,f320(f57(a369),x19691)),f320(f57(f37(a245,x19692)),f341(x19692,f149(x19692,x19691))))))) 7.68/7.79 [1970]P5(f311(a236,x19701))+~P5(f268(a261,f354(x19702,x19701)))+~P5(f311(a236,f99(f96(f31(a241,f305(f60(a372),x19701)),f329(f71(f26(a247,x19702)),f285(x19702,f174(x19702,x19701))))))) 7.68/7.79 [1971]P5(f311(a236,x19711))+~P5(f269(a260,f364(x19712,x19711)))+~P5(f311(a236,f99(f96(f31(a241,f305(f60(a372),x19711)),f339(f81(f42(a248,x19712)),f283(x19712,f147(x19712,x19711))))))) 7.68/7.79 [1972]P5(f311(a236,x19721))+~P5(f311(a236,f361(x19722,x19721)))+~P5(f311(a236,f99(f96(f31(a241,f305(f60(a372),x19721)),f282(f77(f51(a244,x19722)),f280(x19722,f140(x19722,x19721))))))) 7.68/7.79 [1973]P5(f311(a236,x19731))+~P5(f270(a239,f363(x19732,x19731)))+~P5(f311(a236,f99(f96(f31(a241,f305(f60(a372),x19731)),f271(f78(f49(a242,x19732)),f284(x19732,f231(x19732,x19731))))))) 7.68/7.79 [1974]P5(f311(a236,x19741))+~P5(f312(a253,f355(x19742,x19741)))+~P5(f311(a236,f99(f96(f31(a241,f305(f60(a372),x19741)),f305(f60(f44(a243,x19742)),f282(x19742,f173(x19742,x19741))))))) 7.68/7.79 [1975]P5(f311(a236,x19751))+~P5(f295(a255,f356(x19752,x19751)))+~P5(f311(a236,f99(f96(f31(a241,f305(f60(a372),x19751)),f288(f65(f25(a245,x19752)),f276(x19752,f157(x19752,x19751))))))) 7.68/7.79 [1976]P5(f312(a253,x19761))+~P5(f268(a261,f366(x19762,x19761)))+~P5(f312(a253,f101(f92(f39(a241,f304(f64(a371),x19761)),f322(f72(f20(a247,x19762)),f324(x19762,f138(x19762,x19761))))))) 7.68/7.79 [1977]P5(f312(a253,x19771))+~P5(f269(a260,f353(x19772,x19771)))+~P5(f312(a253,f101(f92(f39(a241,f304(f64(a371),x19771)),f340(f62(f27(a248,x19772)),f289(x19772,f214(x19772,x19771))))))) 7.68/7.79 [1978]P5(f295(a255,x19781))+~P5(f268(a261,f349(x19782,x19781)))+~P5(f295(a255,f90(f91(f36(a241,f313(f66(a373),x19781)),f326(f59(f19(a247,x19782)),f318(x19782,f197(x19782,x19781))))))) 7.68/7.79 [1979]P5(f295(a255,x19791))+~P5(f269(a260,f348(x19792,x19791)))+~P5(f295(a255,f90(f91(f36(a241,f313(f66(a373),x19791)),f336(f56(f47(a248,x19792)),f291(x19792,f158(x19792,x19791))))))) 7.68/7.79 [1238]~E(f267(f378(x12381),x12383),x12382)+E(x12381,f267(f382(x12382),x12383))+~P5(f331(f327(a384,x12383),x12381)) 7.68/7.79 [1239]~E(x12391,f267(f382(x12393),x12392))+E(f267(f378(x12391),x12392),x12393)+~P5(f331(f327(a384,x12392),x12391)) 7.68/7.79 [1385]P5(f268(a261,x13851))+~P5(f268(a261,x13852))+~P5(f268(f273(a385,x13851),f368(x13853,x13852))) 7.68/7.79 [1386]P5(f268(a261,x13861))+~P5(f269(a260,x13862))+~P5(f268(f273(a385,x13861),f375(x13863,x13862))) 7.68/7.79 [1387]P5(f268(a261,x13871))+~P5(f311(a236,x13872))+~P5(f268(f273(a385,x13871),f354(x13873,x13872))) 7.68/7.79 [1388]P5(f268(a261,x13881))+~P5(f270(a239,x13882))+~P5(f268(f273(a385,x13881),f360(x13883,x13882))) 7.68/7.79 [1389]P5(f268(a261,x13891))+~P5(f312(a253,x13892))+~P5(f268(f273(a385,x13891),f366(x13893,x13892))) 7.68/7.79 [1390]P5(f268(a261,x13901))+~P5(f295(a255,x13902))+~P5(f268(f273(a385,x13901),f349(x13903,x13902))) 7.68/7.79 [1391]P5(f269(a260,x13911))+~P5(f268(a261,x13912))+~P5(f269(f309(a389,x13911),f367(x13913,x13912))) 7.68/7.79 [1392]P5(f269(a260,x13921))+~P5(f269(a260,x13922))+~P5(f269(f309(a389,x13921),f374(x13923,x13922))) 7.68/7.79 [1393]P5(f269(a260,x13931))+~P5(f311(a236,x13932))+~P5(f269(f309(a389,x13931),f364(x13933,x13932))) 7.68/7.79 [1394]P5(f269(a260,x13941))+~P5(f270(a239,x13942))+~P5(f269(f309(a389,x13941),f352(x13943,x13942))) 7.68/7.79 [1395]P5(f269(a260,x13951))+~P5(f312(a253,x13952))+~P5(f269(f309(a389,x13951),f353(x13953,x13952))) 7.68/7.79 [1396]P5(f269(a260,x13961))+~P5(f295(a255,x13962))+~P5(f269(f309(a389,x13961),f348(x13963,x13962))) 7.68/7.79 [1397]P5(f311(a236,x13971))+~P5(f268(a261,x13972))+~P5(f311(f294(a386,x13971),f350(x13973,x13972))) 7.68/7.79 [1398]P5(f311(a236,x13981))+~P5(f269(a260,x13982))+~P5(f311(f294(a386,x13981),f332(x13983,x13982))) 7.68/7.79 [1399]P5(f311(a236,x13991))+~P5(f311(a236,x13992))+~P5(f311(f294(a386,x13991),f361(x13993,x13992))) 7.68/7.79 [1400]P5(f311(a236,x14001))+~P5(f270(a239,x14002))+~P5(f311(f294(a386,x14001),f351(x14003,x14002))) 7.68/7.79 [1401]P5(f311(a236,x14011))+~P5(f312(a253,x14012))+~P5(f311(f294(a386,x14011),f365(x14013,x14012))) 7.68/7.79 [1402]P5(f311(a236,x14021))+~P5(f295(a255,x14022))+~P5(f311(f294(a386,x14021),f362(x14023,x14022))) 7.68/7.79 [1403]P5(f270(a239,x14031))+~P5(f268(a261,x14032))+~P5(f270(f298(a387,x14031),f358(x14033,x14032))) 7.68/7.79 [1404]P5(f270(a239,x14041))+~P5(f269(a260,x14042))+~P5(f270(f298(a387,x14041),f359(x14043,x14042))) 7.68/7.79 [1405]P5(f312(a253,x14051))+~P5(f268(a261,x14052))+~P5(f312(f293(a388,x14051),f333(x14053,x14052))) 7.68/7.79 [1406]P5(f312(a253,x14061))+~P5(f269(a260,x14062))+~P5(f312(f293(a388,x14061),f347(x14063,x14062))) 7.68/7.79 [1407]P5(f295(a255,x14071))+~P5(f268(a261,x14072))+~P5(f295(f310(a391,x14071),f334(x14073,x14072))) 7.68/7.79 [1408]P5(f295(a255,x14081))+~P5(f269(a260,x14082))+~P5(f295(f310(a391,x14081),f357(x14083,x14082))) 7.68/7.79 [1457]~P5(f268(f273(a385,x14571),x14573))+P5(f268(f273(a385,x14571),x14572))+~P5(f268(f273(a385,x14573),x14572)) 7.68/7.79 [1461]~P5(f268(f328(a376,x14611),x14613))+P5(f268(f328(a376,x14611),x14612))+~P5(f268(f273(a385,x14613),x14612)) 7.68/7.79 [1464]~P5(f269(f309(a389,x14641),x14643))+P5(f269(f309(a389,x14641),x14642))+~P5(f269(f309(a389,x14643),x14642)) 7.68/7.79 [1468]~P5(f269(f336(a369,x14681),x14683))+P5(f269(f336(a369,x14681),x14682))+~P5(f269(f309(a389,x14683),x14682)) 7.68/7.79 [1471]~P5(f331(f327(a384,x14711),x14713))+P5(f331(f327(a384,x14711),x14712))+~P5(f331(f327(a384,x14713),x14712)) 7.68/7.79 [1473]~P5(f286(f274(a390,x14731),x14733))+P5(f286(f274(a390,x14731),x14732))+~P5(f286(f274(a390,x14733),x14732)) 7.68/7.79 [1476]~P5(f311(f294(a386,x14761),x14763))+P5(f311(f294(a386,x14761),x14762))+~P5(f311(f294(a386,x14763),x14762)) 7.68/7.79 [1480]~P5(f311(f277(a372,x14801),x14803))+P5(f311(f277(a372,x14801),x14802))+~P5(f311(f294(a386,x14803),x14802)) 7.68/7.79 [1481]~P7(x14811)+P6(f177(x14811,x14812,x14813))+~P5(f269(f309(a389,x14811),f364(x14812,x14813))) 7.68/7.79 [1482]~P6(x14821)+P7(f161(x14821,x14822,x14823))+~P5(f311(f294(a386,x14821),f332(x14822,x14823))) 7.68/7.79 [1483]~P4(x14831)+P8(f164(x14831,x14832,x14833))+~P5(f311(f277(a372,x14831),f332(x14832,x14833))) 7.68/7.79 [1484]~P4(x14841)+P8(f191(x14841,x14842,x14843))+~P5(f311(f277(a372,x14841),f332(x14842,x14843))) 7.68/7.79 [1488]~P6(x14882)+E(f332(x14881,f161(x14882,x14881,x14883)),x14882)+~P5(f311(f294(a386,x14882),f332(x14881,x14883))) 7.68/7.79 [1489]~P6(x14892)+E(f350(x14891,f112(x14892,x14891,x14893)),x14892)+~P5(f311(f294(a386,x14892),f350(x14891,x14893))) 7.68/7.79 [1490]~P4(x14902)+E(f344(x14901,f164(x14902,x14901,x14903)),x14902)+~P5(f311(f277(a372,x14902),f332(x14901,x14903))) 7.68/7.79 [1491]~P4(x14912)+E(f330(x14911,f125(x14912,x14911,x14913)),x14912)+~P5(f311(f277(a372,x14912),f350(x14911,x14913))) 7.68/7.79 [1492]~P7(x14922)+E(f364(x14921,f177(x14922,x14921,x14923)),x14922)+~P5(f269(f309(a389,x14922),f364(x14921,x14923))) 7.68/7.79 [1493]~P8(x14932)+E(f335(x14931,f128(x14932,x14931,x14933)),x14932)+~P5(f269(f336(a369,x14932),f367(x14931,x14933))) 7.68/7.79 [1494]~P4(x14942)+E(f344(x14941,f191(x14942,x14941,x14943)),x14942)+~P5(f311(f277(a372,x14942),f332(x14941,x14943))) 7.68/7.79 [1554]P1(f148(x15541,x15542,x15543))+~P5(f268(a261,x15543))+~P5(f268(f273(a385,x15543),f366(x15541,x15542))) 7.68/7.79 [1555]P2(f190(x15551,x15552,x15553))+~P5(f268(a261,x15553))+~P5(f268(f273(a385,x15553),f349(x15551,x15552))) 7.68/7.79 [1556]P6(f129(x15561,x15562,x15563))+~P5(f268(a261,x15563))+~P5(f268(f273(a385,x15563),f354(x15561,x15562))) 7.68/7.79 [1557]P6(f204(x15571,x15572,x15573))+~P5(f270(a239,x15573))+~P5(f270(f298(a387,x15573),f363(x15571,x15572))) 7.68/7.79 [1558]P7(f199(x15581,x15582,x15583))+~P5(f268(a261,x15583))+~P5(f268(f273(a385,x15583),f375(x15581,x15582))) 7.68/7.79 [1559]P7(f131(x15591,x15592,x15593))+~P5(f270(a239,x15593))+~P5(f270(f298(a387,x15593),f359(x15591,x15592))) 7.68/7.79 [1579]E(f354(x15791,f129(x15791,x15792,x15793)),x15793)+~P5(f268(a261,x15793))+~P5(f268(f273(a385,x15793),f354(x15791,x15792))) 7.68/7.79 [1580]E(f349(x15801,f190(x15801,x15802,x15803)),x15803)+~P5(f268(a261,x15803))+~P5(f268(f273(a385,x15803),f349(x15801,x15802))) 7.68/7.79 [1581]E(f363(x15811,f204(x15811,x15812,x15813)),x15813)+~P5(f270(a239,x15813))+~P5(f270(f298(a387,x15813),f363(x15811,x15812))) 7.68/7.79 [1582]E(f368(x15821,f116(x15821,x15822,x15823)),x15823)+~P5(f268(a261,x15823))+~P5(f268(f273(a385,x15823),f368(x15821,x15822))) 7.68/7.79 [1583]E(f375(x15831,f199(x15831,x15832,x15833)),x15833)+~P5(f268(a261,x15833))+~P5(f268(f273(a385,x15833),f375(x15831,x15832))) 7.68/7.79 [1584]E(f366(x15841,f148(x15841,x15842,x15843)),x15843)+~P5(f268(a261,x15843))+~P5(f268(f273(a385,x15843),f366(x15841,x15842))) 7.68/7.79 [1585]E(f358(x15851,f146(x15851,x15852,x15853)),x15853)+~P5(f270(a239,x15853))+~P5(f270(f298(a387,x15853),f358(x15851,x15852))) 7.68/7.79 [1586]E(f359(x15861,f131(x15861,x15862,x15863)),x15863)+~P5(f270(a239,x15863))+~P5(f270(f298(a387,x15863),f359(x15861,x15862))) 7.68/7.79 [1587]E(f360(x15871,f178(x15871,x15872,x15873)),x15873)+~P5(f268(a261,x15873))+~P5(f268(f273(a385,x15873),f360(x15871,x15872))) 7.68/7.79 [1685]~P5(f268(a261,x16853))+~P5(f268(f273(a385,x16853),f368(x16851,x16852)))+P5(f268(a261,f116(x16851,x16852,x16853))) 7.68/7.79 [1686]~P5(f270(a239,x16863))+~P5(f270(f298(a387,x16863),f358(x16861,x16862)))+P5(f268(a261,f146(x16861,x16862,x16863))) 7.68/7.79 [1687]~P5(f268(a261,x16873))+~P5(f268(f273(a385,x16873),f375(x16871,x16872)))+P5(f269(a260,f199(x16871,x16872,x16873))) 7.68/7.79 [1688]~P5(f270(a239,x16883))+~P5(f270(f298(a387,x16883),f359(x16881,x16882)))+P5(f269(a260,f131(x16881,x16882,x16883))) 7.68/7.79 [1689]~P5(f268(a261,x16893))+~P5(f268(f273(a385,x16893),f354(x16891,x16892)))+P5(f311(a236,f129(x16891,x16892,x16893))) 7.68/7.79 [1690]~P5(f270(a239,x16903))+~P5(f270(f298(a387,x16903),f363(x16901,x16902)))+P5(f311(a236,f204(x16901,x16902,x16903))) 7.68/7.79 [1691]~P5(f268(a261,x16913))+~P5(f268(f273(a385,x16913),f360(x16911,x16912)))+P5(f270(a239,f178(x16911,x16912,x16913))) 7.68/7.79 [1692]~P5(f268(a261,x16923))+~P5(f268(f273(a385,x16923),f366(x16921,x16922)))+P5(f312(a253,f148(x16921,x16922,x16923))) 7.68/7.79 [1693]~P5(f268(a261,x16933))+~P5(f268(f273(a385,x16933),f349(x16931,x16932)))+P5(f295(a255,f190(x16931,x16932,x16933))) 7.68/7.79 [1849]P5(f331(f327(a383,f208(x18492,x18493,x18491)),f209(x18492,x18493,x18491)))+~P5(f331(f327(a384,x18492),x18493))+P5(f331(f327(a384,f267(x18491,x18492)),f267(x18491,x18493))) 7.68/7.79 [1622]E(f267(f378(f267(f378(x16221),x16222)),f267(f378(x16223),x16222)),f267(f378(x16221),x16223))+~P5(f331(f327(a384,x16222),x16221))+~P5(f331(f327(a384,x16222),x16223)) 7.68/7.79 [1626]~P5(f331(f327(a383,x16261),x16263))+~P5(f331(f327(a383,x16263),x16262))+P5(f331(f327(a383,f267(a394,x16261)),x16262)) 7.68/7.79 [1724]~P5(f331(x17241,x17242))+~P5(f331(x17241,f182(x17243,x17241,x17242)))+P5(f331(x17241,f267(f378(x17242),x17243))) 7.68/7.79 [1727]~P5(f331(f327(a383,x17273),x17272))+~P5(f331(f327(a383,x17273),x17271))+P5(f331(f327(a383,f267(f378(x17271),x17272)),f267(f378(x17271),x17273))) 7.68/7.79 [1728]~P5(f331(f327(a384,x17282),x17281))+~P5(f331(f327(a383,x17281),x17283))+P5(f331(f327(a383,f267(f378(x17281),x17282)),f267(f378(x17283),x17282))) 7.68/7.79 [1754]~P5(f331(x17541,x17542))+P5(f331(x17541,f267(f378(x17542),x17543)))+P5(f331(x17541,f267(a394,f182(x17543,x17541,x17542)))) 7.68/7.79 [1778]~P6(x17781)+~P5(f311(f294(a386,x17781),f350(x17782,x17783)))+P5(f268(f273(a385,f112(x17781,x17782,x17783)),x17783)) 7.68/7.79 [1779]~P4(x17791)+~P5(f311(f277(a372,x17791),f350(x17792,x17793)))+P5(f268(f328(a376,f125(x17791,x17792,x17793)),x17793)) 7.68/7.79 [1780]~P8(x17801)+~P5(f269(f336(a369,x17801),f367(x17802,x17803)))+P5(f268(f328(a376,f128(x17801,x17802,x17803)),x17803)) 7.68/7.79 [1781]~P6(x17811)+~P5(f311(f294(a386,x17811),f332(x17812,x17813)))+P5(f269(f309(a389,f161(x17811,x17812,x17813)),x17813)) 7.68/7.79 [1782]~P4(x17821)+~P5(f311(f277(a372,x17821),f332(x17822,x17823)))+P5(f269(f336(a369,f164(x17821,x17822,x17823)),x17823)) 7.68/7.79 [1783]~P4(x17831)+~P5(f311(f277(a372,x17831),f332(x17832,x17833)))+P5(f269(f336(a369,f191(x17831,x17832,x17833)),x17833)) 7.68/7.79 [1784]~P7(x17841)+~P5(f269(f309(a389,x17841),f364(x17842,x17843)))+P5(f311(f294(a386,f177(x17841,x17842,x17843)),x17843)) 7.68/7.79 [1799]~P5(f268(a261,x17993))+~P5(f268(f273(a385,x17993),f368(x17991,x17992)))+P5(f268(f273(a385,f116(x17991,x17992,x17993)),x17992)) 7.68/7.79 [1800]~P5(f270(a239,x18003))+~P5(f270(f298(a387,x18003),f358(x18001,x18002)))+P5(f268(f273(a385,f146(x18001,x18002,x18003)),x18002)) 7.68/7.79 [1801]~P5(f268(a261,x18013))+~P5(f268(f273(a385,x18013),f375(x18011,x18012)))+P5(f269(f309(a389,f199(x18011,x18012,x18013)),x18012)) 7.68/7.79 [1802]~P5(f270(a239,x18023))+~P5(f270(f298(a387,x18023),f359(x18021,x18022)))+P5(f269(f309(a389,f131(x18021,x18022,x18023)),x18022)) 7.68/7.79 [1803]~P5(f268(a261,x18033))+~P5(f268(f273(a385,x18033),f354(x18031,x18032)))+P5(f311(f294(a386,f129(x18031,x18032,x18033)),x18032)) 7.68/7.79 [1804]~P5(f270(a239,x18043))+~P5(f270(f298(a387,x18043),f363(x18041,x18042)))+P5(f311(f294(a386,f204(x18041,x18042,x18043)),x18042)) 7.68/7.79 [1805]~P5(f268(a261,x18053))+~P5(f268(f273(a385,x18053),f360(x18051,x18052)))+P5(f270(f298(a387,f178(x18051,x18052,x18053)),x18052)) 7.68/7.79 [1806]~P5(f268(a261,x18063))+~P5(f268(f273(a385,x18063),f366(x18061,x18062)))+P5(f312(f293(a388,f148(x18061,x18062,x18063)),x18062)) 7.68/7.79 [1807]~P5(f268(a261,x18073))+~P5(f268(f273(a385,x18073),f349(x18071,x18072)))+P5(f295(f310(a391,f190(x18071,x18072,x18073)),x18072)) 7.68/7.79 [1945]~P5(f331(f327(a384,x19452),x19453))+P5(f331(f327(a384,f267(x19451,x19452)),f267(x19451,x19453)))+~P5(f331(f327(a383,f267(x19451,f208(x19452,x19453,x19451))),f267(x19451,f209(x19452,x19453,x19451)))) 7.68/7.79 [1749]~P5(f331(f327(a384,x17492),x17493))+~P5(f331(f327(a384,x17491),f267(f378(x17493),x17492)))+P5(f331(f327(a384,f267(f382(x17491),x17492)),x17493)) 7.68/7.79 [1753]~P5(f331(f327(a384,x17533),x17532))+P5(f331(f327(a384,x17531),f267(f378(x17532),x17533)))+~P5(f331(f327(a384,f267(f382(x17531),x17533)),x17532)) 7.68/7.79 [1951]~P5(f331(f327(a384,x19512),x19513))+P5(f268(f273(a385,f327(x19511,x19512)),f327(x19511,x19513)))+~P5(f268(f273(a385,f327(x19511,f153(x19512,x19513,x19511))),f327(x19511,f267(a394,f153(x19512,x19513,x19511))))) 7.68/7.79 [1952]~P5(f331(f327(a384,x19522),x19523))+P5(f269(f309(a389,f323(x19521,x19522)),f323(x19521,x19523)))+~P5(f269(f309(a389,f323(x19521,f127(x19522,x19523,x19521))),f323(x19521,f267(a394,f127(x19522,x19523,x19521))))) 7.68/7.79 [1953]~P5(f331(f327(a384,x19532),x19533))+P5(f331(f327(a384,f267(x19531,x19532)),f267(x19531,x19533)))+~P5(f331(f327(a384,f267(x19531,f201(x19532,x19533,x19531))),f267(x19531,f267(a394,f201(x19532,x19533,x19531))))) 7.68/7.79 [1954]~P5(f331(f327(a384,x19542),x19543))+P5(f286(f274(a390,f331(x19541,x19542)),f331(x19541,x19543)))+~P5(f286(f274(a390,f331(x19541,f222(x19542,x19543,x19541))),f331(x19541,f267(a394,f222(x19542,x19543,x19541))))) 7.68/7.79 [1955]~P5(f331(f327(a384,x19552),x19553))+P5(f311(f294(a386,f329(x19551,x19552)),f329(x19551,x19553)))+~P5(f311(f294(a386,f329(x19551,f166(x19552,x19553,x19551))),f329(x19551,f267(a394,f166(x19552,x19553,x19551))))) 7.68/7.79 [1920]P5(f269(f309(a389,x19201),x19202))+P5(f269(f336(a369,x19203),x19201))+~P5(f269(f309(a389,x19201),f89(f95(f41(a240,f341(f55(a248),x19203)),f320(f57(a369),x19202))))) 7.68/7.79 [1921]P5(f311(f294(a386,x19211),x19212))+P5(f311(f277(a372,x19213),x19211))+~P5(f311(f294(a386,x19211),f99(f96(f31(a240,f282(f77(a244),x19213)),f305(f60(a372),x19212))))) 7.68/7.79 [1889]E(x18891,x18892)+P5(f331(x18893,x18892))+~P5(f331(f94(f21(a246,f52(a238,f327(f16(a247),x18891))),x18893),x18892)) 7.68/7.79 [1894]E(x18941,x18942)+P5(f268(f328(a376,x18941),x18943))+~P5(f268(f328(a376,x18941),f94(f21(a246,f52(a238,f327(f16(a247),x18942))),x18943))) 7.68/7.79 [1896]P5(f268(f273(a385,x18961),x18962))+P5(f268(f328(a376,x18963),x18961))+~P5(f268(f273(a385,x18961),f94(f21(a246,f52(a238,f327(f16(a247),x18963))),x18962))) 7.68/7.79 [1934]~P5(f269(f309(a389,x19342),x19343))+~P5(f269(f336(a369,x19341),x19343))+P5(f269(f309(a389,f89(f95(f41(a240,f341(f55(a248),x19341)),f320(f57(a369),x19342)))),x19343)) 7.68/7.79 [1935]~P5(f311(f294(a386,x19352),x19353))+~P5(f311(f277(a372,x19351),x19353))+P5(f311(f294(a386,f99(f96(f31(a240,f282(f77(a244),x19351)),f305(f60(a372),x19352)))),x19353)) 7.68/7.79 [1927]~P5(f268(f273(a385,x19272),x19273))+~P5(f268(f328(a376,x19271),x19273))+P5(f268(f273(a385,f94(f21(a246,f52(a238,f327(f16(a247),x19271))),x19272)),x19273)) 7.68/7.79 [1367]~E(f267(f382(x13673),x13672),f267(f382(x13671),x13674))+~P5(f331(f327(a383,x13673),x13674))+P5(f331(f327(a383,x13671),x13672)) 7.68/7.79 [1375]~E(x13751,f346(x13752,x13754))+~P5(f269(f336(a369,x13754),x13753))+P5(f268(f328(a376,x13751),f375(x13752,x13753))) 7.68/7.79 [1377]~E(x13771,f285(x13772,x13774))+~P5(f311(f277(a372,x13774),x13773))+P5(f268(f328(a376,x13771),f354(x13772,x13773))) 7.68/7.79 [1378]~E(x13781,f335(x13782,x13784))+~P5(f268(f328(a376,x13784),x13783))+P5(f269(f336(a369,x13781),f367(x13782,x13783))) 7.68/7.79 [1379]~E(f346(x13792,x13794),x13791)+~P5(f269(f336(a369,x13794),x13793))+P5(f268(f328(a376,x13791),f375(x13792,x13793))) 7.68/7.79 [1380]~E(f335(x13802,x13804),x13801)+~P5(f268(f328(a376,x13804),x13803))+P5(f269(f336(a369,x13801),f367(x13802,x13803))) 7.68/7.79 [1383]~E(f344(x13832,x13834),x13831)+~P5(f269(f336(a369,x13834),x13833))+P5(f311(f277(a372,x13831),f332(x13832,x13833))) 7.68/7.79 [1384]~E(f330(x13842,x13844),x13841)+~P5(f268(f328(a376,x13844),x13843))+P5(f311(f277(a372,x13841),f350(x13842,x13843))) 7.68/7.79 [1725]~P5(f331(f327(a384,x17252),x17254))+~P5(f331(f327(a384,x17251),x17253))+P5(f331(f327(a384,f267(f382(x17251),x17252)),f267(f382(x17253),x17254))) 7.68/7.79 [1726]~P5(f331(f327(a383,x17262),x17264))+~P5(f331(f327(a383,x17261),x17263))+P5(f331(f327(a383,f267(f382(x17261),x17262)),f267(f382(x17263),x17264))) 7.68/7.79 [1869]~E(x18692,x18693)+~E(x18694,x18691)+E(f94(f21(a246,f52(a238,f327(f16(a247),x18691))),f94(f21(a246,f52(a238,f327(f16(a247),x18692))),a2)),f94(f21(a246,f52(a238,f327(f16(a247),x18693))),f94(f21(a246,f52(a238,f327(f16(a247),x18694))),a2))) 7.68/7.79 [1924]E(x19241,x19242)+E(x19243,x19241)+~E(f94(f21(a246,f52(a238,f327(f16(a247),x19241))),f94(f21(a246,f52(a238,f327(f16(a247),x19244))),a2)),f94(f21(a246,f52(a238,f327(f16(a247),x19242))),f94(f21(a246,f52(a238,f327(f16(a247),x19243))),a2))) 7.68/7.79 [1926]E(x19261,x19262)+E(x19261,x19263)+~E(f94(f21(a246,f52(a238,f327(f16(a247),x19263))),f94(f21(a246,f52(a238,f327(f16(a247),x19262))),a2)),f94(f21(a246,f52(a238,f327(f16(a247),x19264))),f94(f21(a246,f52(a238,f327(f16(a247),x19261))),a2))) 7.68/7.79 [1221]P1(f168(x12211,x12212))+P5(f312(x12211,x12212))+~P5(f312(x12211,a4))+~P5(f312(a253,x12212)) 7.68/7.79 [1222]P6(f169(x12221,x12222))+P5(f312(x12221,x12222))+~P5(f312(x12221,a4))+~P5(f312(a253,x12222)) 7.68/7.79 [1223]P2(f136(x12231,x12232))+P5(f295(x12231,x12232))+~P5(f295(x12231,a7))+~P5(f295(a255,x12232)) 7.68/7.79 [1224]P7(f137(x12241,x12242))+P5(f295(x12241,x12242))+~P5(f295(x12241,a7))+~P5(f295(a255,x12242)) 7.68/7.79 [1210]~P6(x12102)+~P6(x12101)+E(x12101,x12102)+~P5(f311(f294(a243,x12101),x12102)) 7.68/7.79 [1211]~P4(x12112)+~P4(x12111)+E(x12111,x12112)+~P5(f275(f282(a244,x12111),x12112)) 7.68/7.79 [1212]~P7(x12122)+~P7(x12121)+E(x12121,x12122)+~P5(f269(f309(a245,x12122),x12121)) 7.68/7.79 [1213]~P8(x12132)+~P8(x12131)+E(x12131,x12132)+~P5(f343(f341(a248,x12132),x12131)) 7.68/7.79 [1217]~P7(x12171)+~P8(x12172)+~E(a9,x12171)+~P5(f269(f336(a369,x12172),x12171)) 7.68/7.79 [1275]P5(f270(x12751,x12752))+~P5(f270(x12751,a3))+~P5(f270(a239,x12752))+P5(f270(a239,f150(x12751,x12752))) 7.68/7.79 [1276]P5(f312(x12761,x12762))+~P5(f312(x12761,a4))+~P5(f312(a253,x12762))+P5(f312(a253,f168(x12761,x12762))) 7.68/7.79 [1277]P5(f295(x12771,x12772))+~P5(f295(x12771,a7))+~P5(f295(a255,x12772))+P5(f295(a255,f136(x12771,x12772))) 7.68/7.79 [1286]P5(f270(x12861,x12862))+~P5(f270(x12861,a3))+~P5(f270(a239,x12862))+P5(f270(x12861,f150(x12861,x12862))) 7.68/7.79 [1287]P5(f312(x12871,x12872))+~P5(f312(x12871,a4))+~P5(f312(a253,x12872))+P5(f312(x12871,f168(x12871,x12872))) 7.68/7.79 [1288]P5(f295(x12881,x12882))+~P5(f295(x12881,a7))+~P5(f295(a255,x12882))+P5(f295(x12881,f136(x12881,x12882))) 7.68/7.79 [1349]P5(x13491)+~P5(x13492)+~P5(f286(f274(a390,x13491),x13492))+~P5(f286(f274(a390,x13492),x13491)) 7.68/7.79 [1682]P5(f270(x16821,x16822))+~P5(f270(x16821,a3))+~P5(f270(a239,x16822))+~P5(f270(f303(a370,f151(x16821,x16822)),f150(x16821,x16822))) 7.68/7.79 [1683]P5(f312(x16831,x16832))+~P5(f312(x16831,a4))+~P5(f312(a253,x16832))+~P5(f312(f308(a371,f169(x16831,x16832)),f168(x16831,x16832))) 7.68/7.79 [1684]P5(f295(x16841,x16842))+~P5(f295(x16841,a7))+~P5(f295(a255,x16842))+~P5(f295(f314(a373,f137(x16841,x16842)),f136(x16841,x16842))) 7.68/7.79 [1712]E(x17121,x17122)+~P5(f268(a261,x17121))+~P5(f268(f273(a385,x17122),x17121))+~P5(f331(f327(a384,f301(a256,x17121)),f301(a256,x17122))) 7.68/7.79 [1713]E(x17131,x17132)+~P5(f270(a239,x17131))+~P5(f270(f298(a387,x17132),x17131))+~P5(f331(f327(a384,f321(a254,x17131)),f321(a254,x17132))) 7.68/7.79 [1830]~P4(x18302)+~P4(x18301)+E(x18301,x18302)+~E(f99(f96(f31(a240,f282(f77(a244),x18301)),f305(f60(a372),a8))),f99(f96(f31(a240,f282(f77(a244),x18302)),f305(f60(a372),a8)))) 7.68/7.79 [1831]~P8(x18312)+~P8(x18311)+E(x18311,x18312)+~E(f89(f95(f41(a240,f341(f55(a248),x18311)),f320(f57(a369),a9))),f89(f95(f41(a240,f341(f55(a248),x18312)),f320(f57(a369),a9)))) 7.68/7.79 [1922]P5(f270(x19221,x19222))+~P5(f270(x19221,a3))+~P5(f270(a239,x19222))+~P5(f270(x19221,f93(f45(a240,f273(f53(a242),f151(x19221,x19222))),f290(f58(a370),f150(x19221,x19222))))) 7.68/7.79 [1905]~P4(x19052)+~P4(x19051)+E(x19051,x19052)+~P5(f311(f277(a372,x19051),f99(f96(f31(a240,f282(f77(a244),x19052)),f305(f60(a372),a8))))) 7.68/7.79 [1907]~P8(x19072)+~P8(x19071)+E(x19071,x19072)+~P5(f269(f336(a369,x19071),f89(f95(f41(a240,f341(f55(a248),x19072)),f320(f57(a369),a9))))) 7.68/7.79 [1928]~P7(x19281)+E(x19281,a9)+E(x19281,f89(f95(f41(a240,f341(f55(a248),x19282)),f320(f57(a369),a9))))+~P5(f269(f309(a389,x19281),f89(f95(f41(a240,f341(f55(a248),x19282)),f320(f57(a369),a9))))) 7.68/7.79 [1929]~P6(x19291)+E(a8,x19291)+E(x19291,f99(f96(f31(a240,f282(f77(a244),x19292)),f305(f60(a372),a8))))+~P5(f311(f294(a386,x19291),f99(f96(f31(a240,f282(f77(a244),x19292)),f305(f60(a372),a8))))) 7.68/7.79 [1960]P5(f312(x19601,x19602))+~P5(f312(x19601,a4))+~P5(f312(a253,x19602))+~P5(f312(x19601,f101(f92(f39(a240,f294(f63(a243),f169(x19601,x19602))),f304(f64(a371),f168(x19601,x19602)))))) 7.68/7.79 [1961]P5(f295(x19611,x19612))+~P5(f295(x19611,a7))+~P5(f295(a255,x19612))+~P5(f295(x19611,f90(f91(f36(a240,f309(f54(a245),f137(x19611,x19612))),f313(f66(a373),f136(x19611,x19612)))))) 7.68/7.79 [1291]P5(x12911)+P5(x12912)+~P5(f286(f274(a390,x12913),x12911))+P5(f286(f274(a390,x12913),x12912)) 7.68/7.79 [1294]P5(x12941)+P5(x12942)+~P5(f286(f274(a390,x12941),x12943))+P5(f286(f274(a390,x12942),x12943)) 7.68/7.79 [1299]~P5(x12992)+~P5(x12993)+~P5(f286(f274(a390,x12991),x12993))+P5(f286(f274(a390,x12991),x12992)) 7.68/7.79 [1302]~P5(x13021)+~P5(x13023)+~P5(f286(f274(a390,x13023),x13022))+P5(f286(f274(a390,x13021),x13022)) 7.68/7.79 [1444]E(x14441,x14442)+~E(f267(f378(x14441),x14443),f267(f378(x14442),x14443))+~P5(f331(f327(a384,x14443),x14441))+~P5(f331(f327(a384,x14443),x14442)) 7.68/7.79 [1567]~P7(x15673)+P1(f227(x15671,x15672,x15673))+~P5(f269(a260,x15673))+~P5(f269(f309(a389,x15673),f353(x15671,x15672))) 7.68/7.79 [1568]~P6(x15683)+P1(f120(x15681,x15682,x15683))+~P5(f311(a236,x15683))+~P5(f311(f294(a386,x15683),f365(x15681,x15682))) 7.68/7.79 [1569]~P7(x15693)+P2(f226(x15691,x15692,x15693))+~P5(f269(a260,x15693))+~P5(f269(f309(a389,x15693),f348(x15691,x15692))) 7.68/7.79 [1570]~P6(x15703)+P2(f232(x15701,x15702,x15703))+~P5(f311(a236,x15703))+~P5(f311(f294(a386,x15703),f362(x15701,x15702))) 7.68/7.79 [1571]~P2(x15713)+P6(f235(x15711,x15712,x15713))+~P5(f295(a255,x15713))+~P5(f295(f310(a391,x15713),f356(x15711,x15712))) 7.68/7.79 [1572]~P7(x15723)+P6(f233(x15721,x15722,x15723))+~P5(f269(a260,x15723))+~P5(f269(f309(a389,x15723),f364(x15721,x15722))) 7.68/7.79 [1573]~P1(x15733)+P6(f121(x15731,x15732,x15733))+~P5(f312(a253,x15733))+~P5(f312(f293(a388,x15733),f355(x15731,x15732))) 7.68/7.79 [1574]~P6(x15743)+P6(f122(x15741,x15742,x15743))+~P5(f311(a236,x15743))+~P5(f311(f294(a386,x15743),f361(x15741,x15742))) 7.68/7.79 [1575]~P1(x15753)+P7(f200(x15751,x15752,x15753))+~P5(f312(a253,x15753))+~P5(f312(f293(a388,x15753),f347(x15751,x15752))) 7.68/7.79 [1576]~P2(x15763)+P7(f234(x15761,x15762,x15763))+~P5(f295(a255,x15763))+~P5(f295(f310(a391,x15763),f357(x15761,x15762))) 7.68/7.79 [1577]~P7(x15773)+P7(f107(x15771,x15772,x15773))+~P5(f269(a260,x15773))+~P5(f269(f309(a389,x15773),f374(x15771,x15772))) 7.68/7.79 [1578]~P6(x15783)+P7(f130(x15781,x15782,x15783))+~P5(f311(a236,x15783))+~P5(f311(f294(a386,x15783),f332(x15781,x15782))) 7.68/7.79 [1588]~P6(x15883)+E(f332(x15881,f130(x15881,x15882,x15883)),x15883)+~P5(f311(a236,x15883))+~P5(f311(f294(a386,x15883),f332(x15881,x15882))) 7.68/7.79 [1589]~P7(x15893)+E(f374(x15891,f107(x15891,x15892,x15893)),x15893)+~P5(f269(a260,x15893))+~P5(f269(f309(a389,x15893),f374(x15891,x15892))) 7.68/7.79 [1590]~P1(x15903)+E(f355(x15901,f121(x15901,x15902,x15903)),x15903)+~P5(f312(a253,x15903))+~P5(f312(f293(a388,x15903),f355(x15901,x15902))) 7.68/7.79 [1591]~P6(x15913)+E(f350(x15911,f187(x15911,x15912,x15913)),x15913)+~P5(f311(a236,x15913))+~P5(f311(f294(a386,x15913),f350(x15911,x15912))) 7.68/7.79 [1592]~P7(x15923)+E(f364(x15921,f233(x15921,x15922,x15923)),x15923)+~P5(f269(a260,x15923))+~P5(f269(f309(a389,x15923),f364(x15921,x15922))) 7.68/7.79 [1593]~P6(x15933)+E(f361(x15931,f122(x15931,x15932,x15933)),x15933)+~P5(f311(a236,x15933))+~P5(f311(f294(a386,x15933),f361(x15931,x15932))) 7.68/7.79 [1594]~P7(x15943)+E(f367(x15941,f220(x15941,x15942,x15943)),x15943)+~P5(f269(a260,x15943))+~P5(f269(f309(a389,x15943),f367(x15941,x15942))) 7.68/7.79 [1595]~P2(x15953)+E(f357(x15951,f234(x15951,x15952,x15953)),x15953)+~P5(f295(a255,x15953))+~P5(f295(f310(a391,x15953),f357(x15951,x15952))) 7.68/7.79 [1596]~P7(x15963)+E(f352(x15961,f188(x15961,x15962,x15963)),x15963)+~P5(f269(a260,x15963))+~P5(f269(f309(a389,x15963),f352(x15961,x15962))) 7.68/7.79 [1597]~P7(x15973)+E(f348(x15971,f226(x15971,x15972,x15973)),x15973)+~P5(f269(a260,x15973))+~P5(f269(f309(a389,x15973),f348(x15971,x15972))) 7.68/7.79 [1598]~P6(x15983)+E(f362(x15981,f232(x15981,x15982,x15983)),x15983)+~P5(f311(a236,x15983))+~P5(f311(f294(a386,x15983),f362(x15981,x15982))) 7.68/7.79 [1599]~P7(x15993)+E(f353(x15991,f227(x15991,x15992,x15993)),x15993)+~P5(f269(a260,x15993))+~P5(f269(f309(a389,x15993),f353(x15991,x15992))) 7.68/7.79 [1600]~P2(x16003)+E(f356(x16001,f235(x16001,x16002,x16003)),x16003)+~P5(f295(a255,x16003))+~P5(f295(f310(a391,x16003),f356(x16001,x16002))) 7.68/7.79 [1601]~P1(x16013)+E(f347(x16011,f200(x16011,x16012,x16013)),x16013)+~P5(f312(a253,x16013))+~P5(f312(f293(a388,x16013),f347(x16011,x16012))) 7.68/7.79 [1602]~P6(x16023)+E(f365(x16021,f120(x16021,x16022,x16023)),x16023)+~P5(f311(a236,x16023))+~P5(f311(f294(a386,x16023),f365(x16021,x16022))) 7.68/7.79 [1603]~P2(x16033)+E(f334(x16031,f115(x16031,x16032,x16033)),x16033)+~P5(f295(a255,x16033))+~P5(f295(f310(a391,x16033),f334(x16031,x16032))) 7.68/7.79 [1604]~P6(x16043)+E(f351(x16041,f160(x16041,x16042,x16043)),x16043)+~P5(f311(a236,x16043))+~P5(f311(f294(a386,x16043),f351(x16041,x16042))) 7.68/7.79 [1605]~P1(x16053)+E(f333(x16051,f126(x16051,x16052,x16053)),x16053)+~P5(f312(a253,x16053))+~P5(f312(f293(a388,x16053),f333(x16051,x16052))) 7.68/7.79 [1694]~P6(x16943)+~P5(f311(a236,x16943))+~P5(f311(f294(a386,x16943),f350(x16941,x16942)))+P5(f268(a261,f187(x16941,x16942,x16943))) 7.68/7.79 [1695]~P7(x16953)+~P5(f269(a260,x16953))+~P5(f269(f309(a389,x16953),f367(x16951,x16952)))+P5(f268(a261,f220(x16951,x16952,x16953))) 7.68/7.79 [1696]~P2(x16963)+~P5(f295(a255,x16963))+~P5(f295(f310(a391,x16963),f334(x16961,x16962)))+P5(f268(a261,f115(x16961,x16962,x16963))) 7.68/7.79 [1697]~P1(x16973)+~P5(f312(a253,x16973))+~P5(f312(f293(a388,x16973),f333(x16971,x16972)))+P5(f268(a261,f126(x16971,x16972,x16973))) 7.68/7.79 [1698]~P1(x16983)+~P5(f312(a253,x16983))+~P5(f312(f293(a388,x16983),f347(x16981,x16982)))+P5(f269(a260,f200(x16981,x16982,x16983))) 7.68/7.79 [1699]~P2(x16993)+~P5(f295(a255,x16993))+~P5(f295(f310(a391,x16993),f357(x16991,x16992)))+P5(f269(a260,f234(x16991,x16992,x16993))) 7.68/7.79 [1700]~P7(x17003)+~P5(f269(a260,x17003))+~P5(f269(f309(a389,x17003),f374(x17001,x17002)))+P5(f269(a260,f107(x17001,x17002,x17003))) 7.68/7.79 [1701]~P6(x17013)+~P5(f311(a236,x17013))+~P5(f311(f294(a386,x17013),f332(x17011,x17012)))+P5(f269(a260,f130(x17011,x17012,x17013))) 7.68/7.79 [1702]~P2(x17023)+~P5(f295(a255,x17023))+~P5(f295(f310(a391,x17023),f356(x17021,x17022)))+P5(f311(a236,f235(x17021,x17022,x17023))) 7.68/7.79 [1703]~P7(x17033)+~P5(f269(a260,x17033))+~P5(f269(f309(a389,x17033),f364(x17031,x17032)))+P5(f311(a236,f233(x17031,x17032,x17033))) 7.68/7.79 [1704]~P1(x17043)+~P5(f312(a253,x17043))+~P5(f312(f293(a388,x17043),f355(x17041,x17042)))+P5(f311(a236,f121(x17041,x17042,x17043))) 7.68/7.79 [1705]~P6(x17053)+~P5(f311(a236,x17053))+~P5(f311(f294(a386,x17053),f361(x17051,x17052)))+P5(f311(a236,f122(x17051,x17052,x17053))) 7.68/7.79 [1706]~P6(x17063)+~P5(f311(a236,x17063))+~P5(f311(f294(a386,x17063),f351(x17061,x17062)))+P5(f270(a239,f160(x17061,x17062,x17063))) 7.68/7.79 [1707]~P7(x17073)+~P5(f269(a260,x17073))+~P5(f269(f309(a389,x17073),f352(x17071,x17072)))+P5(f270(a239,f188(x17071,x17072,x17073))) 7.68/7.79 [1708]~P7(x17083)+~P5(f269(a260,x17083))+~P5(f269(f309(a389,x17083),f353(x17081,x17082)))+P5(f312(a253,f227(x17081,x17082,x17083))) 7.68/7.79 [1709]~P6(x17093)+~P5(f311(a236,x17093))+~P5(f311(f294(a386,x17093),f365(x17091,x17092)))+P5(f312(a253,f120(x17091,x17092,x17093))) 7.68/7.79 [1710]~P7(x17103)+~P5(f269(a260,x17103))+~P5(f269(f309(a389,x17103),f348(x17101,x17102)))+P5(f295(a255,f226(x17101,x17102,x17103))) 7.68/7.79 [1711]~P6(x17113)+~P5(f311(a236,x17113))+~P5(f311(f294(a386,x17113),f362(x17111,x17112)))+P5(f295(a255,f232(x17111,x17112,x17113))) 7.68/7.79 [1746]P5(f331(x17461,x17462))+~P5(f331(x17461,x17463))+~P5(f331(x17461,f179(x17461,x17462,x17463)))+~P5(f331(f327(a384,x17462),x17463)) 7.68/7.79 [1773]~P5(f331(x17731,x17733))+P5(f331(x17731,x17732))+~P5(f331(f327(a384,x17732),x17733))+P5(f331(x17731,f267(a394,f179(x17731,x17732,x17733)))) 7.68/7.79 [1774]~P5(f331(x17741,x17743))+P5(f331(x17741,x17742))+~P5(f331(f327(a384,x17742),x17743))+P5(f331(f327(a383,f179(x17741,x17742,x17743)),x17743)) 7.68/7.79 [1808]~P6(x18083)+~P5(f311(a236,x18083))+~P5(f311(f294(a386,x18083),f350(x18081,x18082)))+P5(f268(f273(a385,f187(x18081,x18082,x18083)),x18082)) 7.68/7.79 [1809]~P7(x18093)+~P5(f269(a260,x18093))+~P5(f269(f309(a389,x18093),f367(x18091,x18092)))+P5(f268(f273(a385,f220(x18091,x18092,x18093)),x18092)) 7.68/7.79 [1810]~P2(x18103)+~P5(f295(a255,x18103))+~P5(f295(f310(a391,x18103),f334(x18101,x18102)))+P5(f268(f273(a385,f115(x18101,x18102,x18103)),x18102)) 7.68/7.79 [1811]~P1(x18113)+~P5(f312(a253,x18113))+~P5(f312(f293(a388,x18113),f333(x18111,x18112)))+P5(f268(f273(a385,f126(x18111,x18112,x18113)),x18112)) 7.68/7.79 [1812]~P1(x18123)+~P5(f312(a253,x18123))+~P5(f312(f293(a388,x18123),f347(x18121,x18122)))+P5(f269(f309(a389,f200(x18121,x18122,x18123)),x18122)) 7.68/7.79 [1813]~P2(x18133)+~P5(f295(a255,x18133))+~P5(f295(f310(a391,x18133),f357(x18131,x18132)))+P5(f269(f309(a389,f234(x18131,x18132,x18133)),x18132)) 7.68/7.79 [1814]~P7(x18143)+~P5(f269(a260,x18143))+~P5(f269(f309(a389,x18143),f374(x18141,x18142)))+P5(f269(f309(a389,f107(x18141,x18142,x18143)),x18142)) 7.68/7.79 [1815]~P6(x18153)+~P5(f311(a236,x18153))+~P5(f311(f294(a386,x18153),f332(x18151,x18152)))+P5(f269(f309(a389,f130(x18151,x18152,x18153)),x18152)) 7.68/7.79 [1816]~P2(x18163)+~P5(f295(a255,x18163))+~P5(f295(f310(a391,x18163),f356(x18161,x18162)))+P5(f311(f294(a386,f235(x18161,x18162,x18163)),x18162)) 7.68/7.79 [1817]~P7(x18173)+~P5(f269(a260,x18173))+~P5(f269(f309(a389,x18173),f364(x18171,x18172)))+P5(f311(f294(a386,f233(x18171,x18172,x18173)),x18172)) 7.68/7.79 [1818]~P1(x18183)+~P5(f312(a253,x18183))+~P5(f312(f293(a388,x18183),f355(x18181,x18182)))+P5(f311(f294(a386,f121(x18181,x18182,x18183)),x18182)) 7.68/7.79 [1819]~P6(x18193)+~P5(f311(a236,x18193))+~P5(f311(f294(a386,x18193),f361(x18191,x18192)))+P5(f311(f294(a386,f122(x18191,x18192,x18193)),x18192)) 7.68/7.79 [1820]~P6(x18203)+~P5(f311(a236,x18203))+~P5(f311(f294(a386,x18203),f351(x18201,x18202)))+P5(f270(f298(a387,f160(x18201,x18202,x18203)),x18202)) 7.68/7.79 [1821]~P7(x18213)+~P5(f269(a260,x18213))+~P5(f269(f309(a389,x18213),f352(x18211,x18212)))+P5(f270(f298(a387,f188(x18211,x18212,x18213)),x18212)) 7.68/7.79 [1822]~P7(x18223)+~P5(f269(a260,x18223))+~P5(f269(f309(a389,x18223),f353(x18221,x18222)))+P5(f312(f293(a388,f227(x18221,x18222,x18223)),x18222)) 7.68/7.79 [1823]~P6(x18233)+~P5(f311(a236,x18233))+~P5(f311(f294(a386,x18233),f365(x18231,x18232)))+P5(f312(f293(a388,f120(x18231,x18232,x18233)),x18232)) 7.68/7.79 [1824]~P7(x18243)+~P5(f269(a260,x18243))+~P5(f269(f309(a389,x18243),f348(x18241,x18242)))+P5(f295(f310(a391,f226(x18241,x18242,x18243)),x18242)) 7.68/7.79 [1825]~P6(x18253)+~P5(f311(a236,x18253))+~P5(f311(f294(a386,x18253),f362(x18251,x18252)))+P5(f295(f310(a391,f232(x18251,x18252,x18253)),x18252)) 7.68/7.79 [1826]~P5(f331(f327(a384,x18263),x18261))+P5(f331(f327(a384,x18261),x18262))+~P5(f331(f327(a384,x18263),x18262))+~P5(f331(f327(a384,f267(f378(x18261),x18263)),f267(f378(x18262),x18263))) 7.68/7.79 [1827]~P5(f331(f327(a384,x18273),x18271))+P5(f331(f327(a383,x18271),x18272))+~P5(f331(f327(a384,x18273),x18272))+~P5(f331(f327(a383,f267(f378(x18271),x18273)),f267(f378(x18272),x18273))) 7.68/7.79 [1829]E(x18291,x18292)+P5(f268(f328(a376,x18293),x18291))+P5(f268(f328(a376,x18293),x18292))+~E(f94(f21(a246,f52(a238,f327(f16(a247),x18293))),x18291),f94(f21(a246,f52(a238,f327(f16(a247),x18293))),x18292)) 7.68/7.79 [1851]~E(x18511,x18513)+~P8(x18513)+~P8(x18511)+P5(f343(f89(f95(f41(a240,f341(f55(a248),x18511)),f320(f57(a369),x18512))),x18513)) 7.68/7.79 [1852]~E(x18523,x18521)+~P4(x18521)+~P4(x18523)+P5(f275(f99(f96(f31(a240,f282(f77(a244),x18521)),f305(f60(a372),x18522))),x18523)) 7.68/7.79 [1865]~P8(x18651)+~P8(x18653)+~P5(f343(x18652,x18653))+P5(f343(f89(f95(f41(a240,f341(f55(a248),x18651)),f320(f57(a369),x18652))),x18653)) 7.68/7.79 [1866]~P4(x18661)+~P4(x18663)+~P5(f275(x18662,x18663))+P5(f275(f99(f96(f31(a240,f282(f77(a244),x18661)),f305(f60(a372),x18662))),x18663)) 7.68/7.79 [1867]~E(x18672,x18671)+~P8(x18671)+~P8(x18672)+P5(f269(f336(a369,x18671),f89(f95(f41(a240,f341(f55(a248),x18672)),f320(f57(a369),x18673))))) 7.68/7.79 [1868]~E(x18682,x18681)+~P4(x18681)+~P4(x18682)+P5(f311(f277(a372,x18681),f99(f96(f31(a240,f282(f77(a244),x18682)),f305(f60(a372),x18683))))) 7.68/7.79 [1421]~P6(x14211)+~E(x14211,f350(x14212,x14214))+~P5(f268(f273(a385,x14214),x14213))+P5(f311(f294(a386,x14211),f350(x14212,x14213))) 7.68/7.79 [1422]~P6(x14224)+~E(f354(x14222,x14224),x14221)+~P5(f311(f294(a386,x14224),x14223))+P5(f268(f273(a385,x14221),f354(x14222,x14223))) 7.68/7.79 [1358]~P6(x13582)+~P6(x13581)+E(x13581,x13582)+~P5(f311(f294(a386,x13582),x13581))+~P5(f311(f294(a386,x13581),x13582)) 7.68/7.79 [1364]~P7(x13642)+~P7(x13641)+E(x13641,x13642)+~P5(f269(f309(a389,x13642),x13641))+~P5(f269(f309(a389,x13641),x13642)) 7.68/7.79 [1529]P5(f269(x15291,x15292))+P7(f215(x15291,x15293,x15292))+~P5(f269(x15291,a9))+~P5(f269(a260,x15292))+~P5(f269(f309(a389,x15292),x15293)) 7.68/7.79 [1530]P5(f269(x15301,x15302))+P8(f216(x15301,x15303,x15302))+~P5(f269(x15301,a9))+~P5(f269(a260,x15302))+~P5(f269(f309(a389,x15302),x15303)) 7.68/7.79 [1531]P5(f311(x15311,x15312))+P6(f113(x15311,x15313,x15312))+~P5(f311(x15311,a8))+~P5(f311(a236,x15312))+~P5(f311(f294(a386,x15312),x15313)) 7.68/7.79 [1532]P5(f311(x15321,x15322))+P4(f114(x15321,x15323,x15322))+~P5(f311(x15321,a8))+~P5(f311(a236,x15322))+~P5(f311(f294(a386,x15322),x15323)) 7.68/7.79 [1533]P5(f312(x15331,x15332))+P1(f205(x15331,x15333,x15332))+~P5(f312(x15331,a4))+~P5(f312(a253,x15332))+~P5(f312(f293(a388,x15332),x15333)) 7.68/7.79 [1534]P5(f312(x15341,x15342))+P6(f206(x15341,x15343,x15342))+~P5(f312(x15341,a4))+~P5(f312(a253,x15342))+~P5(f312(f293(a388,x15342),x15343)) 7.68/7.79 [1535]P5(f295(x15351,x15352))+P2(f162(x15351,x15353,x15352))+~P5(f295(x15351,a7))+~P5(f295(a255,x15352))+~P5(f295(f310(a391,x15352),x15353)) 7.68/7.79 [1536]P5(f295(x15361,x15362))+P7(f163(x15361,x15363,x15362))+~P5(f295(x15361,a7))+~P5(f295(a255,x15362))+~P5(f295(f310(a391,x15362),x15363)) 7.68/7.79 [1670]P5(f268(x16701,x16702))+~P5(f268(x16701,a2))+~P5(f268(a261,x16702))+~P5(f268(f273(a385,x16702),x16703))+P5(f268(a261,f186(x16701,x16703,x16702))) 7.68/7.79 [1671]P5(f269(x16711,x16712))+~P5(f269(x16711,a9))+~P5(f269(a260,x16712))+~P5(f269(f309(a389,x16712),x16713))+P5(f269(a260,f215(x16711,x16713,x16712))) 7.68/7.79 [1672]P5(f311(x16721,x16722))+~P5(f311(x16721,a8))+~P5(f311(a236,x16722))+~P5(f311(f294(a386,x16722),x16723))+P5(f311(a236,f113(x16721,x16723,x16722))) 7.68/7.79 [1673]P5(f270(x16731,x16732))+~P5(f270(x16731,a3))+~P5(f270(a239,x16732))+~P5(f270(f298(a387,x16732),x16733))+P5(f270(a239,f228(x16731,x16733,x16732))) 7.68/7.79 [1674]P5(f312(x16741,x16742))+~P5(f312(x16741,a4))+~P5(f312(a253,x16742))+~P5(f312(f293(a388,x16742),x16743))+P5(f312(a253,f205(x16741,x16743,x16742))) 7.68/7.79 [1675]P5(f295(x16751,x16752))+~P5(f295(x16751,a7))+~P5(f295(a255,x16752))+~P5(f295(f310(a391,x16752),x16753))+P5(f295(a255,f162(x16751,x16753,x16752))) 7.68/7.79 [1676]P5(f268(x16761,x16762))+~P5(f268(x16761,a2))+~P5(f268(a261,x16762))+P5(f268(x16761,f186(x16761,x16763,x16762)))+~P5(f268(f273(a385,x16762),x16763)) 7.68/7.79 [1677]P5(f269(x16771,x16772))+~P5(f269(x16771,a9))+~P5(f269(a260,x16772))+P5(f269(x16771,f215(x16771,x16773,x16772)))+~P5(f269(f309(a389,x16772),x16773)) 7.68/7.79 [1678]P5(f311(x16781,x16782))+~P5(f311(x16781,a8))+~P5(f311(a236,x16782))+P5(f311(x16781,f113(x16781,x16783,x16782)))+~P5(f311(f294(a386,x16782),x16783)) 7.68/7.79 [1679]P5(f270(x16791,x16792))+~P5(f270(x16791,a3))+~P5(f270(a239,x16792))+P5(f270(x16791,f228(x16791,x16793,x16792)))+~P5(f270(f298(a387,x16792),x16793)) 7.68/7.79 [1680]P5(f312(x16801,x16802))+~P5(f312(x16801,a4))+~P5(f312(a253,x16802))+P5(f312(x16801,f205(x16801,x16803,x16802)))+~P5(f312(f293(a388,x16802),x16803)) 7.68/7.79 [1681]P5(f295(x16811,x16812))+~P5(f295(x16811,a7))+~P5(f295(a255,x16812))+P5(f295(x16811,f162(x16811,x16813,x16812)))+~P5(f295(f310(a391,x16812),x16813)) 7.68/7.79 [1882]P5(f268(x18821,x18822))+~P5(f268(x18821,a2))+~P5(f268(a261,x18822))+~P5(f268(f328(a376,f183(x18821,x18823,x18822)),f186(x18821,x18823,x18822)))+~P5(f268(f273(a385,x18822),x18823)) 7.68/7.79 [1883]P5(f269(x18831,x18832))+~P5(f269(x18831,a9))+~P5(f269(a260,x18832))+~P5(f269(f336(a369,f216(x18831,x18833,x18832)),f215(x18831,x18833,x18832)))+~P5(f269(f309(a389,x18832),x18833)) 7.68/7.79 [1884]P5(f311(x18841,x18842))+~P5(f311(x18841,a8))+~P5(f311(a236,x18842))+~P5(f311(f277(a372,f114(x18841,x18843,x18842)),f113(x18841,x18843,x18842)))+~P5(f311(f294(a386,x18842),x18843)) 7.68/7.79 [1885]P5(f270(x18851,x18852))+~P5(f270(x18851,a3))+~P5(f270(a239,x18852))+~P5(f270(f303(a370,f229(x18851,x18853,x18852)),f228(x18851,x18853,x18852)))+~P5(f270(f298(a387,x18852),x18853)) 7.68/7.79 [1886]P5(f312(x18861,x18862))+~P5(f312(x18861,a4))+~P5(f312(a253,x18862))+~P5(f312(f308(a371,f206(x18861,x18863,x18862)),f205(x18861,x18863,x18862)))+~P5(f312(f293(a388,x18862),x18863)) 7.68/7.79 [1887]P5(f295(x18871,x18872))+~P5(f295(x18871,a7))+~P5(f295(a255,x18872))+~P5(f295(f314(a373,f163(x18871,x18873,x18872)),f162(x18871,x18873,x18872)))+~P5(f295(f310(a391,x18872),x18873)) 7.68/7.79 [1793]P5(f268(x17931,x17932))+~P5(f268(x17931,a2))+~P5(f268(a261,x17932))+~P5(f268(f273(a385,x17932),x17933))+P5(f268(f328(a376,f183(x17931,x17933,x17932)),x17933)) 7.68/7.79 [1794]P5(f269(x17941,x17942))+~P5(f269(x17941,a9))+~P5(f269(a260,x17942))+~P5(f269(f309(a389,x17942),x17943))+P5(f269(f336(a369,f216(x17941,x17943,x17942)),x17943)) 7.68/7.79 [1795]P5(f311(x17951,x17952))+~P5(f311(x17951,a8))+~P5(f311(a236,x17952))+~P5(f311(f294(a386,x17952),x17953))+P5(f311(f277(a372,f114(x17951,x17953,x17952)),x17953)) 7.68/7.79 [1796]P5(f270(x17961,x17962))+~P5(f270(x17961,a3))+~P5(f270(a239,x17962))+~P5(f270(f298(a387,x17962),x17963))+P5(f270(f303(a370,f229(x17961,x17963,x17962)),x17963)) 7.68/7.79 [1797]P5(f312(x17971,x17972))+~P5(f312(x17971,a4))+~P5(f312(a253,x17972))+~P5(f312(f293(a388,x17972),x17973))+P5(f312(f308(a371,f206(x17971,x17973,x17972)),x17973)) 7.68/7.79 [1798]P5(f295(x17981,x17982))+~P5(f295(x17981,a7))+~P5(f295(a255,x17982))+~P5(f295(f310(a391,x17982),x17983))+P5(f295(f314(a373,f163(x17981,x17983,x17982)),x17983)) 7.68/7.79 [1990]P5(f268(x19901,x19902))+~P5(f268(x19901,a2))+~P5(f268(a261,x19902))+~P5(f268(f273(a385,x19902),x19903))+~P5(f268(x19901,f94(f21(a246,f52(a238,f327(f16(a247),f183(x19901,x19903,x19902)))),f186(x19901,x19903,x19902)))) 7.68/7.79 [1980]P5(f270(x19801,x19802))+~P5(f270(x19801,a3))+~P5(f270(a239,x19802))+~P5(f270(f298(a387,x19802),x19803))+~P5(f270(x19801,f93(f45(a240,f273(f53(a242),f229(x19801,x19803,x19802))),f290(f58(a370),f228(x19801,x19803,x19802))))) 7.68/7.79 [1902]~P8(x19022)+~P8(x19021)+E(x19021,x19022)+P5(f343(x19023,x19022))+~P5(f343(f89(f95(f41(a240,f341(f55(a248),x19021)),f320(f57(a369),x19023))),x19022)) 7.68/7.79 [1903]~P4(x19032)+~P4(x19031)+E(x19031,x19032)+P5(f275(x19033,x19032))+~P5(f275(f99(f96(f31(a240,f282(f77(a244),x19031)),f305(f60(a372),x19033))),x19032)) 7.68/7.79 [1915]~P8(x19152)+~P8(x19151)+E(x19151,x19152)+P5(f269(f336(a369,x19152),x19153))+~P5(f269(f336(a369,x19152),f89(f95(f41(a240,f341(f55(a248),x19151)),f320(f57(a369),x19153))))) 7.68/7.79 [1916]~P8(x19162)+~P8(x19161)+E(x19161,x19162)+P5(f269(f336(a369,x19161),x19163))+~P5(f269(f336(a369,x19161),f89(f95(f41(a240,f341(f55(a248),x19162)),f320(f57(a369),x19163))))) 7.68/7.79 [1918]~P4(x19182)+~P4(x19181)+E(x19181,x19182)+P5(f311(f277(a372,x19181),x19183))+~P5(f311(f277(a372,x19181),f99(f96(f31(a240,f282(f77(a244),x19182)),f305(f60(a372),x19183))))) 7.68/7.79 [1991]P5(f269(x19911,x19912))+~P5(f269(x19911,a9))+~P5(f269(a260,x19912))+~P5(f269(f309(a389,x19912),x19913))+~P5(f269(x19911,f89(f95(f41(a240,f341(f55(a248),f216(x19911,x19913,x19912))),f320(f57(a369),f215(x19911,x19913,x19912)))))) 7.68/7.79 [1992]P5(f311(x19921,x19922))+~P5(f311(x19921,a8))+~P5(f311(a236,x19922))+~P5(f311(f294(a386,x19922),x19923))+~P5(f311(x19921,f99(f96(f31(a240,f282(f77(a244),f114(x19921,x19923,x19922))),f305(f60(a372),f113(x19921,x19923,x19922)))))) 7.68/7.79 [1993]P5(f312(x19931,x19932))+~P5(f312(x19931,a4))+~P5(f312(a253,x19932))+~P5(f312(f293(a388,x19932),x19933))+~P5(f312(x19931,f101(f92(f39(a240,f294(f63(a243),f206(x19931,x19933,x19932))),f304(f64(a371),f205(x19931,x19933,x19932)))))) 7.68/7.79 [1994]P5(f295(x19941,x19942))+~P5(f295(x19941,a7))+~P5(f295(a255,x19942))+~P5(f295(f310(a391,x19942),x19943))+~P5(f295(x19941,f90(f91(f36(a240,f309(f54(a245),f163(x19941,x19943,x19942))),f313(f66(a373),f162(x19941,x19943,x19942)))))) 7.68/7.79 [1425]~P6(x14251)+~P7(x14254)+~E(x14251,f332(x14252,x14254))+~P5(f269(f309(a389,x14254),x14253))+P5(f311(f294(a386,x14251),f332(x14252,x14253))) 7.68/7.79 [1426]~P4(x14261)+~P8(x14264)+~E(x14261,f344(x14262,x14264))+~P5(f269(f336(a369,x14264),x14263))+P5(f311(f277(a372,x14261),f332(x14262,x14263))) 7.68/7.79 [1427]~P6(x14274)+~P7(x14271)+~E(f364(x14272,x14274),x14271)+~P5(f311(f294(a386,x14274),x14273))+P5(f269(f309(a389,x14271),f364(x14272,x14273))) 7.68/7.79 [1720]~P1(x17202)+~P1(x17201)+E(x17201,x17202)+~P5(f312(a253,x17201))+~P5(f312(f293(a388,x17202),x17201))+~P5(f331(f327(a384,f306(a251,x17201)),f306(a251,x17202))) 7.68/7.79 [1721]~P2(x17212)+~P2(x17211)+E(x17211,x17212)+~P5(f295(a255,x17211))+~P5(f295(f310(a391,x17212),x17211))+~P5(f331(f327(a384,f315(a252,x17211)),f315(a252,x17212))) 7.68/7.79 [1722]~P6(x17222)+~P6(x17221)+E(x17221,x17222)+~P5(f311(a236,x17222))+~P5(f311(f294(a386,x17221),x17222))+~P5(f331(f327(a384,f324(a257,x17222)),f324(a257,x17221))) 7.68/7.79 [1723]~P7(x17232)+~P7(x17231)+E(x17231,x17232)+~P5(f269(a260,x17232))+~P5(f269(f309(a389,x17231),x17232))+~P5(f331(f327(a384,f318(a259,x17232)),f318(a259,x17231))) 7.68/7.79 [1843]~P7(x18432)+~P7(x18431)+E(x18431,x18432)+P5(f269(f336(a369,x18433),x18431))+~E(f89(f95(f41(a240,f341(f55(a248),x18433)),f320(f57(a369),x18431))),f89(f95(f41(a240,f341(f55(a248),x18433)),f320(f57(a369),x18432))))+P5(f269(f336(a369,x18433),x18432)) 7.68/7.79 [1844]~P6(x18442)+~P6(x18441)+E(x18441,x18442)+P5(f311(f277(a372,x18443),x18441))+~E(f99(f96(f31(a240,f282(f77(a244),x18443)),f305(f60(a372),x18441))),f99(f96(f31(a240,f282(f77(a244),x18443)),f305(f60(a372),x18442))))+P5(f311(f277(a372,x18443),x18442)) 7.68/7.79 [1962]~E(x19623,x19622)+~E(x19621,x19624)+~P4(x19622)+~P4(x19623)+~P4(x19624)+~P4(x19621)+E(f99(f96(f31(a240,f282(f77(a244),x19621)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x19622)),f305(f60(a372),a8)))))),f99(f96(f31(a240,f282(f77(a244),x19623)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x19624)),f305(f60(a372),a8))))))) 7.68/7.79 [1963]~E(x19632,x19633)+~E(x19631,x19634)+~P8(x19633)+~P8(x19632)+~P8(x19634)+~P8(x19631)+E(f89(f95(f41(a240,f341(f55(a248),x19631)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x19632)),f320(f57(a369),a9)))))),f89(f95(f41(a240,f341(f55(a248),x19633)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x19634)),f320(f57(a369),a9))))))) 7.68/7.79 [1982]~P4(x19824)+~P4(x19822)+~P4(x19821)+~P4(x19823)+E(x19821,x19822)+E(x19823,x19821)+~E(f99(f96(f31(a240,f282(f77(a244),x19822)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x19823)),f305(f60(a372),a8)))))),f99(f96(f31(a240,f282(f77(a244),x19824)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x19821)),f305(f60(a372),a8))))))) 7.68/7.79 [1983]~P4(x19834)+~P4(x19832)+~P4(x19831)+~P4(x19833)+E(x19831,x19832)+E(x19833,x19831)+~E(f99(f96(f31(a240,f282(f77(a244),x19833)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x19832)),f305(f60(a372),a8)))))),f99(f96(f31(a240,f282(f77(a244),x19831)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x19834)),f305(f60(a372),a8))))))) 7.68/7.79 [1984]~P8(x19844)+~P8(x19842)+~P8(x19841)+~P8(x19843)+E(x19841,x19842)+E(x19843,x19841)+~E(f89(f95(f41(a240,f341(f55(a248),x19842)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x19843)),f320(f57(a369),a9)))))),f89(f95(f41(a240,f341(f55(a248),x19844)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x19841)),f320(f57(a369),a9))))))) 7.68/7.79 [1985]~P8(x19854)+~P8(x19852)+~P8(x19851)+~P8(x19853)+E(x19851,x19852)+E(x19853,x19851)+~E(f89(f95(f41(a240,f341(f55(a248),x19853)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x19852)),f320(f57(a369),a9)))))),f89(f95(f41(a240,f341(f55(a248),x19851)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x19854)),f320(f57(a369),a9))))))) 7.68/7.79 [1986]~P4(x19864)+~P4(x19862)+~P4(x19863)+~P4(x19861)+E(x19861,x19862)+E(x19861,x19863)+~E(f99(f96(f31(a240,f282(f77(a244),x19862)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x19863)),f305(f60(a372),a8)))))),f99(f96(f31(a240,f282(f77(a244),x19864)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x19861)),f305(f60(a372),a8))))))) 7.68/7.79 [1987]~P4(x19874)+~P4(x19872)+~P4(x19873)+~P4(x19871)+E(x19871,x19872)+E(x19871,x19873)+~E(f99(f96(f31(a240,f282(f77(a244),x19871)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x19874)),f305(f60(a372),a8)))))),f99(f96(f31(a240,f282(f77(a244),x19873)),f305(f60(a372),f99(f96(f31(a240,f282(f77(a244),x19872)),f305(f60(a372),a8))))))) 7.68/7.79 [1988]~P8(x19884)+~P8(x19882)+~P8(x19883)+~P8(x19881)+E(x19881,x19882)+E(x19881,x19883)+~E(f89(f95(f41(a240,f341(f55(a248),x19882)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x19883)),f320(f57(a369),a9)))))),f89(f95(f41(a240,f341(f55(a248),x19884)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x19881)),f320(f57(a369),a9))))))) 7.68/7.79 [1989]~P8(x19894)+~P8(x19892)+~P8(x19893)+~P8(x19891)+E(x19891,x19892)+E(x19891,x19893)+~E(f89(f95(f41(a240,f341(f55(a248),x19891)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x19894)),f320(f57(a369),a9)))))),f89(f95(f41(a240,f341(f55(a248),x19893)),f320(f57(a369),f89(f95(f41(a240,f341(f55(a248),x19892)),f320(f57(a369),a9))))))) 7.68/7.79 %EqnAxiom 7.68/7.79 [1]E(x11,x11) 7.68/7.79 [2]E(x22,x21)+~E(x21,x22) 7.68/7.79 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) 7.68/7.79 [4]~E(x41,x42)+E(f13(x41),f13(x42)) 7.68/7.79 [5]~E(x51,x52)+E(f14(x51),f14(x52)) 7.68/7.79 [6]~E(x61,x62)+E(f88(x61),f88(x62)) 7.68/7.79 [7]~E(x71,x72)+E(f89(x71),f89(x72)) 7.68/7.79 [8]~E(x81,x82)+E(f15(x81),f15(x82)) 7.68/7.79 [9]~E(x91,x92)+E(f90(x91),f90(x92)) 7.68/7.79 [10]~E(x101,x102)+E(f85(x101),f85(x102)) 7.68/7.79 [11]~E(x111,x112)+E(f99(x111),f99(x112)) 7.68/7.79 [12]~E(x121,x122)+E(f86(x121),f86(x122)) 7.68/7.79 [13]~E(x131,x132)+E(f101(x131),f101(x132)) 7.68/7.79 [14]~E(x141,x142)+E(f397(x141),f397(x142)) 7.68/7.79 [15]~E(x151,x152)+E(f401(x151),f401(x152)) 7.68/7.79 [16]~E(x161,x162)+E(f266(x161),f266(x162)) 7.68/7.79 [17]~E(x171,x172)+E(f403(x171),f403(x172)) 7.68/7.79 [18]~E(x181,x182)+E(f267(x181,x183),f267(x182,x183)) 7.68/7.79 [19]~E(x191,x192)+E(f267(x193,x191),f267(x193,x192)) 7.68/7.79 [20]~E(x201,x202)+E(f332(x201,x203),f332(x202,x203)) 7.68/7.79 [21]~E(x211,x212)+E(f332(x213,x211),f332(x213,x212)) 7.68/7.79 [22]~E(x221,x222)+E(f378(x221),f378(x222)) 7.68/7.79 [23]~E(x231,x232)+E(f60(x231),f60(x232)) 7.68/7.79 [24]~E(x241,x242)+E(f323(x241,x243),f323(x242,x243)) 7.68/7.79 [25]~E(x251,x252)+E(f323(x253,x251),f323(x253,x252)) 7.68/7.79 [26]~E(x261,x262)+E(f96(x261,x263),f96(x262,x263)) 7.68/7.79 [27]~E(x271,x272)+E(f96(x273,x271),f96(x273,x272)) 7.68/7.79 [28]~E(x281,x282)+E(f127(x281,x283,x284),f127(x282,x283,x284)) 7.68/7.79 [29]~E(x291,x292)+E(f127(x293,x291,x294),f127(x293,x292,x294)) 7.68/7.79 [30]~E(x301,x302)+E(f127(x303,x304,x301),f127(x303,x304,x302)) 7.68/7.79 [31]~E(x311,x312)+E(f305(x311,x313),f305(x312,x313)) 7.68/7.79 [32]~E(x321,x322)+E(f305(x323,x321),f305(x323,x322)) 7.68/7.79 [33]~E(x331,x332)+E(f268(x331,x333),f268(x332,x333)) 7.68/7.79 [34]~E(x341,x342)+E(f268(x343,x341),f268(x343,x342)) 7.68/7.79 [35]~E(x351,x352)+E(f269(x351,x353),f269(x352,x353)) 7.68/7.79 [36]~E(x361,x362)+E(f269(x363,x361),f269(x363,x362)) 7.68/7.79 [37]~E(x371,x372)+E(f294(x371,x373),f294(x372,x373)) 7.68/7.79 [38]~E(x381,x382)+E(f294(x383,x381),f294(x383,x382)) 7.68/7.79 [39]~E(x391,x392)+E(f311(x391,x393),f311(x392,x393)) 7.68/7.79 [40]~E(x401,x402)+E(f311(x403,x401),f311(x403,x402)) 7.68/7.79 [41]~E(x411,x412)+E(f270(x411,x413),f270(x412,x413)) 7.68/7.79 [42]~E(x421,x422)+E(f270(x423,x421),f270(x423,x422)) 7.68/7.79 [43]~E(x431,x432)+E(f312(x431,x433),f312(x432,x433)) 7.68/7.79 [44]~E(x441,x442)+E(f312(x443,x441),f312(x443,x442)) 7.68/7.79 [45]~E(x451,x452)+E(f295(x451,x453),f295(x452,x453)) 7.68/7.79 [46]~E(x461,x462)+E(f295(x463,x461),f295(x463,x462)) 7.68/7.79 [47]~E(x471,x472)+E(f382(x471),f382(x472)) 7.68/7.79 [48]~E(x481,x482)+E(f327(x481,x483),f327(x482,x483)) 7.68/7.79 [49]~E(x491,x492)+E(f327(x493,x491),f327(x493,x492)) 7.68/7.79 [50]~E(x501,x502)+E(f31(x501,x503),f31(x502,x503)) 7.68/7.79 [51]~E(x511,x512)+E(f31(x513,x511),f31(x513,x512)) 7.68/7.79 [52]~E(x521,x522)+E(f322(x521,x523),f322(x522,x523)) 7.68/7.79 [53]~E(x531,x532)+E(f322(x533,x531),f322(x533,x532)) 7.68/7.79 [54]~E(x541,x542)+E(f333(x541,x543),f333(x542,x543)) 7.68/7.79 [55]~E(x551,x552)+E(f333(x553,x551),f333(x553,x552)) 7.68/7.79 [56]~E(x561,x562)+E(f334(x561,x563),f334(x562,x563)) 7.68/7.79 [57]~E(x571,x572)+E(f334(x573,x571),f334(x573,x572)) 7.68/7.79 [58]~E(x581,x582)+E(f326(x581,x583),f326(x582,x583)) 7.68/7.79 [59]~E(x591,x592)+E(f326(x593,x591),f326(x593,x592)) 7.68/7.79 [60]~E(x601,x602)+E(f350(x601,x603),f350(x602,x603)) 7.68/7.79 [61]~E(x611,x612)+E(f350(x613,x611),f350(x613,x612)) 7.68/7.79 [62]~E(x621,x622)+E(f329(x621,x623),f329(x622,x623)) 7.68/7.79 [63]~E(x631,x632)+E(f329(x633,x631),f329(x633,x632)) 7.68/7.79 [64]~E(x641,x642)+E(f351(x641,x643),f351(x642,x643)) 7.68/7.79 [65]~E(x651,x652)+E(f351(x653,x651),f351(x653,x652)) 7.68/7.79 [66]~E(x661,x662)+E(f271(x661,x663),f271(x662,x663)) 7.68/7.79 [67]~E(x671,x672)+E(f271(x673,x671),f271(x673,x672)) 7.68/7.79 [68]~E(x681,x682)+E(f330(x681,x683),f330(x682,x683)) 7.68/7.79 [69]~E(x691,x692)+E(f330(x693,x691),f330(x693,x692)) 7.68/7.79 [70]~E(x701,x702)+E(f316(x701,x703),f316(x702,x703)) 7.68/7.79 [71]~E(x711,x712)+E(f316(x713,x711),f316(x713,x712)) 7.68/7.79 [72]~E(x721,x722)+E(f319(x721,x723),f319(x722,x723)) 7.68/7.79 [73]~E(x731,x732)+E(f319(x733,x731),f319(x733,x732)) 7.68/7.79 [74]~E(x741,x742)+E(f367(x741,x743),f367(x742,x743)) 7.68/7.79 [75]~E(x751,x752)+E(f367(x753,x751),f367(x753,x752)) 7.68/7.79 [76]~E(x761,x762)+E(f352(x761,x763),f352(x762,x763)) 7.68/7.79 [77]~E(x771,x772)+E(f352(x773,x771),f352(x773,x772)) 7.68/7.79 [78]~E(x781,x782)+E(f335(x781,x783),f335(x782,x783)) 7.68/7.79 [79]~E(x791,x792)+E(f335(x793,x791),f335(x793,x792)) 7.68/7.79 [80]~E(x801,x802)+E(f272(x801,x803),f272(x802,x803)) 7.68/7.79 [81]~E(x811,x812)+E(f272(x813,x811),f272(x813,x812)) 7.68/7.79 [82]~E(x821,x822)+E(f21(x821,x823),f21(x822,x823)) 7.68/7.79 [83]~E(x831,x832)+E(f21(x833,x831),f21(x833,x832)) 7.68/7.79 [84]~E(x841,x842)+E(f331(x841,x843),f331(x842,x843)) 7.68/7.79 [85]~E(x851,x852)+E(f331(x853,x851),f331(x853,x852)) 7.68/7.79 [86]~E(x861,x862)+E(f273(x861,x863),f273(x862,x863)) 7.68/7.79 [87]~E(x871,x872)+E(f273(x873,x871),f273(x873,x872)) 7.68/7.79 [88]~E(x881,x882)+E(f317(x881,x883),f317(x882,x883)) 7.68/7.79 [89]~E(x891,x892)+E(f317(x893,x891),f317(x893,x892)) 7.68/7.79 [90]~E(x901,x902)+E(f299(x901,x903),f299(x902,x903)) 7.68/7.79 [91]~E(x911,x912)+E(f299(x913,x911),f299(x913,x912)) 7.68/7.79 [92]~E(x921,x922)+E(f300(x921,x923),f300(x922,x923)) 7.68/7.79 [93]~E(x931,x932)+E(f300(x933,x931),f300(x933,x932)) 7.68/7.79 [94]~E(x941,x942)+E(f41(x941,x943),f41(x942,x943)) 7.68/7.79 [95]~E(x951,x952)+E(f41(x953,x951),f41(x953,x952)) 7.68/7.79 [96]~E(x961,x962)+E(f282(x961,x963),f282(x962,x963)) 7.68/7.79 [97]~E(x971,x972)+E(f282(x973,x971),f282(x973,x972)) 7.68/7.79 [98]~E(x981,x982)+E(f221(x981,x983),f221(x982,x983)) 7.68/7.79 [99]~E(x991,x992)+E(f221(x993,x991),f221(x993,x992)) 7.68/7.79 [100]~E(x1001,x1002)+E(f52(x1001,x1003),f52(x1002,x1003)) 7.68/7.79 [101]~E(x1011,x1012)+E(f52(x1013,x1011),f52(x1013,x1012)) 7.68/7.79 [102]~E(x1021,x1022)+E(f77(x1021),f77(x1022)) 7.68/7.79 [103]~E(x1031,x1032)+E(f304(x1031,x1033),f304(x1032,x1033)) 7.68/7.79 [104]~E(x1041,x1042)+E(f304(x1043,x1041),f304(x1043,x1042)) 7.68/7.79 [105]~E(x1051,x1052)+E(f392(x1051),f392(x1052)) 7.68/7.79 [106]~E(x1061,x1062)+E(f16(x1061),f16(x1062)) 7.68/7.79 [107]~E(x1071,x1072)+E(f95(x1071,x1073),f95(x1072,x1073)) 7.68/7.79 [108]~E(x1081,x1082)+E(f95(x1083,x1081),f95(x1083,x1082)) 7.68/7.79 [109]~E(x1091,x1092)+E(f301(x1091,x1093),f301(x1092,x1093)) 7.68/7.79 [110]~E(x1101,x1102)+E(f301(x1103,x1101),f301(x1103,x1102)) 7.68/7.79 [111]~E(x1111,x1112)+E(f364(x1111,x1113),f364(x1112,x1113)) 7.68/7.79 [112]~E(x1121,x1122)+E(f364(x1123,x1121),f364(x1123,x1122)) 7.68/7.79 [113]~E(x1131,x1132)+E(f277(x1131,x1133),f277(x1132,x1133)) 7.68/7.79 [114]~E(x1141,x1142)+E(f277(x1143,x1141),f277(x1143,x1142)) 7.68/7.79 [115]~E(x1151,x1152)+E(f324(x1151,x1153),f324(x1152,x1153)) 7.68/7.79 [116]~E(x1161,x1162)+E(f324(x1163,x1161),f324(x1163,x1162)) 7.68/7.79 [117]~E(x1171,x1172)+E(f263(x1171,x1173),f263(x1172,x1173)) 7.68/7.79 [118]~E(x1181,x1182)+E(f263(x1183,x1181),f263(x1183,x1182)) 7.68/7.79 [119]~E(x1191,x1192)+E(f402(x1191),f402(x1192)) 7.68/7.79 [120]~E(x1201,x1202)+E(f320(x1201,x1203),f320(x1202,x1203)) 7.68/7.79 [121]~E(x1211,x1212)+E(f320(x1213,x1211),f320(x1213,x1212)) 7.68/7.79 [122]~E(x1221,x1222)+E(f398(x1221),f398(x1222)) 7.68/7.79 [123]~E(x1231,x1232)+E(f303(x1231,x1233),f303(x1232,x1233)) 7.68/7.79 [124]~E(x1241,x1242)+E(f303(x1243,x1241),f303(x1243,x1242)) 7.68/7.79 [125]~E(x1251,x1252)+E(f343(x1251,x1253),f343(x1252,x1253)) 7.68/7.79 [126]~E(x1261,x1262)+E(f343(x1263,x1261),f343(x1263,x1262)) 7.68/7.79 [127]~E(x1271,x1272)+E(f175(x1271,x1273),f175(x1272,x1273)) 7.68/7.79 [128]~E(x1281,x1282)+E(f175(x1283,x1281),f175(x1283,x1282)) 7.68/7.79 [129]~E(x1291,x1292)+E(f93(x1291,x1293),f93(x1292,x1293)) 7.68/7.79 [130]~E(x1301,x1302)+E(f93(x1303,x1301),f93(x1303,x1302)) 7.68/7.79 [131]~E(x1311,x1312)+E(f341(x1311,x1313),f341(x1312,x1313)) 7.68/7.79 [132]~E(x1321,x1322)+E(f341(x1323,x1321),f341(x1323,x1322)) 7.68/7.79 [133]~E(x1331,x1332)+E(f306(x1331,x1333),f306(x1332,x1333)) 7.68/7.79 [134]~E(x1341,x1342)+E(f306(x1343,x1341),f306(x1343,x1342)) 7.68/7.79 [135]~E(x1351,x1352)+E(f290(x1351,x1353),f290(x1352,x1353)) 7.68/7.79 [136]~E(x1361,x1362)+E(f290(x1363,x1361),f290(x1363,x1362)) 7.68/7.79 [137]~E(x1371,x1372)+E(f228(x1371,x1373,x1374),f228(x1372,x1373,x1374)) 7.68/7.79 [138]~E(x1381,x1382)+E(f228(x1383,x1381,x1384),f228(x1383,x1382,x1384)) 7.68/7.79 [139]~E(x1391,x1392)+E(f228(x1393,x1394,x1391),f228(x1393,x1394,x1392)) 7.68/7.79 [140]~E(x1401,x1402)+E(f58(x1401),f58(x1402)) 7.68/7.79 [141]~E(x1411,x1412)+E(f57(x1411),f57(x1412)) 7.68/7.79 [142]~E(x1421,x1422)+E(f45(x1421,x1423),f45(x1422,x1423)) 7.68/7.79 [143]~E(x1431,x1432)+E(f45(x1433,x1431),f45(x1433,x1432)) 7.68/7.79 [144]~E(x1441,x1442)+E(f336(x1441,x1443),f336(x1442,x1443)) 7.68/7.79 [145]~E(x1451,x1452)+E(f336(x1453,x1451),f336(x1453,x1452)) 7.68/7.79 [146]~E(x1461,x1462)+E(f94(x1461,x1463),f94(x1462,x1463)) 7.68/7.79 [147]~E(x1471,x1472)+E(f94(x1473,x1471),f94(x1473,x1472)) 7.68/7.79 [148]~E(x1481,x1482)+E(f54(x1481),f54(x1482)) 7.68/7.79 [149]~E(x1491,x1492)+E(f131(x1491,x1493,x1494),f131(x1492,x1493,x1494)) 7.68/7.79 [150]~E(x1501,x1502)+E(f131(x1503,x1501,x1504),f131(x1503,x1502,x1504)) 7.68/7.79 [151]~E(x1511,x1512)+E(f131(x1513,x1514,x1511),f131(x1513,x1514,x1512)) 7.68/7.79 [152]~E(x1521,x1522)+E(f375(x1521,x1523),f375(x1522,x1523)) 7.68/7.79 [153]~E(x1531,x1532)+E(f375(x1533,x1531),f375(x1533,x1532)) 7.68/7.79 [154]~E(x1541,x1542)+E(f313(x1541,x1543),f313(x1542,x1543)) 7.68/7.79 [155]~E(x1551,x1552)+E(f313(x1553,x1551),f313(x1553,x1552)) 7.68/7.79 [156]~E(x1561,x1562)+E(f309(x1561,x1563),f309(x1562,x1563)) 7.68/7.79 [157]~E(x1571,x1572)+E(f309(x1573,x1571),f309(x1573,x1572)) 7.68/7.79 [158]~E(x1581,x1582)+E(f345(x1581,x1583),f345(x1582,x1583)) 7.68/7.79 [159]~E(x1591,x1592)+E(f345(x1593,x1591),f345(x1593,x1592)) 7.68/7.79 [160]~E(x1601,x1602)+E(f149(x1601,x1603),f149(x1602,x1603)) 7.68/7.79 [161]~E(x1611,x1612)+E(f149(x1613,x1611),f149(x1613,x1612)) 7.68/7.79 [162]~E(x1621,x1622)+E(f190(x1621,x1623,x1624),f190(x1622,x1623,x1624)) 7.68/7.79 [163]~E(x1631,x1632)+E(f190(x1633,x1631,x1634),f190(x1633,x1632,x1634)) 7.68/7.79 [164]~E(x1641,x1642)+E(f190(x1643,x1644,x1641),f190(x1643,x1644,x1642)) 7.68/7.79 [165]~E(x1651,x1652)+E(f129(x1651,x1653,x1654),f129(x1652,x1653,x1654)) 7.68/7.79 [166]~E(x1661,x1662)+E(f129(x1663,x1661,x1664),f129(x1663,x1662,x1664)) 7.68/7.79 [167]~E(x1671,x1672)+E(f129(x1673,x1674,x1671),f129(x1673,x1674,x1672)) 7.68/7.79 [168]~E(x1681,x1682)+E(f26(x1681,x1683),f26(x1682,x1683)) 7.68/7.79 [169]~E(x1691,x1692)+E(f26(x1693,x1691),f26(x1693,x1692)) 7.68/7.79 [170]~E(x1701,x1702)+E(f293(x1701,x1703),f293(x1702,x1703)) 7.68/7.79 [171]~E(x1711,x1712)+E(f293(x1713,x1711),f293(x1713,x1712)) 7.68/7.79 [172]~E(x1721,x1722)+E(f321(x1721,x1723),f321(x1722,x1723)) 7.68/7.79 [173]~E(x1731,x1732)+E(f321(x1733,x1731),f321(x1733,x1732)) 7.68/7.79 [174]~E(x1741,x1742)+E(f35(x1741,x1743),f35(x1742,x1743)) 7.68/7.79 [175]~E(x1751,x1752)+E(f35(x1753,x1751),f35(x1753,x1752)) 7.68/7.79 [176]~E(x1761,x1762)+E(f232(x1761,x1763,x1764),f232(x1762,x1763,x1764)) 7.68/7.79 [177]~E(x1771,x1772)+E(f232(x1773,x1771,x1774),f232(x1773,x1772,x1774)) 7.68/7.79 [178]~E(x1781,x1782)+E(f232(x1783,x1784,x1781),f232(x1783,x1784,x1782)) 7.68/7.79 [179]~E(x1791,x1792)+E(f274(x1791,x1793),f274(x1792,x1793)) 7.68/7.79 [180]~E(x1801,x1802)+E(f274(x1803,x1801),f274(x1803,x1802)) 7.68/7.79 [181]~E(x1811,x1812)+E(f286(x1811,x1813),f286(x1812,x1813)) 7.68/7.79 [182]~E(x1821,x1822)+E(f286(x1823,x1821),f286(x1823,x1822)) 7.68/7.79 [183]~E(x1831,x1832)+E(f328(x1831,x1833),f328(x1832,x1833)) 7.68/7.79 [184]~E(x1841,x1842)+E(f328(x1843,x1841),f328(x1843,x1842)) 7.68/7.79 [185]~E(x1851,x1852)+E(f296(x1851,x1853),f296(x1852,x1853)) 7.68/7.79 [186]~E(x1861,x1862)+E(f296(x1863,x1861),f296(x1863,x1862)) 7.68/7.79 [187]~E(x1871,x1872)+E(f157(x1871,x1873),f157(x1872,x1873)) 7.68/7.79 [188]~E(x1881,x1882)+E(f157(x1883,x1881),f157(x1883,x1882)) 7.68/7.79 [189]~E(x1891,x1892)+E(f275(x1891,x1893),f275(x1892,x1893)) 7.68/7.79 [190]~E(x1901,x1902)+E(f275(x1903,x1901),f275(x1903,x1902)) 7.68/7.79 [191]~E(x1911,x1912)+E(f53(x1911),f53(x1912)) 7.68/7.79 [192]~E(x1921,x1922)+E(f184(x1921,x1923),f184(x1922,x1923)) 7.68/7.79 [193]~E(x1931,x1932)+E(f184(x1933,x1931),f184(x1933,x1932)) 7.68/7.79 [194]~E(x1941,x1942)+E(f346(x1941,x1943),f346(x1942,x1943)) 7.68/7.79 [195]~E(x1951,x1952)+E(f346(x1953,x1951),f346(x1953,x1952)) 7.68/7.79 [196]~E(x1961,x1962)+E(f130(x1961,x1963,x1964),f130(x1962,x1963,x1964)) 7.68/7.79 [197]~E(x1971,x1972)+E(f130(x1973,x1971,x1974),f130(x1973,x1972,x1974)) 7.68/7.79 [198]~E(x1981,x1982)+E(f130(x1983,x1984,x1981),f130(x1983,x1984,x1982)) 7.68/7.79 [199]~E(x1991,x1992)+E(f181(x1991,x1993),f181(x1992,x1993)) 7.68/7.79 [200]~E(x2001,x2002)+E(f181(x2003,x2001),f181(x2003,x2002)) 7.68/7.79 [201]~E(x2011,x2012)+E(f215(x2011,x2013,x2014),f215(x2012,x2013,x2014)) 7.68/7.79 [202]~E(x2021,x2022)+E(f215(x2023,x2021,x2024),f215(x2023,x2022,x2024)) 7.68/7.79 [203]~E(x2031,x2032)+E(f215(x2033,x2034,x2031),f215(x2033,x2034,x2032)) 7.68/7.79 [204]~E(x2041,x2042)+E(f71(x2041),f71(x2042)) 7.68/7.79 [205]~E(x2051,x2052)+E(f55(x2051),f55(x2052)) 7.68/7.79 [206]~E(x2061,x2062)+E(f106(x2061,x2063,x2064),f106(x2062,x2063,x2064)) 7.68/7.79 [207]~E(x2071,x2072)+E(f106(x2073,x2071,x2074),f106(x2073,x2072,x2074)) 7.68/7.79 [208]~E(x2081,x2082)+E(f106(x2083,x2084,x2081),f106(x2083,x2084,x2082)) 7.68/7.79 [209]~E(x2091,x2092)+E(f339(x2091,x2093),f339(x2092,x2093)) 7.68/7.79 [210]~E(x2101,x2102)+E(f339(x2103,x2101),f339(x2103,x2102)) 7.68/7.79 [211]~E(x2111,x2112)+E(f318(x2111,x2113),f318(x2112,x2113)) 7.68/7.79 [212]~E(x2121,x2122)+E(f318(x2123,x2121),f318(x2123,x2122)) 7.68/7.79 [213]~E(x2131,x2132)+E(f204(x2131,x2133,x2134),f204(x2132,x2133,x2134)) 7.68/7.79 [214]~E(x2141,x2142)+E(f204(x2143,x2141,x2144),f204(x2143,x2142,x2144)) 7.68/7.79 [215]~E(x2151,x2152)+E(f204(x2153,x2154,x2151),f204(x2153,x2154,x2152)) 7.68/7.79 [216]~E(x2161,x2162)+E(f191(x2161,x2163,x2164),f191(x2162,x2163,x2164)) 7.68/7.79 [217]~E(x2171,x2172)+E(f191(x2173,x2171,x2174),f191(x2173,x2172,x2174)) 7.68/7.79 [218]~E(x2181,x2182)+E(f191(x2183,x2184,x2181),f191(x2183,x2184,x2182)) 7.68/7.79 [219]~E(x2191,x2192)+E(f196(x2191,x2193),f196(x2192,x2193)) 7.68/7.79 [220]~E(x2201,x2202)+E(f196(x2203,x2201),f196(x2203,x2202)) 7.68/7.79 [221]~E(x2211,x2212)+E(f39(x2211,x2213),f39(x2212,x2213)) 7.68/7.79 [222]~E(x2221,x2222)+E(f39(x2223,x2221),f39(x2223,x2222)) 7.68/7.79 [223]~E(x2231,x2232)+E(f314(x2231,x2233),f314(x2232,x2233)) 7.68/7.79 [224]~E(x2241,x2242)+E(f314(x2243,x2241),f314(x2243,x2242)) 7.68/7.79 [225]~E(x2251,x2252)+E(f116(x2251,x2253,x2254),f116(x2252,x2253,x2254)) 7.68/7.79 [226]~E(x2261,x2262)+E(f116(x2263,x2261,x2264),f116(x2263,x2262,x2264)) 7.68/7.79 [227]~E(x2271,x2272)+E(f116(x2273,x2274,x2271),f116(x2273,x2274,x2272)) 7.68/7.79 [228]~E(x2281,x2282)+E(f67(x2281),f67(x2282)) 7.68/7.79 [229]~E(x2291,x2292)+E(f17(x2291,x2293),f17(x2292,x2293)) 7.68/7.79 [230]~E(x2301,x2302)+E(f17(x2303,x2301),f17(x2303,x2302)) 7.68/7.79 [231]~E(x2311,x2312)+E(f337(x2311,x2313),f337(x2312,x2313)) 7.68/7.79 [232]~E(x2321,x2322)+E(f337(x2323,x2321),f337(x2323,x2322)) 7.68/7.79 [233]~E(x2331,x2332)+E(f338(x2331,x2333),f338(x2332,x2333)) 7.68/7.79 [234]~E(x2341,x2342)+E(f338(x2343,x2341),f338(x2343,x2342)) 7.68/7.79 [235]~E(x2351,x2352)+E(f61(x2351),f61(x2352)) 7.68/7.79 [236]~E(x2361,x2362)+E(f18(x2361,x2363),f18(x2362,x2363)) 7.68/7.79 [237]~E(x2371,x2372)+E(f18(x2373,x2371),f18(x2373,x2372)) 7.68/7.79 [238]~E(x2381,x2382)+E(f360(x2381,x2383),f360(x2382,x2383)) 7.68/7.79 [239]~E(x2391,x2392)+E(f360(x2393,x2391),f360(x2393,x2392)) 7.68/7.79 [240]~E(x2401,x2402)+E(f229(x2401,x2403,x2404),f229(x2402,x2403,x2404)) 7.68/7.79 [241]~E(x2411,x2412)+E(f229(x2413,x2411,x2414),f229(x2413,x2412,x2414)) 7.68/7.79 [242]~E(x2421,x2422)+E(f229(x2423,x2424,x2421),f229(x2423,x2424,x2422)) 7.68/7.79 [243]~E(x2431,x2432)+E(f92(x2431,x2433),f92(x2432,x2433)) 7.68/7.79 [244]~E(x2441,x2442)+E(f92(x2443,x2441),f92(x2443,x2442)) 7.68/7.79 [245]~E(x2451,x2452)+E(f19(x2451,x2453),f19(x2452,x2453)) 7.68/7.79 [246]~E(x2461,x2462)+E(f19(x2463,x2461),f19(x2463,x2462)) 7.68/7.79 [247]~E(x2471,x2472)+E(f287(x2471,x2473),f287(x2472,x2473)) 7.68/7.79 [248]~E(x2481,x2482)+E(f287(x2483,x2481),f287(x2483,x2482)) 7.68/7.79 [249]~E(x2491,x2492)+E(f173(x2491,x2493),f173(x2492,x2493)) 7.68/7.79 [250]~E(x2501,x2502)+E(f173(x2503,x2501),f173(x2503,x2502)) 7.68/7.79 [251]~E(x2511,x2512)+E(f91(x2511,x2513),f91(x2512,x2513)) 7.68/7.79 [252]~E(x2521,x2522)+E(f91(x2523,x2521),f91(x2523,x2522)) 7.68/7.79 [253]~E(x2531,x2532)+E(f20(x2531,x2533),f20(x2532,x2533)) 7.68/7.79 [254]~E(x2541,x2542)+E(f20(x2543,x2541),f20(x2543,x2542)) 7.68/7.79 [255]~E(x2551,x2552)+E(f307(x2551,x2553),f307(x2552,x2553)) 7.68/7.79 [256]~E(x2561,x2562)+E(f307(x2563,x2561),f307(x2563,x2562)) 7.68/7.79 [257]~E(x2571,x2572)+E(f354(x2571,x2573),f354(x2572,x2573)) 7.68/7.79 [258]~E(x2581,x2582)+E(f354(x2583,x2581),f354(x2583,x2582)) 7.68/7.79 [259]~E(x2591,x2592)+E(f368(x2591,x2593),f368(x2592,x2593)) 7.68/7.79 [260]~E(x2601,x2602)+E(f368(x2603,x2601),f368(x2603,x2602)) 7.68/7.79 [261]~E(x2611,x2612)+E(f63(x2611),f63(x2612)) 7.68/7.79 [262]~E(x2621,x2622)+E(f186(x2621,x2623,x2624),f186(x2622,x2623,x2624)) 7.68/7.79 [263]~E(x2631,x2632)+E(f186(x2633,x2631,x2634),f186(x2633,x2632,x2634)) 7.68/7.79 [264]~E(x2641,x2642)+E(f186(x2643,x2644,x2641),f186(x2643,x2644,x2642)) 7.68/7.79 [265]~E(x2651,x2652)+E(f30(x2651,x2653),f30(x2652,x2653)) 7.68/7.79 [266]~E(x2661,x2662)+E(f30(x2663,x2661),f30(x2663,x2662)) 7.68/7.79 [267]~E(x2671,x2672)+E(f357(x2671,x2673),f357(x2672,x2673)) 7.68/7.79 [268]~E(x2681,x2682)+E(f357(x2683,x2681),f357(x2683,x2682)) 7.68/7.79 [269]~E(x2691,x2692)+E(f50(x2691,x2693),f50(x2692,x2693)) 7.68/7.79 [270]~E(x2701,x2702)+E(f50(x2703,x2701),f50(x2703,x2702)) 7.68/7.79 [271]~E(x2711,x2712)+E(f195(x2711),f195(x2712)) 7.68/7.79 [272]~E(x2721,x2722)+E(f172(x2721,x2723,x2724),f172(x2722,x2723,x2724)) 7.68/7.79 [273]~E(x2731,x2732)+E(f172(x2733,x2731,x2734),f172(x2733,x2732,x2734)) 7.68/7.79 [274]~E(x2741,x2742)+E(f172(x2743,x2744,x2741),f172(x2743,x2744,x2742)) 7.68/7.79 [275]~E(x2751,x2752)+E(f141(x2751,x2753),f141(x2752,x2753)) 7.68/7.79 [276]~E(x2761,x2762)+E(f141(x2763,x2761),f141(x2763,x2762)) 7.68/7.79 [277]~E(x2771,x2772)+E(f37(x2771,x2773),f37(x2772,x2773)) 7.68/7.79 [278]~E(x2781,x2782)+E(f37(x2783,x2781),f37(x2783,x2782)) 7.68/7.79 [279]~E(x2791,x2792)+E(f310(x2791,x2793),f310(x2792,x2793)) 7.68/7.79 [280]~E(x2801,x2802)+E(f310(x2803,x2801),f310(x2803,x2802)) 7.68/7.79 [281]~E(x2811,x2812)+E(f105(x2811),f105(x2812)) 7.68/7.79 [282]~E(x2821,x2822)+E(f161(x2821,x2823,x2824),f161(x2822,x2823,x2824)) 7.68/7.79 [283]~E(x2831,x2832)+E(f161(x2833,x2831,x2834),f161(x2833,x2832,x2834)) 7.68/7.79 [284]~E(x2841,x2842)+E(f161(x2843,x2844,x2841),f161(x2843,x2844,x2842)) 7.68/7.79 [285]~E(x2851,x2852)+E(f64(x2851),f64(x2852)) 7.68/7.79 [286]~E(x2861,x2862)+E(f325(x2861,x2863),f325(x2862,x2863)) 7.68/7.79 [287]~E(x2871,x2872)+E(f325(x2873,x2871),f325(x2873,x2872)) 7.68/7.79 [288]~E(x2881,x2882)+E(f315(x2881,x2883),f315(x2882,x2883)) 7.68/7.79 [289]~E(x2891,x2892)+E(f315(x2893,x2891),f315(x2893,x2892)) 7.68/7.79 [290]~E(x2901,x2902)+E(f347(x2901,x2903),f347(x2902,x2903)) 7.68/7.79 [291]~E(x2911,x2912)+E(f347(x2913,x2911),f347(x2913,x2912)) 7.68/7.79 [292]~E(x2921,x2922)+E(f361(x2921,x2923),f361(x2922,x2923)) 7.68/7.79 [293]~E(x2931,x2932)+E(f361(x2933,x2931),f361(x2933,x2932)) 7.68/7.79 [294]~E(x2941,x2942)+E(f342(x2941,x2943),f342(x2942,x2943)) 7.68/7.79 [295]~E(x2951,x2952)+E(f342(x2953,x2951),f342(x2953,x2952)) 7.68/7.79 [296]~E(x2961,x2962)+E(f349(x2961,x2963),f349(x2962,x2963)) 7.68/7.79 [297]~E(x2971,x2972)+E(f349(x2973,x2971),f349(x2973,x2972)) 7.68/7.79 [298]~E(x2981,x2982)+E(f187(x2981,x2983,x2984),f187(x2982,x2983,x2984)) 7.68/7.79 [299]~E(x2991,x2992)+E(f187(x2993,x2991,x2994),f187(x2993,x2992,x2994)) 7.68/7.79 [300]~E(x3001,x3002)+E(f187(x3003,x3004,x3001),f187(x3003,x3004,x3002)) 7.68/7.79 [301]~E(x3011,x3012)+E(f205(x3011,x3013,x3014),f205(x3012,x3013,x3014)) 7.68/7.79 [302]~E(x3021,x3022)+E(f205(x3023,x3021,x3024),f205(x3023,x3022,x3024)) 7.68/7.79 [303]~E(x3031,x3032)+E(f205(x3033,x3034,x3031),f205(x3033,x3034,x3032)) 7.68/7.79 [304]~E(x3041,x3042)+E(f281(x3041,x3043),f281(x3042,x3043)) 7.68/7.79 [305]~E(x3051,x3052)+E(f281(x3053,x3051),f281(x3053,x3052)) 7.68/7.79 [306]~E(x3061,x3062)+E(f136(x3061,x3063),f136(x3062,x3063)) 7.68/7.79 [307]~E(x3071,x3072)+E(f136(x3073,x3071),f136(x3073,x3072)) 7.68/7.79 [308]~E(x3081,x3082)+E(f284(x3081,x3083),f284(x3082,x3083)) 7.68/7.79 [309]~E(x3091,x3092)+E(f284(x3093,x3091),f284(x3093,x3092)) 7.68/7.79 [310]~E(x3101,x3102)+E(f42(x3101,x3103),f42(x3102,x3103)) 7.68/7.79 [311]~E(x3111,x3112)+E(f42(x3113,x3111),f42(x3113,x3112)) 7.68/7.79 [312]~E(x3121,x3122)+E(f276(x3121,x3123),f276(x3122,x3123)) 7.68/7.79 [313]~E(x3131,x3132)+E(f276(x3133,x3131),f276(x3133,x3132)) 7.68/7.79 [314]~E(x3141,x3142)+E(f283(x3141,x3143),f283(x3142,x3143)) 7.68/7.79 [315]~E(x3151,x3152)+E(f283(x3153,x3151),f283(x3153,x3152)) 7.68/7.79 [316]~E(x3161,x3162)+E(f185(x3161,x3163),f185(x3162,x3163)) 7.68/7.79 [317]~E(x3171,x3172)+E(f185(x3173,x3171),f185(x3173,x3172)) 7.68/7.79 [318]~E(x3181,x3182)+E(f66(x3181),f66(x3182)) 7.68/7.79 [319]~E(x3191,x3192)+E(f164(x3191,x3193,x3194),f164(x3192,x3193,x3194)) 7.68/7.79 [320]~E(x3201,x3202)+E(f164(x3203,x3201,x3204),f164(x3203,x3202,x3204)) 7.68/7.79 [321]~E(x3211,x3212)+E(f164(x3213,x3214,x3211),f164(x3213,x3214,x3212)) 7.68/7.79 [322]~E(x3221,x3222)+E(f22(x3221,x3223),f22(x3222,x3223)) 7.68/7.79 [323]~E(x3231,x3232)+E(f22(x3233,x3231),f22(x3233,x3232)) 7.68/7.79 [324]~E(x3241,x3242)+E(f363(x3241,x3243),f363(x3242,x3243)) 7.68/7.79 [325]~E(x3251,x3252)+E(f363(x3253,x3251),f363(x3253,x3252)) 7.68/7.79 [326]~E(x3261,x3262)+E(f27(x3261,x3263),f27(x3262,x3263)) 7.68/7.79 [327]~E(x3271,x3272)+E(f27(x3273,x3271),f27(x3273,x3272)) 7.68/7.79 [328]~E(x3281,x3282)+E(f169(x3281,x3283),f169(x3282,x3283)) 7.68/7.79 [329]~E(x3291,x3292)+E(f169(x3293,x3291),f169(x3293,x3292)) 7.68/7.79 [330]~E(x3301,x3302)+E(f289(x3301,x3303),f289(x3302,x3303)) 7.68/7.79 [331]~E(x3311,x3312)+E(f289(x3313,x3311),f289(x3313,x3312)) 7.68/7.79 [332]~E(x3321,x3322)+E(f36(x3321,x3323),f36(x3322,x3323)) 7.68/7.79 [333]~E(x3331,x3332)+E(f36(x3333,x3331),f36(x3333,x3332)) 7.68/7.79 [334]~E(x3341,x3342)+E(f33(x3341,x3343),f33(x3342,x3343)) 7.68/7.79 [335]~E(x3351,x3352)+E(f33(x3353,x3351),f33(x3353,x3352)) 7.68/7.79 [336]~E(x3361,x3362)+E(f298(x3361,x3363),f298(x3362,x3363)) 7.68/7.79 [337]~E(x3371,x3372)+E(f298(x3373,x3371),f298(x3373,x3372)) 7.68/7.79 [338]~E(x3381,x3382)+E(f344(x3381,x3383),f344(x3382,x3383)) 7.68/7.79 [339]~E(x3391,x3392)+E(f344(x3393,x3391),f344(x3393,x3392)) 7.68/7.79 [340]~E(x3401,x3402)+E(f174(x3401,x3403),f174(x3402,x3403)) 7.68/7.79 [341]~E(x3411,x3412)+E(f174(x3413,x3411),f174(x3413,x3412)) 7.68/7.79 [342]~E(x3421,x3422)+E(f216(x3421,x3423,x3424),f216(x3422,x3423,x3424)) 7.68/7.79 [343]~E(x3431,x3432)+E(f216(x3433,x3431,x3434),f216(x3433,x3432,x3434)) 7.68/7.79 [344]~E(x3441,x3442)+E(f216(x3443,x3444,x3441),f216(x3443,x3444,x3442)) 7.68/7.79 [345]~E(x3451,x3452)+E(f179(x3451,x3453,x3454),f179(x3452,x3453,x3454)) 7.68/7.79 [346]~E(x3461,x3462)+E(f179(x3463,x3461,x3464),f179(x3463,x3462,x3464)) 7.68/7.79 [347]~E(x3471,x3472)+E(f179(x3473,x3474,x3471),f179(x3473,x3474,x3472)) 7.68/7.79 [348]~E(x3481,x3482)+E(f38(x3481,x3483),f38(x3482,x3483)) 7.68/7.79 [349]~E(x3491,x3492)+E(f38(x3493,x3491),f38(x3493,x3492)) 7.68/7.79 [350]~E(x3501,x3502)+E(f218(x3501,x3503),f218(x3502,x3503)) 7.68/7.79 [351]~E(x3511,x3512)+E(f218(x3513,x3511),f218(x3513,x3512)) 7.68/7.79 [352]~E(x3521,x3522)+E(f200(x3521,x3523,x3524),f200(x3522,x3523,x3524)) 7.68/7.79 [353]~E(x3531,x3532)+E(f200(x3533,x3531,x3534),f200(x3533,x3532,x3534)) 7.68/7.79 [354]~E(x3541,x3542)+E(f200(x3543,x3544,x3541),f200(x3543,x3544,x3542)) 7.68/7.79 [355]~E(x3551,x3552)+E(f122(x3551,x3553,x3554),f122(x3552,x3553,x3554)) 7.68/7.79 [356]~E(x3561,x3562)+E(f122(x3563,x3561,x3564),f122(x3563,x3562,x3564)) 7.68/7.79 [357]~E(x3571,x3572)+E(f122(x3573,x3574,x3571),f122(x3573,x3574,x3572)) 7.68/7.79 [358]~E(x3581,x3582)+E(f374(x3581,x3583),f374(x3582,x3583)) 7.68/7.79 [359]~E(x3591,x3592)+E(f374(x3593,x3591),f374(x3593,x3592)) 7.68/7.79 [360]~E(x3601,x3602)+E(f201(x3601,x3603,x3604),f201(x3602,x3603,x3604)) 7.68/7.79 [361]~E(x3611,x3612)+E(f201(x3613,x3611,x3614),f201(x3613,x3612,x3614)) 7.68/7.79 [362]~E(x3621,x3622)+E(f201(x3623,x3624,x3621),f201(x3623,x3624,x3622)) 7.68/7.79 [363]~E(x3631,x3632)+E(f162(x3631,x3633,x3634),f162(x3632,x3633,x3634)) 7.68/7.79 [364]~E(x3641,x3642)+E(f162(x3643,x3641,x3644),f162(x3643,x3642,x3644)) 7.68/7.79 [365]~E(x3651,x3652)+E(f162(x3653,x3654,x3651),f162(x3653,x3654,x3652)) 7.68/7.79 [366]~E(x3661,x3662)+E(f160(x3661,x3663,x3664),f160(x3662,x3663,x3664)) 7.68/7.79 [367]~E(x3671,x3672)+E(f160(x3673,x3671,x3674),f160(x3673,x3672,x3674)) 7.68/7.79 [368]~E(x3681,x3682)+E(f160(x3683,x3684,x3681),f160(x3683,x3684,x3682)) 7.68/7.79 [369]~E(x3691,x3692)+E(f34(x3691,x3693),f34(x3692,x3693)) 7.68/7.79 [370]~E(x3701,x3702)+E(f34(x3703,x3701),f34(x3703,x3702)) 7.68/7.79 [371]~E(x3711,x3712)+E(f176(x3711,x3713,x3714),f176(x3712,x3713,x3714)) 7.68/7.79 [372]~E(x3721,x3722)+E(f176(x3723,x3721,x3724),f176(x3723,x3722,x3724)) 7.68/7.79 [373]~E(x3731,x3732)+E(f176(x3733,x3734,x3731),f176(x3733,x3734,x3732)) 7.68/7.79 [374]~E(x3741,x3742)+E(f48(x3741,x3743),f48(x3742,x3743)) 7.68/7.79 [375]~E(x3751,x3752)+E(f48(x3753,x3751),f48(x3753,x3752)) 7.68/7.79 [376]~E(x3761,x3762)+E(f285(x3761,x3763),f285(x3762,x3763)) 7.68/7.79 [377]~E(x3771,x3772)+E(f285(x3773,x3771),f285(x3773,x3772)) 7.68/7.79 [378]~E(x3781,x3782)+E(f356(x3781,x3783),f356(x3782,x3783)) 7.68/7.79 [379]~E(x3791,x3792)+E(f356(x3793,x3791),f356(x3793,x3792)) 7.68/7.79 [380]~E(x3801,x3802)+E(f278(x3801,x3803),f278(x3802,x3803)) 7.68/7.79 [381]~E(x3811,x3812)+E(f278(x3813,x3811),f278(x3813,x3812)) 7.68/7.79 [382]~E(x3821,x3822)+E(f43(x3821,x3823),f43(x3822,x3823)) 7.68/7.79 [383]~E(x3831,x3832)+E(f43(x3833,x3831),f43(x3833,x3832)) 7.68/7.79 [384]~E(x3841,x3842)+E(f348(x3841,x3843),f348(x3842,x3843)) 7.68/7.79 [385]~E(x3851,x3852)+E(f348(x3853,x3851),f348(x3853,x3852)) 7.68/7.79 [386]~E(x3861,x3862)+E(f231(x3861,x3863),f231(x3862,x3863)) 7.68/7.79 [387]~E(x3871,x3872)+E(f231(x3873,x3871),f231(x3873,x3872)) 7.68/7.79 [388]~E(x3881,x3882)+E(f107(x3881,x3883,x3884),f107(x3882,x3883,x3884)) 7.68/7.79 [389]~E(x3891,x3892)+E(f107(x3893,x3891,x3894),f107(x3893,x3892,x3894)) 7.68/7.79 [390]~E(x3901,x3902)+E(f107(x3903,x3904,x3901),f107(x3903,x3904,x3902)) 7.68/7.79 [391]~E(x3911,x3912)+E(f68(x3911),f68(x3912)) 7.68/7.79 [392]~E(x3921,x3922)+E(f70(x3921),f70(x3922)) 7.68/7.79 [393]~E(x3931,x3932)+E(f32(x3931,x3933),f32(x3932,x3933)) 7.68/7.79 [394]~E(x3941,x3942)+E(f32(x3943,x3941),f32(x3943,x3942)) 7.68/7.79 [395]~E(x3951,x3952)+E(f128(x3951,x3953,x3954),f128(x3952,x3953,x3954)) 7.68/7.79 [396]~E(x3961,x3962)+E(f128(x3963,x3961,x3964),f128(x3963,x3962,x3964)) 7.68/7.79 [397]~E(x3971,x3972)+E(f128(x3973,x3974,x3971),f128(x3973,x3974,x3972)) 7.68/7.79 [398]~E(x3981,x3982)+E(f51(x3981,x3983),f51(x3982,x3983)) 7.68/7.79 [399]~E(x3991,x3992)+E(f51(x3993,x3991),f51(x3993,x3992)) 7.68/7.79 [400]~E(x4001,x4002)+E(f165(x4001,x4003),f165(x4002,x4003)) 7.68/7.79 [401]~E(x4011,x4012)+E(f165(x4013,x4011),f165(x4013,x4012)) 7.68/7.79 [402]~E(x4021,x4022)+E(f280(x4021,x4023),f280(x4022,x4023)) 7.68/7.79 [403]~E(x4031,x4032)+E(f280(x4033,x4031),f280(x4033,x4032)) 7.68/7.79 [404]~E(x4041,x4042)+E(f183(x4041,x4043,x4044),f183(x4042,x4043,x4044)) 7.68/7.79 [405]~E(x4051,x4052)+E(f183(x4053,x4051,x4054),f183(x4053,x4052,x4054)) 7.68/7.79 [406]~E(x4061,x4062)+E(f183(x4063,x4064,x4061),f183(x4063,x4064,x4062)) 7.68/7.79 [407]~E(x4071,x4072)+E(f44(x4071,x4073),f44(x4072,x4073)) 7.68/7.79 [408]~E(x4081,x4082)+E(f44(x4083,x4081),f44(x4083,x4082)) 7.68/7.79 [409]~E(x4091,x4092)+E(f217(x4091,x4093,x4094),f217(x4092,x4093,x4094)) 7.68/7.79 [410]~E(x4101,x4102)+E(f217(x4103,x4101,x4104),f217(x4103,x4102,x4104)) 7.68/7.79 [411]~E(x4111,x4112)+E(f217(x4113,x4114,x4111),f217(x4113,x4114,x4112)) 7.68/7.79 [412]~E(x4121,x4122)+E(f46(x4121,x4123),f46(x4122,x4123)) 7.68/7.79 [413]~E(x4131,x4132)+E(f46(x4133,x4131),f46(x4133,x4132)) 7.68/7.79 [414]~E(x4141,x4142)+E(f154(x4141,x4143,x4144),f154(x4142,x4143,x4144)) 7.68/7.79 [415]~E(x4151,x4152)+E(f154(x4153,x4151,x4154),f154(x4153,x4152,x4154)) 7.68/7.79 [416]~E(x4161,x4162)+E(f154(x4163,x4164,x4161),f154(x4163,x4164,x4162)) 7.68/7.79 [417]~E(x4171,x4172)+E(f23(x4171,x4173),f23(x4172,x4173)) 7.68/7.79 [418]~E(x4181,x4182)+E(f23(x4183,x4181),f23(x4183,x4182)) 7.68/7.79 [419]~E(x4191,x4192)+E(f225(x4191,x4193),f225(x4192,x4193)) 7.68/7.79 [420]~E(x4201,x4202)+E(f225(x4203,x4201),f225(x4203,x4202)) 7.68/7.79 [421]~E(x4211,x4212)+E(f365(x4211,x4213),f365(x4212,x4213)) 7.68/7.79 [422]~E(x4221,x4222)+E(f365(x4223,x4221),f365(x4223,x4222)) 7.68/7.79 [423]~E(x4231,x4232)+E(f113(x4231,x4233,x4234),f113(x4232,x4233,x4234)) 7.68/7.79 [424]~E(x4241,x4242)+E(f113(x4243,x4241,x4244),f113(x4243,x4242,x4244)) 7.68/7.79 [425]~E(x4251,x4252)+E(f113(x4253,x4254,x4251),f113(x4253,x4254,x4252)) 7.68/7.79 [426]~E(x4261,x4262)+E(f220(x4261,x4263,x4264),f220(x4262,x4263,x4264)) 7.68/7.79 [427]~E(x4271,x4272)+E(f220(x4273,x4271,x4274),f220(x4273,x4272,x4274)) 7.68/7.79 [428]~E(x4281,x4282)+E(f220(x4283,x4284,x4281),f220(x4283,x4284,x4282)) 7.68/7.79 [429]~E(x4291,x4292)+E(f308(x4291,x4293),f308(x4292,x4293)) 7.68/7.79 [430]~E(x4301,x4302)+E(f308(x4303,x4301),f308(x4303,x4302)) 7.68/7.79 [431]~E(x4311,x4312)+E(f206(x4311,x4313,x4314),f206(x4312,x4313,x4314)) 7.68/7.79 [432]~E(x4321,x4322)+E(f206(x4323,x4321,x4324),f206(x4323,x4322,x4324)) 7.68/7.79 [433]~E(x4331,x4332)+E(f206(x4333,x4334,x4331),f206(x4333,x4334,x4332)) 7.68/7.79 [434]~E(x4341,x4342)+E(f139(x4341,x4343,x4344),f139(x4342,x4343,x4344)) 7.68/7.79 [435]~E(x4351,x4352)+E(f139(x4353,x4351,x4354),f139(x4353,x4352,x4354)) 7.68/7.79 [436]~E(x4361,x4362)+E(f139(x4363,x4364,x4361),f139(x4363,x4364,x4362)) 7.68/7.79 [437]~E(x4371,x4372)+E(f235(x4371,x4373,x4374),f235(x4372,x4373,x4374)) 7.68/7.79 [438]~E(x4381,x4382)+E(f235(x4383,x4381,x4384),f235(x4383,x4382,x4384)) 7.68/7.79 [439]~E(x4391,x4392)+E(f235(x4393,x4394,x4391),f235(x4393,x4394,x4392)) 7.68/7.79 [440]~E(x4401,x4402)+E(f302(x4401,x4403),f302(x4402,x4403)) 7.68/7.79 [441]~E(x4411,x4412)+E(f302(x4413,x4411),f302(x4413,x4412)) 7.68/7.79 [442]~E(x4421,x4422)+E(f359(x4421,x4423),f359(x4422,x4423)) 7.68/7.79 [443]~E(x4431,x4432)+E(f359(x4433,x4431),f359(x4433,x4432)) 7.68/7.79 [444]~E(x4441,x4442)+E(f119(x4441),f119(x4442)) 7.68/7.79 [445]~E(x4451,x4452)+E(f97(x4451),f97(x4452)) 7.68/7.79 [446]~E(x4461,x4462)+E(f87(x4461),f87(x4462)) 7.68/7.79 [447]~E(x4471,x4472)+E(f362(x4471,x4473),f362(x4472,x4473)) 7.68/7.79 [448]~E(x4481,x4482)+E(f362(x4483,x4481),f362(x4483,x4482)) 7.68/7.79 [449]~E(x4491,x4492)+E(f168(x4491,x4493),f168(x4492,x4493)) 7.68/7.79 [450]~E(x4501,x4502)+E(f168(x4503,x4501),f168(x4503,x4502)) 7.68/7.79 [451]~E(x4511,x4512)+E(f353(x4511,x4513),f353(x4512,x4513)) 7.68/7.79 [452]~E(x4521,x4522)+E(f353(x4523,x4521),f353(x4523,x4522)) 7.68/7.79 [453]~E(x4531,x4532)+E(f150(x4531,x4533),f150(x4532,x4533)) 7.68/7.79 [454]~E(x4541,x4542)+E(f150(x4543,x4541),f150(x4543,x4542)) 7.68/7.79 [455]~E(x4551,x4552)+E(f28(x4551,x4553),f28(x4552,x4553)) 7.68/7.79 [456]~E(x4561,x4562)+E(f28(x4563,x4561),f28(x4563,x4562)) 7.68/7.79 [457]~E(x4571,x4572)+E(f120(x4571,x4573,x4574),f120(x4572,x4573,x4574)) 7.68/7.79 [458]~E(x4581,x4582)+E(f120(x4583,x4581,x4584),f120(x4583,x4582,x4584)) 7.68/7.79 [459]~E(x4591,x4592)+E(f120(x4593,x4594,x4591),f120(x4593,x4594,x4592)) 7.68/7.79 [460]~E(x4601,x4602)+E(f358(x4601,x4603),f358(x4602,x4603)) 7.68/7.79 [461]~E(x4611,x4612)+E(f358(x4613,x4611),f358(x4613,x4612)) 7.68/7.79 [462]~E(x4621,x4622)+E(f188(x4621,x4623,x4624),f188(x4622,x4623,x4624)) 7.68/7.79 [463]~E(x4631,x4632)+E(f188(x4633,x4631,x4634),f188(x4633,x4632,x4634)) 7.68/7.79 [464]~E(x4641,x4642)+E(f188(x4643,x4644,x4641),f188(x4643,x4644,x4642)) 7.68/7.79 [465]~E(x4651,x4652)+E(f24(x4651,x4653),f24(x4652,x4653)) 7.68/7.79 [466]~E(x4661,x4662)+E(f24(x4663,x4661),f24(x4663,x4662)) 7.68/7.79 [467]~E(x4671,x4672)+E(f366(x4671,x4673),f366(x4672,x4673)) 7.68/7.79 [468]~E(x4681,x4682)+E(f366(x4683,x4681),f366(x4683,x4682)) 7.68/7.79 [469]~E(x4691,x4692)+E(f25(x4691,x4693),f25(x4692,x4693)) 7.68/7.79 [470]~E(x4701,x4702)+E(f25(x4703,x4701),f25(x4703,x4702)) 7.68/7.79 [471]~E(x4711,x4712)+E(f355(x4711,x4713),f355(x4712,x4713)) 7.68/7.79 [472]~E(x4721,x4722)+E(f355(x4723,x4721),f355(x4723,x4722)) 7.68/7.79 [473]~E(x4731,x4732)+E(f223(x4731),f223(x4732)) 7.68/7.79 [474]~E(x4741,x4742)+E(f117(x4741,x4743),f117(x4742,x4743)) 7.68/7.79 [475]~E(x4751,x4752)+E(f117(x4753,x4751),f117(x4753,x4752)) 7.68/7.79 [476]~E(x4761,x4762)+E(f138(x4761,x4763),f138(x4762,x4763)) 7.68/7.79 [477]~E(x4771,x4772)+E(f138(x4773,x4771),f138(x4773,x4772)) 7.68/7.79 [478]~E(x4781,x4782)+E(f222(x4781,x4783,x4784),f222(x4782,x4783,x4784)) 7.68/7.79 [479]~E(x4791,x4792)+E(f222(x4793,x4791,x4794),f222(x4793,x4792,x4794)) 7.68/7.79 [480]~E(x4801,x4802)+E(f222(x4803,x4804,x4801),f222(x4803,x4804,x4802)) 7.68/7.79 [481]~E(x4811,x4812)+E(f29(x4811,x4813),f29(x4812,x4813)) 7.68/7.79 [482]~E(x4821,x4822)+E(f29(x4823,x4821),f29(x4823,x4822)) 7.68/7.79 [483]~E(x4831,x4832)+E(f40(x4831,x4833),f40(x4832,x4833)) 7.68/7.79 [484]~E(x4841,x4842)+E(f40(x4843,x4841),f40(x4843,x4842)) 7.68/7.79 [485]~E(x4851,x4852)+E(f47(x4851,x4853),f47(x4852,x4853)) 7.68/7.79 [486]~E(x4861,x4862)+E(f47(x4863,x4861),f47(x4863,x4862)) 7.68/7.79 [487]~E(x4871,x4872)+E(f213(x4871,x4873),f213(x4872,x4873)) 7.68/7.79 [488]~E(x4881,x4882)+E(f213(x4883,x4881),f213(x4883,x4882)) 7.68/7.79 [489]~E(x4891,x4892)+E(f291(x4891,x4893),f291(x4892,x4893)) 7.68/7.79 [490]~E(x4901,x4902)+E(f291(x4903,x4901),f291(x4903,x4902)) 7.68/7.79 [491]~E(x4911,x4912)+E(f224(x4911),f224(x4912)) 7.68/7.79 [492]~E(x4921,x4922)+E(f49(x4921,x4923),f49(x4922,x4923)) 7.68/7.79 [493]~E(x4931,x4932)+E(f49(x4933,x4931),f49(x4933,x4932)) 7.68/7.79 [494]~E(x4941,x4942)+E(f279(x4941,x4943),f279(x4942,x4943)) 7.68/7.79 [495]~E(x4951,x4952)+E(f279(x4953,x4951),f279(x4953,x4952)) 7.68/7.79 [496]~E(x4961,x4962)+E(f207(x4961,x4963),f207(x4962,x4963)) 7.68/7.79 [497]~E(x4971,x4972)+E(f207(x4973,x4971),f207(x4973,x4972)) 7.68/7.79 [498]~E(x4981,x4982)+E(f143(x4981,x4983,x4984),f143(x4982,x4983,x4984)) 7.68/7.79 [499]~E(x4991,x4992)+E(f143(x4993,x4991,x4994),f143(x4993,x4992,x4994)) 7.68/7.79 [500]~E(x5001,x5002)+E(f143(x5003,x5004,x5001),f143(x5003,x5004,x5002)) 7.68/7.79 [501]~E(x5011,x5012)+E(f151(x5011,x5013),f151(x5012,x5013)) 7.68/7.79 [502]~E(x5021,x5022)+E(f151(x5023,x5021),f151(x5023,x5022)) 7.68/7.79 [503]~E(x5031,x5032)+E(f133(x5031,x5033),f133(x5032,x5033)) 7.68/7.79 [504]~E(x5041,x5042)+E(f133(x5043,x5041),f133(x5043,x5042)) 7.68/7.79 [505]~E(x5051,x5052)+E(f114(x5051,x5053,x5054),f114(x5052,x5053,x5054)) 7.68/7.79 [506]~E(x5061,x5062)+E(f114(x5063,x5061,x5064),f114(x5063,x5062,x5064)) 7.68/7.79 [507]~E(x5071,x5072)+E(f114(x5073,x5074,x5071),f114(x5073,x5074,x5072)) 7.68/7.79 [508]~E(x5081,x5082)+E(f156(x5081),f156(x5082)) 7.68/7.79 [509]~E(x5091,x5092)+E(f80(x5091),f80(x5092)) 7.68/7.79 [510]~E(x5101,x5102)+E(f292(x5101,x5103),f292(x5102,x5103)) 7.68/7.79 [511]~E(x5111,x5112)+E(f292(x5113,x5111),f292(x5113,x5112)) 7.68/7.79 [512]~E(x5121,x5122)+E(f180(x5121,x5123),f180(x5122,x5123)) 7.68/7.79 [513]~E(x5131,x5132)+E(f180(x5133,x5131),f180(x5133,x5132)) 7.68/7.79 [514]~E(x5141,x5142)+E(f142(x5141,x5143,x5144),f142(x5142,x5143,x5144)) 7.68/7.79 [515]~E(x5151,x5152)+E(f142(x5153,x5151,x5154),f142(x5153,x5152,x5154)) 7.68/7.79 [516]~E(x5161,x5162)+E(f142(x5163,x5164,x5161),f142(x5163,x5164,x5162)) 7.68/7.79 [517]~E(x5171,x5172)+E(f297(x5171,x5173),f297(x5172,x5173)) 7.68/7.79 [518]~E(x5181,x5182)+E(f297(x5183,x5181),f297(x5183,x5182)) 7.68/7.79 [519]~E(x5191,x5192)+E(f340(x5191,x5193),f340(x5192,x5193)) 7.68/7.79 [520]~E(x5201,x5202)+E(f340(x5203,x5201),f340(x5203,x5202)) 7.68/7.79 [521]~E(x5211,x5212)+E(f214(x5211,x5213),f214(x5212,x5213)) 7.68/7.79 [522]~E(x5221,x5222)+E(f214(x5223,x5221),f214(x5223,x5222)) 7.68/7.79 [523]~E(x5231,x5232)+E(f288(x5231,x5233),f288(x5232,x5233)) 7.68/7.79 [524]~E(x5241,x5242)+E(f288(x5243,x5241),f288(x5243,x5242)) 7.68/7.79 [525]~E(x5251,x5252)+E(f62(x5251),f62(x5252)) 7.68/7.79 [526]~E(x5261,x5262)+E(f104(x5261),f104(x5262)) 7.68/7.79 [527]~E(x5271,x5272)+E(f109(x5271),f109(x5272)) 7.68/7.79 [528]~E(x5281,x5282)+E(f59(x5281),f59(x5282)) 7.68/7.79 [529]~E(x5291,x5292)+E(f65(x5291),f65(x5292)) 7.68/7.79 [530]~E(x5301,x5302)+E(f140(x5301,x5303),f140(x5302,x5303)) 7.68/7.79 [531]~E(x5311,x5312)+E(f140(x5313,x5311),f140(x5313,x5312)) 7.68/7.79 [532]~E(x5321,x5322)+E(f227(x5321,x5323,x5324),f227(x5322,x5323,x5324)) 7.68/7.79 [533]~E(x5331,x5332)+E(f227(x5333,x5331,x5334),f227(x5333,x5332,x5334)) 7.68/7.79 [534]~E(x5341,x5342)+E(f227(x5343,x5344,x5341),f227(x5343,x5344,x5342)) 7.68/7.79 [535]~E(x5351,x5352)+E(f381(x5351,x5353),f381(x5352,x5353)) 7.68/7.79 [536]~E(x5361,x5362)+E(f381(x5363,x5361),f381(x5363,x5362)) 7.68/7.79 [537]~E(x5371,x5372)+E(f194(x5371),f194(x5372)) 7.68/7.79 [538]~E(x5381,x5382)+E(f110(x5381,x5383),f110(x5382,x5383)) 7.68/7.79 [539]~E(x5391,x5392)+E(f110(x5393,x5391),f110(x5393,x5392)) 7.68/7.79 [540]~E(x5401,x5402)+E(f108(x5401),f108(x5402)) 7.68/7.79 [541]~E(x5411,x5412)+E(f182(x5411,x5413,x5414),f182(x5412,x5413,x5414)) 7.68/7.79 [542]~E(x5421,x5422)+E(f182(x5423,x5421,x5424),f182(x5423,x5422,x5424)) 7.68/7.79 [543]~E(x5431,x5432)+E(f182(x5433,x5434,x5431),f182(x5433,x5434,x5432)) 7.68/7.79 [544]~E(x5441,x5442)+E(f192(x5441),f192(x5442)) 7.68/7.79 [545]~E(x5451,x5452)+E(f153(x5451,x5453,x5454),f153(x5452,x5453,x5454)) 7.68/7.79 [546]~E(x5461,x5462)+E(f153(x5463,x5461,x5464),f153(x5463,x5462,x5464)) 7.68/7.79 [547]~E(x5471,x5472)+E(f153(x5473,x5474,x5471),f153(x5473,x5474,x5472)) 7.68/7.79 [548]~E(x5481,x5482)+E(f158(x5481,x5483),f158(x5482,x5483)) 7.68/7.79 [549]~E(x5491,x5492)+E(f158(x5493,x5491),f158(x5493,x5492)) 7.68/7.79 [550]~E(x5501,x5502)+E(f125(x5501,x5503,x5504),f125(x5502,x5503,x5504)) 7.68/7.79 [551]~E(x5511,x5512)+E(f125(x5513,x5511,x5514),f125(x5513,x5512,x5514)) 7.68/7.79 [552]~E(x5521,x5522)+E(f125(x5523,x5524,x5521),f125(x5523,x5524,x5522)) 7.68/7.79 [553]~E(x5531,x5532)+E(f167(x5531,x5533),f167(x5532,x5533)) 7.68/7.79 [554]~E(x5541,x5542)+E(f167(x5543,x5541),f167(x5543,x5542)) 7.68/7.79 [555]~E(x5551,x5552)+E(f177(x5551,x5553,x5554),f177(x5552,x5553,x5554)) 7.68/7.79 [556]~E(x5561,x5562)+E(f177(x5563,x5561,x5564),f177(x5563,x5562,x5564)) 7.68/7.79 [557]~E(x5571,x5572)+E(f177(x5573,x5574,x5571),f177(x5573,x5574,x5572)) 7.68/7.79 [558]~E(x5581,x5582)+E(f170(x5581,x5583),f170(x5582,x5583)) 7.68/7.79 [559]~E(x5591,x5592)+E(f170(x5593,x5591),f170(x5593,x5592)) 7.68/7.79 [560]~E(x5601,x5602)+E(f212(x5601),f212(x5602)) 7.68/7.79 [561]~E(x5611,x5612)+E(f210(x5611,x5613),f210(x5612,x5613)) 7.68/7.79 [562]~E(x5621,x5622)+E(f210(x5623,x5621),f210(x5623,x5622)) 7.68/7.79 [563]~E(x5631,x5632)+E(f75(x5631),f75(x5632)) 7.68/7.79 [564]~E(x5641,x5642)+E(f233(x5641,x5643,x5644),f233(x5642,x5643,x5644)) 7.68/7.79 [565]~E(x5651,x5652)+E(f233(x5653,x5651,x5654),f233(x5653,x5652,x5654)) 7.68/7.79 [566]~E(x5661,x5662)+E(f233(x5663,x5664,x5661),f233(x5663,x5664,x5662)) 7.68/7.79 [567]~E(x5671,x5672)+E(f112(x5671,x5673,x5674),f112(x5672,x5673,x5674)) 7.68/7.79 [568]~E(x5681,x5682)+E(f112(x5683,x5681,x5684),f112(x5683,x5682,x5684)) 7.68/7.79 [569]~E(x5691,x5692)+E(f112(x5693,x5694,x5691),f112(x5693,x5694,x5692)) 7.68/7.79 [570]~E(x5701,x5702)+E(f202(x5701,x5703),f202(x5702,x5703)) 7.68/7.79 [571]~E(x5711,x5712)+E(f202(x5713,x5711),f202(x5713,x5712)) 7.68/7.79 [572]~E(x5721,x5722)+E(f197(x5721,x5723),f197(x5722,x5723)) 7.68/7.79 [573]~E(x5731,x5732)+E(f197(x5733,x5731),f197(x5733,x5732)) 7.68/7.79 [574]~E(x5741,x5742)+E(f132(x5741),f132(x5742)) 7.68/7.79 [575]~E(x5751,x5752)+E(f115(x5751,x5753,x5754),f115(x5752,x5753,x5754)) 7.68/7.79 [576]~E(x5761,x5762)+E(f115(x5763,x5761,x5764),f115(x5763,x5762,x5764)) 7.68/7.79 [577]~E(x5771,x5772)+E(f115(x5773,x5774,x5771),f115(x5773,x5774,x5772)) 7.68/7.79 [578]~E(x5781,x5782)+E(f219(x5781,x5783),f219(x5782,x5783)) 7.68/7.79 [579]~E(x5791,x5792)+E(f219(x5793,x5791),f219(x5793,x5792)) 7.68/7.79 [580]~E(x5801,x5802)+E(f147(x5801,x5803),f147(x5802,x5803)) 7.68/7.79 [581]~E(x5811,x5812)+E(f147(x5813,x5811),f147(x5813,x5812)) 7.68/7.79 [582]~E(x5821,x5822)+E(f69(x5821),f69(x5822)) 7.68/7.79 [583]~E(x5831,x5832)+E(f102(x5831),f102(x5832)) 7.68/7.79 [584]~E(x5841,x5842)+E(f178(x5841,x5843,x5844),f178(x5842,x5843,x5844)) 7.68/7.79 [585]~E(x5851,x5852)+E(f178(x5853,x5851,x5854),f178(x5853,x5852,x5854)) 7.68/7.79 [586]~E(x5861,x5862)+E(f178(x5863,x5864,x5861),f178(x5863,x5864,x5862)) 7.68/7.79 [587]~E(x5871,x5872)+E(f163(x5871,x5873,x5874),f163(x5872,x5873,x5874)) 7.68/7.79 [588]~E(x5881,x5882)+E(f163(x5883,x5881,x5884),f163(x5883,x5882,x5884)) 7.68/7.79 [589]~E(x5891,x5892)+E(f163(x5893,x5894,x5891),f163(x5893,x5894,x5892)) 7.68/7.79 [590]~E(x5901,x5902)+E(f78(x5901),f78(x5902)) 7.68/7.79 [591]~E(x5911,x5912)+E(f82(x5911),f82(x5912)) 7.68/7.79 [592]~E(x5921,x5922)+E(f126(x5921,x5923,x5924),f126(x5922,x5923,x5924)) 7.68/7.79 [593]~E(x5931,x5932)+E(f126(x5933,x5931,x5934),f126(x5933,x5932,x5934)) 7.68/7.79 [594]~E(x5941,x5942)+E(f126(x5943,x5944,x5941),f126(x5943,x5944,x5942)) 7.68/7.79 [595]~E(x5951,x5952)+E(f79(x5951),f79(x5952)) 7.68/7.79 [596]~E(x5961,x5962)+E(f56(x5961),f56(x5962)) 7.68/7.79 [597]~E(x5971,x5972)+E(f199(x5971,x5973,x5974),f199(x5972,x5973,x5974)) 7.68/7.79 [598]~E(x5981,x5982)+E(f199(x5983,x5981,x5984),f199(x5983,x5982,x5984)) 7.68/7.79 [599]~E(x5991,x5992)+E(f199(x5993,x5994,x5991),f199(x5993,x5994,x5992)) 7.68/7.79 [600]~E(x6001,x6002)+E(f76(x6001),f76(x6002)) 7.68/7.79 [601]~E(x6011,x6012)+E(f234(x6011,x6013,x6014),f234(x6012,x6013,x6014)) 7.68/7.79 [602]~E(x6021,x6022)+E(f234(x6023,x6021,x6024),f234(x6023,x6022,x6024)) 7.68/7.79 [603]~E(x6031,x6032)+E(f234(x6033,x6034,x6031),f234(x6033,x6034,x6032)) 7.68/7.79 [604]~E(x6041,x6042)+E(f166(x6041,x6043,x6044),f166(x6042,x6043,x6044)) 7.68/7.79 [605]~E(x6051,x6052)+E(f166(x6053,x6051,x6054),f166(x6053,x6052,x6054)) 7.68/7.79 [606]~E(x6061,x6062)+E(f166(x6063,x6064,x6061),f166(x6063,x6064,x6062)) 7.68/7.79 [607]~E(x6071,x6072)+E(f155(x6071),f155(x6072)) 7.68/7.79 [608]~E(x6081,x6082)+E(f146(x6081,x6083,x6084),f146(x6082,x6083,x6084)) 7.68/7.79 [609]~E(x6091,x6092)+E(f146(x6093,x6091,x6094),f146(x6093,x6092,x6094)) 7.68/7.79 [610]~E(x6101,x6102)+E(f146(x6103,x6104,x6101),f146(x6103,x6104,x6102)) 7.68/7.79 [611]~E(x6111,x6112)+E(f72(x6111),f72(x6112)) 7.68/7.79 [612]~E(x6121,x6122)+E(f395(x6121),f395(x6122)) 7.68/7.79 [613]~E(x6131,x6132)+E(f135(x6131,x6133,x6134),f135(x6132,x6133,x6134)) 7.68/7.79 [614]~E(x6141,x6142)+E(f135(x6143,x6141,x6144),f135(x6143,x6142,x6144)) 7.68/7.79 [615]~E(x6151,x6152)+E(f135(x6153,x6154,x6151),f135(x6153,x6154,x6152)) 7.68/7.79 [616]~E(x6161,x6162)+E(f198(x6161,x6163),f198(x6162,x6163)) 7.68/7.79 [617]~E(x6171,x6172)+E(f198(x6173,x6171),f198(x6173,x6172)) 7.68/7.79 [618]~E(x6181,x6182)+E(f193(x6181),f193(x6182)) 7.68/7.79 [619]~E(x6191,x6192)+E(f159(x6191,x6193),f159(x6192,x6193)) 7.68/7.79 [620]~E(x6201,x6202)+E(f159(x6203,x6201),f159(x6203,x6202)) 7.68/7.79 [621]~E(x6211,x6212)+E(f145(x6211,x6213),f145(x6212,x6213)) 7.68/7.79 [622]~E(x6221,x6222)+E(f145(x6223,x6221),f145(x6223,x6222)) 7.68/7.79 [623]~E(x6231,x6232)+E(f74(x6231),f74(x6232)) 7.68/7.79 [624]~E(x6241,x6242)+E(f144(x6241,x6243,x6244),f144(x6242,x6243,x6244)) 7.68/7.79 [625]~E(x6251,x6252)+E(f144(x6253,x6251,x6254),f144(x6253,x6252,x6254)) 7.68/7.79 [626]~E(x6261,x6262)+E(f144(x6263,x6264,x6261),f144(x6263,x6264,x6262)) 7.68/7.79 [627]~E(x6271,x6272)+E(f103(x6271),f103(x6272)) 7.68/7.79 [628]~E(x6281,x6282)+E(f73(x6281),f73(x6282)) 7.68/7.79 [629]~E(x6291,x6292)+E(f171(x6291),f171(x6292)) 7.68/7.79 [630]~E(x6301,x6302)+E(f111(x6301,x6303),f111(x6302,x6303)) 7.68/7.79 [631]~E(x6311,x6312)+E(f111(x6313,x6311),f111(x6313,x6312)) 7.68/7.79 [632]~E(x6321,x6322)+E(f208(x6321,x6323,x6324),f208(x6322,x6323,x6324)) 7.68/7.79 [633]~E(x6331,x6332)+E(f208(x6333,x6331,x6334),f208(x6333,x6332,x6334)) 7.68/7.79 [634]~E(x6341,x6342)+E(f208(x6343,x6344,x6341),f208(x6343,x6344,x6342)) 7.68/7.79 [635]~E(x6351,x6352)+E(f124(x6351,x6353,x6354),f124(x6352,x6353,x6354)) 7.68/7.79 [636]~E(x6361,x6362)+E(f124(x6363,x6361,x6364),f124(x6363,x6362,x6364)) 7.68/7.79 [637]~E(x6371,x6372)+E(f124(x6373,x6374,x6371),f124(x6373,x6374,x6372)) 7.68/7.79 [638]~E(x6381,x6382)+E(f84(x6381),f84(x6382)) 7.68/7.79 [639]~E(x6391,x6392)+E(f209(x6391,x6393,x6394),f209(x6392,x6393,x6394)) 7.68/7.79 [640]~E(x6401,x6402)+E(f209(x6403,x6401,x6404),f209(x6403,x6402,x6404)) 7.68/7.79 [641]~E(x6411,x6412)+E(f209(x6413,x6414,x6411),f209(x6413,x6414,x6412)) 7.68/7.79 [642]~E(x6421,x6422)+E(f123(x6421),f123(x6422)) 7.68/7.79 [643]~E(x6431,x6432)+E(f121(x6431,x6433,x6434),f121(x6432,x6433,x6434)) 7.68/7.79 [644]~E(x6441,x6442)+E(f121(x6443,x6441,x6444),f121(x6443,x6442,x6444)) 7.68/7.79 [645]~E(x6451,x6452)+E(f121(x6453,x6454,x6451),f121(x6453,x6454,x6452)) 7.68/7.79 [646]~E(x6461,x6462)+E(f189(x6461,x6463,x6464),f189(x6462,x6463,x6464)) 7.68/7.79 [647]~E(x6471,x6472)+E(f189(x6473,x6471,x6474),f189(x6473,x6472,x6474)) 7.68/7.79 [648]~E(x6481,x6482)+E(f189(x6483,x6484,x6481),f189(x6483,x6484,x6482)) 7.68/7.79 [649]~E(x6491,x6492)+E(f83(x6491),f83(x6492)) 7.68/7.79 [650]~E(x6501,x6502)+E(f6(x6501),f6(x6502)) 7.68/7.79 [651]~E(x6511,x6512)+E(f226(x6511,x6513,x6514),f226(x6512,x6513,x6514)) 7.68/7.79 [652]~E(x6521,x6522)+E(f226(x6523,x6521,x6524),f226(x6523,x6522,x6524)) 7.68/7.79 [653]~E(x6531,x6532)+E(f226(x6533,x6534,x6531),f226(x6533,x6534,x6532)) 7.68/7.79 [654]~E(x6541,x6542)+E(f400(x6541),f400(x6542)) 7.68/7.79 [655]~E(x6551,x6552)+E(f148(x6551,x6553,x6554),f148(x6552,x6553,x6554)) 7.68/7.79 [656]~E(x6561,x6562)+E(f148(x6563,x6561,x6564),f148(x6563,x6562,x6564)) 7.68/7.79 [657]~E(x6571,x6572)+E(f148(x6573,x6574,x6571),f148(x6573,x6574,x6572)) 7.68/7.79 [658]~E(x6581,x6582)+E(f81(x6581),f81(x6582)) 7.68/7.79 [659]~E(x6591,x6592)+E(f98(x6591),f98(x6592)) 7.68/7.79 [660]~E(x6601,x6602)+E(f399(x6601),f399(x6602)) 7.68/7.79 [661]~E(x6611,x6612)+E(f137(x6611,x6613),f137(x6612,x6613)) 7.68/7.79 [662]~E(x6621,x6622)+E(f137(x6623,x6621),f137(x6623,x6622)) 7.68/7.79 [663]~E(x6631,x6632)+E(f152(x6631,x6633),f152(x6632,x6633)) 7.68/7.79 [664]~E(x6641,x6642)+E(f152(x6643,x6641),f152(x6643,x6642)) 7.68/7.79 [665]~E(x6651,x6652)+E(f230(x6651),f230(x6652)) 7.68/7.79 [666]~E(x6661,x6662)+E(f134(x6661,x6663),f134(x6662,x6663)) 7.68/7.79 [667]~E(x6671,x6672)+E(f134(x6673,x6671),f134(x6673,x6672)) 7.68/7.79 [668]~E(x6681,x6682)+E(f100(x6681),f100(x6682)) 7.68/7.79 [669]~E(x6691,x6692)+E(f211(x6691,x6693),f211(x6692,x6693)) 7.68/7.79 [670]~E(x6701,x6702)+E(f211(x6703,x6701),f211(x6703,x6702)) 7.68/7.79 [671]~E(x6711,x6712)+E(f118(x6711,x6713),f118(x6712,x6713)) 7.68/7.79 [672]~E(x6721,x6722)+E(f118(x6723,x6721),f118(x6723,x6722)) 7.68/7.79 [673]~E(x6731,x6732)+E(f203(x6731,x6733),f203(x6732,x6733)) 7.68/7.79 [674]~E(x6741,x6742)+E(f203(x6743,x6741),f203(x6743,x6742)) 7.68/7.79 [675]~P1(x6751)+P1(x6752)+~E(x6751,x6752) 7.68/7.79 [676]~P5(x6761)+P5(x6762)+~E(x6761,x6762) 7.68/7.79 [677]~P2(x6771)+P2(x6772)+~E(x6771,x6772) 7.68/7.79 [678]~P7(x6781)+P7(x6782)+~E(x6781,x6782) 7.68/7.79 [679]~P6(x6791)+P6(x6792)+~E(x6791,x6792) 7.68/7.79 [680]~P8(x6801)+P8(x6802)+~E(x6801,x6802) 7.68/7.79 [681]~P4(x6811)+P4(x6812)+~E(x6811,x6812) 7.68/7.79 [682]~P3(x6821)+P3(x6822)+~E(x6821,x6822) 7.68/7.79 7.68/7.79 %------------------------------------------- 7.68/7.80 cnf(1998,plain, 7.68/7.80 (P5(f311(f294(a386,x19981),f99(f96(f31(a240,f282(f77(a244),x19982)),f305(f60(a372),x19981)))))), 7.68/7.80 inference(rename_variables,[],[902])). 7.68/7.80 cnf(2004,plain, 7.68/7.80 (P5(f269(f309(a389,x20041),f89(f95(f41(a240,f341(f55(a248),x20042)),f320(f57(a369),x20041)))))), 7.68/7.80 inference(rename_variables,[],[900])). 7.68/7.80 cnf(2007,plain, 7.68/7.80 (P5(f269(f309(a389,x20071),f89(f95(f41(a240,f341(f55(a248),x20072)),f320(f57(a369),x20071)))))), 7.68/7.80 inference(rename_variables,[],[900])). 7.68/7.80 cnf(2010,plain, 7.68/7.80 (P5(f268(f273(a385,x20101),f94(f21(a246,f52(a238,f327(f16(a247),x20102))),x20101)))), 7.68/7.80 inference(rename_variables,[],[894])). 7.68/7.80 cnf(2013,plain, 7.68/7.80 (P5(f268(f273(a385,x20131),f94(f21(a246,f52(a238,f327(f16(a247),x20132))),x20131)))), 7.68/7.80 inference(rename_variables,[],[894])). 7.68/7.80 cnf(2024,plain, 7.68/7.80 (~P5(f311(f277(a372,x20241),a8))), 7.68/7.80 inference(rename_variables,[],[924])). 7.68/7.80 cnf(2027,plain, 7.68/7.80 (~P5(f269(f336(a369,x20271),a9))), 7.68/7.80 inference(rename_variables,[],[921])). 7.68/7.80 cnf(2034,plain, 7.68/7.80 (P5(f331(f327(a383,x20341),f267(a394,x20341)))), 7.68/7.80 inference(rename_variables,[],[855])). 7.68/7.80 cnf(2037,plain, 7.68/7.80 (P5(f331(f327(a384,x20371),x20371))), 7.68/7.80 inference(rename_variables,[],[765])). 7.68/7.80 cnf(2040,plain, 7.68/7.80 (~P5(f331(f327(a383,x20401),x20401))), 7.68/7.80 inference(rename_variables,[],[926])). 7.68/7.80 cnf(2043,plain, 7.68/7.80 (P5(f331(f327(a383,x20431),f267(a394,f267(f382(x20432),x20431))))), 7.68/7.80 inference(rename_variables,[],[872])). 7.68/7.80 cnf(2046,plain, 7.68/7.80 (P5(f331(f327(a384,x20461),f267(f382(x20462),x20461)))), 7.68/7.80 inference(rename_variables,[],[861])). 7.68/7.80 cnf(2049,plain, 7.68/7.80 (P5(f331(f327(a384,x20491),f267(f382(x20492),x20491)))), 7.68/7.80 inference(rename_variables,[],[861])). 7.68/7.80 cnf(2054,plain, 7.68/7.80 (P5(f331(f327(a383,x20541),f267(a394,f267(f382(x20542),x20541))))), 7.68/7.80 inference(rename_variables,[],[872])). 7.68/7.80 cnf(2059,plain, 7.68/7.80 (P5(f331(f327(a383,x20591),f267(a394,x20591)))), 7.68/7.80 inference(rename_variables,[],[855])). 7.68/7.80 cnf(2062,plain, 7.68/7.80 (P5(f331(f327(a384,x20621),f267(f382(x20622),x20621)))), 7.68/7.80 inference(rename_variables,[],[861])). 7.68/7.80 cnf(2065,plain, 7.68/7.80 (~P5(f331(f327(a383,x20651),x20651))), 7.68/7.80 inference(rename_variables,[],[926])). 7.68/7.80 cnf(2068,plain, 7.68/7.80 (P5(f331(f327(a383,x20681),f267(a394,x20681)))), 7.68/7.80 inference(rename_variables,[],[855])). 7.68/7.80 cnf(2074,plain, 7.68/7.80 (P5(f331(f327(a384,x20741),x20741))), 7.68/7.80 inference(rename_variables,[],[765])). 7.68/7.80 cnf(2077,plain, 7.68/7.80 (P5(f268(f273(a385,x20771),x20771))), 7.68/7.80 inference(rename_variables,[],[761])). 7.68/7.80 cnf(2082,plain, 7.68/7.80 (P5(f268(f273(a385,x20821),x20821))), 7.68/7.80 inference(rename_variables,[],[761])). 7.68/7.80 cnf(2087,plain, 7.68/7.80 (P5(f331(f327(a383,x20871),f267(a394,x20871)))), 7.68/7.80 inference(rename_variables,[],[855])). 7.68/7.80 cnf(2090,plain, 7.68/7.80 (P5(f331(f327(a384,x20901),x20901))), 7.68/7.80 inference(rename_variables,[],[765])). 7.68/7.80 cnf(2097,plain, 7.68/7.80 (~P5(f331(f327(a383,f267(f382(x20971),x20972)),x20971))), 7.68/7.80 inference(rename_variables,[],[932])). 7.68/7.80 cnf(2100,plain, 7.68/7.80 (~P5(f331(f327(a383,f267(f382(x21001),x21002)),x21002))), 7.68/7.80 inference(rename_variables,[],[931])). 7.68/7.80 cnf(2103,plain, 7.68/7.80 (~P5(f331(f327(a384,f267(a394,x21031)),x21031))), 7.68/7.80 inference(rename_variables,[],[928])). 7.68/7.80 cnf(2106,plain, 7.68/7.80 (~P5(f331(f327(a384,f267(a394,x21061)),x21061))), 7.68/7.80 inference(rename_variables,[],[928])). 7.68/7.80 cnf(2111,plain, 7.68/7.80 (~P5(f331(f327(a383,x21111),x21111))), 7.68/7.80 inference(rename_variables,[],[926])). 7.68/7.80 cnf(2114,plain, 7.68/7.80 (~P5(f331(f327(a383,f267(f382(x21141),x21142)),x21141))), 7.68/7.80 inference(rename_variables,[],[932])). 7.68/7.80 cnf(2117,plain, 7.68/7.80 (~P5(f331(f327(a384,f267(a394,x21171)),x21171))), 7.68/7.80 inference(rename_variables,[],[928])). 7.68/7.80 cnf(2173,plain, 7.68/7.80 (P5(f331(f327(a384,f267(f378(x21731),x21732)),x21731))), 7.68/7.80 inference(rename_variables,[],[871])). 7.68/7.80 cnf(2176,plain, 7.68/7.80 (P5(f331(f327(a384,f267(f378(x21761),x21762)),x21761))), 7.68/7.80 inference(rename_variables,[],[871])). 7.68/7.80 cnf(2226,plain, 7.68/7.80 (~E(f267(a394,x22261),x22261)), 7.68/7.80 inference(rename_variables,[],[917])). 7.68/7.80 cnf(2230,plain, 7.68/7.80 (~P5(f268(f328(a376,x22301),a2))), 7.68/7.80 inference(rename_variables,[],[919])). 7.68/7.80 cnf(2233,plain, 7.68/7.80 (~P5(f268(f328(a376,x22331),a2))), 7.68/7.80 inference(rename_variables,[],[919])). 7.68/7.80 cnf(2236,plain, 7.68/7.80 (P5(f331(f327(a384,x22361),x22361))), 7.68/7.80 inference(rename_variables,[],[765])). 7.68/7.80 cnf(2237,plain, 7.68/7.80 (P5(f331(f327(a384,a11),x22371))), 7.68/7.80 inference(rename_variables,[],[755])). 7.68/7.80 cnf(2246,plain, 7.68/7.80 (P5(f331(f327(a383,x22461),f267(a394,f267(f382(x22462),x22461))))), 7.68/7.80 inference(rename_variables,[],[872])). 7.68/7.80 cnf(2253,plain, 7.68/7.80 (P5(f268(f273(a385,a2),x22531))), 7.68/7.80 inference(rename_variables,[],[751])). 7.68/7.80 cnf(2256,plain, 7.68/7.80 (P5(f268(f273(a385,a2),x22561))), 7.68/7.80 inference(rename_variables,[],[751])). 7.68/7.80 cnf(2259,plain, 7.68/7.80 (P5(f268(f273(a385,x22591),x22591))), 7.68/7.80 inference(rename_variables,[],[761])). 7.68/7.80 cnf(2262,plain, 7.68/7.80 (P5(f268(f273(a385,a2),x22621))), 7.68/7.80 inference(rename_variables,[],[751])). 7.68/7.80 cnf(2265,plain, 7.68/7.80 (P5(f268(f273(a385,a2),x22651))), 7.68/7.80 inference(rename_variables,[],[751])). 7.68/7.80 cnf(2268,plain, 7.68/7.80 (P5(f268(f273(a385,a2),x22681))), 7.68/7.80 inference(rename_variables,[],[751])). 7.68/7.80 cnf(2271,plain, 7.68/7.80 (P5(f268(f273(a385,x22711),x22711))), 7.68/7.80 inference(rename_variables,[],[761])). 7.68/7.80 cnf(2274,plain, 7.68/7.80 (P5(f268(f273(a385,a2),x22741))), 7.68/7.80 inference(rename_variables,[],[751])). 7.68/7.80 cnf(2277,plain, 7.68/7.80 (P5(f268(f273(a385,a2),x22771))), 7.68/7.80 inference(rename_variables,[],[751])). 7.68/7.80 cnf(2280,plain, 7.68/7.80 (P5(f268(f273(a385,a2),x22801))), 7.68/7.80 inference(rename_variables,[],[751])). 7.68/7.80 cnf(2283,plain, 7.68/7.80 (P5(f269(f309(a389,a9),x22831))), 7.68/7.80 inference(rename_variables,[],[753])). 7.68/7.80 cnf(2286,plain, 7.68/7.80 (P5(f311(f294(a386,x22861),x22861))), 7.68/7.80 inference(rename_variables,[],[768])). 7.68/7.80 cnf(2289,plain, 7.68/7.80 (P5(f311(f294(a386,a8),x22891))), 7.68/7.80 inference(rename_variables,[],[759])). 7.68/7.80 cnf(2292,plain, 7.68/7.80 (P5(f311(f294(a386,a8),x22921))), 7.68/7.80 inference(rename_variables,[],[759])). 7.68/7.80 cnf(2295,plain, 7.68/7.80 (P5(f269(f309(a389,a9),x22951))), 7.68/7.80 inference(rename_variables,[],[753])). 7.68/7.80 cnf(2303,plain, 7.68/7.80 (P5(f311(f294(a386,x23031),x23031))), 7.68/7.80 inference(rename_variables,[],[768])). 7.68/7.80 cnf(2306,plain, 7.68/7.80 (P5(f311(f294(a386,x23061),x23061))), 7.68/7.80 inference(rename_variables,[],[768])). 7.68/7.80 cnf(2309,plain, 7.68/7.80 (P5(f311(f294(a386,x23091),x23091))), 7.68/7.80 inference(rename_variables,[],[768])). 7.68/7.80 cnf(2312,plain, 7.68/7.80 (P5(f311(f294(a386,x23121),x23121))), 7.68/7.80 inference(rename_variables,[],[768])). 7.68/7.80 cnf(2315,plain, 7.68/7.80 (P5(f311(f294(a386,x23151),x23151))), 7.68/7.80 inference(rename_variables,[],[768])). 7.68/7.80 cnf(2318,plain, 7.68/7.80 (P5(f311(f294(a386,x23181),x23181))), 7.68/7.80 inference(rename_variables,[],[768])). 7.68/7.80 cnf(2321,plain, 7.68/7.80 (P5(f269(f309(a389,x23211),x23211))), 7.68/7.80 inference(rename_variables,[],[763])). 7.68/7.80 cnf(2324,plain, 7.68/7.80 (P5(f269(f309(a389,x23241),x23241))), 7.68/7.80 inference(rename_variables,[],[763])). 7.68/7.80 cnf(2327,plain, 7.68/7.80 (P5(f269(f309(a389,x23271),x23271))), 7.68/7.80 inference(rename_variables,[],[763])). 7.68/7.80 cnf(2330,plain, 7.68/7.80 (P5(f269(f309(a389,x23301),x23301))), 7.68/7.80 inference(rename_variables,[],[763])). 7.68/7.80 cnf(2333,plain, 7.68/7.80 (P5(f269(f309(a389,x23331),x23331))), 7.68/7.80 inference(rename_variables,[],[763])). 7.68/7.80 cnf(2336,plain, 7.68/7.80 (P5(f269(f309(a389,x23361),x23361))), 7.68/7.80 inference(rename_variables,[],[763])). 7.68/7.80 cnf(2339,plain, 7.68/7.80 (P5(f268(f273(a385,x23391),x23391))), 7.68/7.80 inference(rename_variables,[],[761])). 7.68/7.80 cnf(2342,plain, 7.68/7.80 (P5(f268(f273(a385,x23421),x23421))), 7.68/7.80 inference(rename_variables,[],[761])). 7.68/7.80 cnf(2345,plain, 7.68/7.80 (P5(f268(f273(a385,x23451),x23451))), 7.68/7.80 inference(rename_variables,[],[761])). 7.68/7.80 cnf(2348,plain, 7.68/7.80 (P5(f268(f273(a385,x23481),x23481))), 7.68/7.80 inference(rename_variables,[],[761])). 7.68/7.80 cnf(2351,plain, 7.68/7.80 (P5(f268(f273(a385,x23511),x23511))), 7.68/7.80 inference(rename_variables,[],[761])). 7.68/7.80 cnf(2354,plain, 7.68/7.80 (P5(f268(f273(a385,x23541),x23541))), 7.68/7.80 inference(rename_variables,[],[761])). 7.68/7.80 cnf(2361,plain, 7.68/7.80 (P5(f331(f327(a383,a11),f267(a394,x23611)))), 7.68/7.80 inference(rename_variables,[],[852])). 7.68/7.80 cnf(2367,plain, 7.68/7.80 (~P5(f331(f327(a383,f267(f382(x23671),x23672)),x23671))), 7.68/7.80 inference(rename_variables,[],[932])). 7.68/7.80 cnf(2368,plain, 7.68/7.80 (P5(f331(f327(a384,a11),x23681))), 7.68/7.80 inference(rename_variables,[],[755])). 7.68/7.80 cnf(2375,plain, 7.68/7.80 (~P5(f331(f327(a383,x23751),a11))), 7.68/7.80 inference(rename_variables,[],[922])). 7.68/7.80 cnf(2385,plain, 7.68/7.80 (P5(f331(f327(a384,x23851),x23851))), 7.68/7.80 inference(rename_variables,[],[765])). 7.68/7.80 cnf(2388,plain, 7.68/7.80 (P5(f331(f327(a384,x23881),x23881))), 7.68/7.80 inference(rename_variables,[],[765])). 7.68/7.80 cnf(2395,plain, 7.68/7.80 (~E(f267(a394,x23951),x23951)), 7.68/7.80 inference(rename_variables,[],[917])). 7.68/7.80 cnf(2414,plain, 7.68/7.80 (P5(f311(f294(a386,x24141),x24141))), 7.68/7.80 inference(rename_variables,[],[768])). 7.68/7.80 cnf(2418,plain, 7.68/7.80 (P5(f311(f294(a386,a8),x24181))), 7.68/7.80 inference(rename_variables,[],[759])). 7.68/7.80 cnf(2421,plain, 7.68/7.80 (P5(f269(f309(a389,a9),x24211))), 7.68/7.80 inference(rename_variables,[],[753])). 7.68/7.80 cnf(2424,plain, 7.68/7.80 (P5(f311(f294(a386,a8),x24241))), 7.68/7.80 inference(rename_variables,[],[759])). 7.68/7.80 cnf(2427,plain, 7.68/7.80 (P5(f269(f309(a389,a9),x24271))), 7.68/7.80 inference(rename_variables,[],[753])). 7.68/7.80 cnf(2430,plain, 7.68/7.80 (P5(f269(f309(a389,x24301),x24301))), 7.68/7.80 inference(rename_variables,[],[763])). 7.68/7.80 cnf(2438,plain, 7.68/7.80 (P5(f311(f294(a386,a8),x24381))), 7.68/7.80 inference(rename_variables,[],[759])). 7.68/7.80 cnf(2441,plain, 7.68/7.80 (P5(f269(f309(a389,a9),x24411))), 7.68/7.80 inference(rename_variables,[],[753])). 7.68/7.80 cnf(2448,plain, 7.68/7.80 (P5(f269(f309(a389,a9),x24481))), 7.68/7.80 inference(rename_variables,[],[753])). 7.68/7.80 cnf(2451,plain, 7.68/7.80 (P5(f311(f294(a386,a8),x24511))), 7.68/7.80 inference(rename_variables,[],[759])). 7.68/7.80 cnf(2454,plain, 7.68/7.80 (P5(f311(f294(a386,a8),x24541))), 7.68/7.80 inference(rename_variables,[],[759])). 7.68/7.80 cnf(2457,plain, 7.68/7.80 (P5(f269(f309(a389,a9),x24571))), 7.68/7.80 inference(rename_variables,[],[753])). 7.68/7.80 cnf(2460,plain, 7.68/7.80 (P5(f311(f294(a386,a8),x24601))), 7.68/7.80 inference(rename_variables,[],[759])). 7.68/7.80 cnf(2463,plain, 7.68/7.80 (P5(f269(f309(a389,a9),x24631))), 7.68/7.80 inference(rename_variables,[],[753])). 7.68/7.80 cnf(2466,plain, 7.68/7.80 (P5(f311(f294(a386,a8),x24661))), 7.68/7.80 inference(rename_variables,[],[759])). 7.68/7.80 cnf(2469,plain, 7.68/7.80 (P5(f269(f309(a389,a9),x24691))), 7.68/7.80 inference(rename_variables,[],[753])). 7.68/7.80 cnf(2472,plain, 7.68/7.80 (P5(f311(f294(a386,a8),x24721))), 7.68/7.80 inference(rename_variables,[],[759])). 7.68/7.80 cnf(2475,plain, 7.68/7.80 (P5(f269(f309(a389,a9),x24751))), 7.68/7.80 inference(rename_variables,[],[753])). 7.68/7.80 cnf(2479,plain, 7.68/7.80 (P5(f331(f327(a384,x24791),x24791))), 7.68/7.80 inference(rename_variables,[],[765])). 7.68/7.80 cnf(3214,plain, 7.68/7.80 (~P5(f268(f328(a376,x32141),a2))), 7.68/7.80 inference(rename_variables,[],[919])). 7.68/7.80 cnf(3247,plain, 7.68/7.80 (P5(f331(f327(a384,x32471),x32471))), 7.68/7.80 inference(rename_variables,[],[765])). 7.68/7.80 cnf(3278,plain, 7.68/7.80 (P5(f331(f327(a384,x32781),x32781))), 7.68/7.80 inference(rename_variables,[],[765])). 7.68/7.80 cnf(3281,plain, 7.68/7.80 (P5(f331(f327(a383,x32811),f267(a394,x32811)))), 7.68/7.80 inference(rename_variables,[],[855])). 7.68/7.80 cnf(3319,plain, 7.68/7.80 ($false), 7.68/7.80 inference(scs_inference,[],[937,683,690,692,693,694,917,2226,2395,704,723,725,730,731,735,706,711,712,713,714,715,716,717,773,718,698,699,700,701,761,2077,2082,2259,2271,2339,2342,2345,2348,2351,2354,763,2321,2324,2327,2330,2333,2336,2430,765,2037,2074,2090,2236,2385,2388,2479,3247,3278,766,768,2286,2303,2306,2309,2312,2315,2318,2414,926,2040,2065,2111,855,2034,2059,2068,2087,3281,874,751,2253,2256,2262,2265,2268,2274,2277,2280,753,2283,2295,2421,2427,2441,2448,2457,2463,2469,2475,755,2237,2368,756,759,2289,2292,2418,2424,2438,2451,2454,2460,2466,2472,852,2361,851,919,2230,2233,3214,921,2027,922,2375,924,2024,749,818,747,861,2046,2049,2062,862,928,2103,2106,2117,841,935,936,871,2173,2176,931,2100,932,2097,2114,2367,872,2043,2054,2246,930,900,2004,2007,902,1998,903,894,2010,2013,895,2,1959,1958,1957,1956,1947,1946,1788,1787,1786,1785,1777,1775,1745,1744,1715,1714,1665,1644,1643,1642,1638,1629,1625,1621,1612,1537,1527,1526,1523,1487,1453,1449,1448,1443,1442,1419,1418,1416,1414,1412,1410,1350,1326,1324,1322,1319,1314,1313,1312,1297,1282,1274,1241,1240,1236,1235,1233,1230,1227,1226,1225,1219,1209,1203,1196,1195,1194,1187,1183,1166,1163,1159,1158,1157,1156,1151,1146,1143,1142,1111,1109,1105,1102,1055,1053,1048,1046,1029,982,947,946,945,944,682,676,3,1935,1780,1779,1753,1749,1728,1726,1626,1624,1622,1587,1584,1583,1582,1580,1579,1558,1556,1555,1554,1492,1489,1488,1482,1481,1468,1461,1402,1401,1400,1399,1398,1397,1396,1395,1394,1393,1392,1391,1390,1389,1388,1387,1386,1385,1383,1374,1369,1367,1339,1332,1289,1285,1283,1263,1239,1238,1237,1079,1077,1070,1069,1067,1065,1060,975,1604,1602,1599,1598,1597,1596,1594,1593,1592,1591,1589,1588,1578,1577,1574,1572,1570,1569,1568,1567,1444,1217,674,673,672,671,670,669,668,667,666,665,664,663,662,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,638,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,622,621,620,619,618,617,616,615,614,613,612,611,610,609,608,607,606,605,604,603,602,601,600,599,598,597,596,595,594,593,592,591,590,589,588,587,586,585,584,583,582,581,580,579,578,577,576,575,574,573,572,571,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,510,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,452,451,450,449,448,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,421,420,419,418,417,416,415,414,413,412,411,410,409,408,407,406,405,404,403,402,401,400,399,398,397,396,395,394,393,392,391,390,389,388,387,386,385,384,383,382,381,380,379,378,377,376,375,374,373,372,371,370,369,368,367,366,365,364,363,362,361,360,359,358,357,356,355,354,353,352,351,350,349,348,347,346,345,344,343,342,341,340,339,338,337,336,335,334,333,332,331,330,329,328,327,326,325,324,323,322,321,320,319,318,317,316,315,314,313,312,311,310,309,308,307,306,305,304,303,302,301,300,299,298,297,296,295,294,293,292,291,290,289,288,287,286,285,284,283,282,281,280,279,278,277,276,275,274,273,272,271,270,269,268,267,266,265,264,263,262,261,260,259,258,257,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1950,1949,1944,1933,1932,1931,1930,1919,1891,1878,1873,1872,1870,1864,1863,1862,1860,1858,1856,1848,1845,1842,1839,1838,1837,1835,1832,1828,1776,1764,1762,1755,1751,1743,1742,1741,1719,1718,1717,1716,1669,1668,1667,1666,1664,1663,1662,1661,1660,1659,1658,1657,1656,1655,1654,1653,1652,1651,1645,1639,1635,1634,1633,1632,1631,1630,1627,1620,1619,1618,1617,1616,1615,1614,1613,1566,1561,1560,1553,1552]), 7.68/7.80 ['proof']). 7.68/7.80 % SZS output end Proof 7.68/7.80 % Total time :6.090000s 8.04/7.85 EOF