TSTP Solution File: SWW294+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW294+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:13:29 EDT 2023
% Result : Theorem 11.41s 11.16s
% Output : CNFRefutation 11.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW294+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 21:04:19 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.61 start to proof:theBenchmark
% 10.88/11.01 %-------------------------------------------
% 10.88/11.01 % File :CSE---1.6
% 10.88/11.01 % Problem :theBenchmark
% 10.88/11.01 % Transform :cnf
% 10.88/11.01 % Format :tptp:raw
% 10.88/11.01 % Command :java -jar mcs_scs.jar %d %s
% 10.88/11.01
% 10.88/11.01 % Result :Theorem 6.950000s
% 10.88/11.01 % Output :CNFRefutation 6.950000s
% 10.88/11.01 %-------------------------------------------
% 10.88/11.01 %------------------------------------------------------------------------------
% 10.88/11.01 % File : SWW294+1 : TPTP v8.1.2. Released v5.2.0.
% 10.88/11.01 % Domain : Software Verification
% 10.88/11.01 % Problem : Hoare's Logic with Procedures 434712, 5000 axioms selected
% 10.88/11.01 % Version : Especial.
% 10.88/11.01 % English :
% 10.88/11.01
% 10.88/11.01 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 10.88/11.01 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 10.88/11.01 % Source : [Bla11]
% 10.88/11.01 % Names : hoare_434712.5000.p [Bla11]
% 10.88/11.01
% 10.88/11.01 % Status : ContradictoryAxioms
% 10.88/11.01 % Rating : 0.47 v8.1.0, 0.50 v7.5.0, 0.53 v7.4.0, 0.60 v7.3.0, 0.55 v7.1.0, 0.52 v7.0.0, 0.63 v6.4.0, 0.62 v6.3.0, 0.58 v6.2.0, 0.80 v6.1.0, 0.87 v5.5.0, 0.85 v5.4.0, 0.86 v5.3.0, 0.89 v5.2.0
% 10.88/11.01 % Syntax : Number of formulae : 5207 (1713 unt; 0 def)
% 10.88/11.01 % Number of atoms : 12583 (4548 equ)
% 10.88/11.01 % Maximal formula atoms : 13 ( 2 avg)
% 10.88/11.01 % Number of connectives : 8473 (1097 ~; 158 |; 712 &)
% 10.88/11.01 % ( 880 <=>;5626 =>; 0 <=; 0 <~>)
% 10.88/11.01 % Maximal formula depth : 22 ( 6 avg)
% 10.88/11.01 % Maximal term depth : 19 ( 2 avg)
% 10.88/11.02 % Number of predicates : 144 ( 143 usr; 1 prp; 0-7 aty)
% 10.88/11.02 % Number of functors : 401 ( 401 usr; 64 con; 0-10 aty)
% 10.88/11.02 % Number of variables : 16753 (16621 !; 132 ?)
% 10.88/11.02 % SPC : FOF_CAX_RFO_SEQ
% 10.88/11.02
% 10.88/11.02 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 10.88/11.02 % 2011-03-01 11:25:13
% 10.88/11.02 %------------------------------------------------------------------------------
% 10.88/11.02 %----Relevant facts (4983)
% 10.88/11.02 fof(fact_ext,axiom,
% 10.88/11.02 ! [V_g_2,V_f_2] :
% 10.88/11.02 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 10.88/11.02 => V_f_2 = V_g_2 ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I6_J,axiom,
% 10.88/11.02 ! [V_pname_H_2,V_pname_2] :
% 10.88/11.02 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 10.88/11.02 <=> V_pname_2 = V_pname_H_2 ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_zero__reorient,axiom,
% 10.88/11.02 ! [V_x_2,T_b] :
% 10.88/11.02 ( class_Groups_Ozero(T_b)
% 10.88/11.02 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 10.88/11.02 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osize_I7_J,axiom,
% 10.88/11.02 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osize_I15_J,axiom,
% 10.88/11.02 ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_bool_Osize_I1_J,axiom,
% 10.88/11.02 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_bool_Osize_I2_J,axiom,
% 10.88/11.02 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_size__literal__def,axiom,
% 10.88/11.02 ! [V_s] : hAPP(c_Nat_Osize__class_Osize(tc_String_Oliteral),V_s) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_char__size,axiom,
% 10.88/11.02 ! [V_c] : c_String_Ochar_Ochar__size(V_c) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_nat_Osize_I1_J,axiom,
% 10.88/11.02 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_bool_Osize_I3_J,axiom,
% 10.88/11.02 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_bool_Osize_I4_J,axiom,
% 10.88/11.02 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_size__char,axiom,
% 10.88/11.02 ! [V_c] : hAPP(c_Nat_Osize__class_Osize(tc_String_Ochar),V_c) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osize_I9_J,axiom,
% 10.88/11.02 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osize_I1_J,axiom,
% 10.88/11.02 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_char_Osize_I1_J,axiom,
% 10.88/11.02 ! [V_nibble2,V_nibble1] : c_String_Ochar_Ochar__size(hAPP(hAPP(c_String_Ochar_OChar,V_nibble1),V_nibble2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_nat_Osize_I3_J,axiom,
% 10.88/11.02 hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osize_I8_J,axiom,
% 10.88/11.02 ! [V_fun_2,V_pname_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osize_I16_J,axiom,
% 10.88/11.02 ! [V_fun_2,V_pname_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osize_I2_J,axiom,
% 10.88/11.02 ! [V_fun_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osize_I10_J,axiom,
% 10.88/11.02 ! [V_fun_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I70_J,axiom,
% 10.88/11.02 ! [V_pname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_semigroup_Oassoc,axiom,
% 10.88/11.02 ! [V_c_2,V_b_2,V_a_2,V_f_2,T_b] :
% 10.88/11.02 ( c_Groups_Osemigroup(T_b,V_f_2)
% 10.88/11.02 => hAPP(hAPP(V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_b_2)),V_c_2) = hAPP(hAPP(V_f_2,V_a_2),hAPP(hAPP(V_f_2,V_b_2),V_c_2)) ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_comm__monoid_Ocomm__neutral,axiom,
% 10.88/11.02 ! [V_a_2,V_z_2,V_f_2,T_b] :
% 10.88/11.02 ( c_Groups_Ocomm__monoid(T_b,V_f_2,V_z_2)
% 10.88/11.02 => hAPP(hAPP(V_f_2,V_a_2),V_z_2) = V_a_2 ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I8_J,axiom,
% 10.88/11.02 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I20_J,axiom,
% 10.88/11.02 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I9_J,axiom,
% 10.88/11.02 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I32_J,axiom,
% 10.88/11.02 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I21_J,axiom,
% 10.88/11.02 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I33_J,axiom,
% 10.88/11.02 ! [V_fun_2,V_vname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I1_J,axiom,
% 10.88/11.02 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 10.88/11.02 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 10.88/11.02 <=> ( V_vname_2 = V_vname_H_2
% 10.88/11.02 & V_fun_2 = V_fun_H_2 ) ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_char_Oinject,axiom,
% 10.88/11.02 ! [V_nibble2_H_2,V_nibble1_H_2,V_nibble2_2,V_nibble1_2] :
% 10.88/11.02 ( hAPP(hAPP(c_String_Ochar_OChar,V_nibble1_2),V_nibble2_2) = hAPP(hAPP(c_String_Ochar_OChar,V_nibble1_H_2),V_nibble2_H_2)
% 10.88/11.02 <=> ( V_nibble1_2 = V_nibble1_H_2
% 10.88/11.02 & V_nibble2_2 = V_nibble2_H_2 ) ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I7_J,axiom,
% 10.88/11.02 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
% 10.88/11.02 ( c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2) = c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2)
% 10.88/11.02 <=> ( V_vname_2 = V_vname_H_2
% 10.88/11.02 & V_pname_2 = V_pname_H_2
% 10.88/11.02 & V_fun_2 = V_fun_H_2 ) ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I64_J,axiom,
% 10.88/11.02 ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2 ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I65_J,axiom,
% 10.88/11.02 ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I71_J,axiom,
% 10.88/11.02 ! [V_fun_2,V_pname_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_nat__size,axiom,
% 10.88/11.02 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 10.88/11.02
% 10.88/11.02 fof(fact_char_Osize_I2_J,axiom,
% 10.88/11.02 ! [V_nibble2,V_nibble1] : hAPP(c_Nat_Osize__class_Osize(tc_String_Ochar),hAPP(hAPP(c_String_Ochar_OChar,V_nibble1),V_nibble2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I31_J,axiom,
% 10.88/11.02 ! [V_fun_2,V_vname_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I30_J,axiom,
% 10.88/11.02 ! [V_pname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I62_J,axiom,
% 10.88/11.02 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_pname_2] : hAPP(c_Com_Ocom_OBODY,V_pname_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I63_J,axiom,
% 10.88/11.02 ! [V_pname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != hAPP(c_Com_Ocom_OBODY,V_pname_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I18_J,axiom,
% 10.88/11.02 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Osimps_I19_J,axiom,
% 10.88/11.02 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 10.88/11.02
% 10.88/11.02 fof(fact_evaln_OSkip,axiom,
% 10.88/11.02 ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_evaln__elim__cases_I1_J,axiom,
% 10.88/11.02 ! [V_t,V_n,V_s] :
% 10.88/11.02 ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t)
% 10.88/11.02 => V_t = V_s ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_evaln_Oequations_I1_J,axiom,
% 10.88/11.02 ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_char_Orecs,axiom,
% 10.88/11.02 ! [V_nibble2_2,V_nibble1_2,V_f1_2,T_b] : c_String_Ochar_Ochar__rec(T_b,V_f1_2,hAPP(hAPP(c_String_Ochar_OChar,V_nibble1_2),V_nibble2_2)) = hAPP(hAPP(V_f1_2,V_nibble1_2),V_nibble2_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_char_Osimps_I2_J,axiom,
% 10.88/11.02 ! [V_nibble2_2,V_nibble1_2,V_f1_2,T_b] : c_String_Ochar_Ochar__case(T_b,V_f1_2,hAPP(hAPP(c_String_Ochar_OChar,V_nibble1_2),V_nibble2_2)) = hAPP(hAPP(V_f1_2,V_nibble1_2),V_nibble2_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_WTs__elim__cases_I8_J,axiom,
% 10.88/11.02 ! [V_a_2,V_Pa_2,V_X_2] :
% 10.88/11.02 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2)))
% 10.88/11.02 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_Pa_2))) ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_WT_OCall,axiom,
% 10.88/11.02 ! [V_a_2,V_X_2,V_pna_2] :
% 10.88/11.02 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pna_2)))
% 10.88/11.02 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pna_2,V_a_2))) ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_WT_Oequations_I8_J,axiom,
% 10.88/11.02 ! [V_a3_2,V_a1_2,V_a2_2] :
% 10.88/11.02 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
% 10.88/11.02 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_evaln_OAssign,axiom,
% 10.88/11.02 ! [V_n_2,V_s_2,V_a_2,V_X_2] : c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2))) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_evaln__elim__cases_I2_J,axiom,
% 10.88/11.02 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] :
% 10.88/11.02 ( c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2)
% 10.88/11.02 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Orecs_I1_J,axiom,
% 10.88/11.02 ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2 ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Orecs_I8_J,axiom,
% 10.88/11.02 ! [V_fun_2,V_pname_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_WT_Oequations_I2_J,axiom,
% 10.88/11.02 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_WT_OAssign,axiom,
% 10.88/11.02 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_WT_Oequations_I1_J,axiom,
% 10.88/11.02 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_WT_OSkip,axiom,
% 10.88/11.02 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_evaln_Oequations_I2_J,axiom,
% 10.88/11.02 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : c_Natural_Oevaln(c_Com_Ocom_OAss(V_a1_2,V_a2_2),V_a3_2,V_a4_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2))) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Orecs_I7_J,axiom,
% 10.88/11.02 ! [V_pname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_com_Orecs_I2_J,axiom,
% 10.88/11.02 ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_evalc_OAssign,axiom,
% 10.88/11.02 ! [V_s_2,V_a_2,V_X_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)))) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_evalc__elim__cases_I2_J,axiom,
% 10.88/11.02 ! [V_t_2,V_s_2,V_a_2,V_X_2] :
% 10.88/11.02 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2))
% 10.88/11.02 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_evalc_Oequations_I2_J,axiom,
% 10.88/11.02 ! [V_a3_2,V_a2_2,V_a1_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_a1_2,V_a2_2)),V_a3_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2)))) ).
% 10.88/11.02
% 10.88/11.02 fof(fact_WTs__elim__cases_I4_J,axiom,
% 10.88/11.02 ! [V_c2,V_c1] :
% 10.88/11.02 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 10.88/11.02 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 10.88/11.02 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln_OSemi,axiom,
% 10.88/11.03 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 10.88/11.03 ( c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1)
% 10.88/11.03 => ( c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
% 10.88/11.03 => c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I67_J,axiom,
% 10.88/11.03 ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_WTs__elim__cases_I5_J,axiom,
% 10.88/11.03 ! [V_c2_2,V_c1_2,V_b_2] :
% 10.88/11.03 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 10.88/11.03 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 10.88/11.03 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln__elim__cases_I5_J,axiom,
% 10.88/11.03 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 10.88/11.03 ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2),V_s_2,V_n_2,V_t_2)
% 10.88/11.03 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.03 => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) )
% 10.88/11.03 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.03 => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln_OIfTrue,axiom,
% 10.88/11.03 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 10.88/11.03 ( hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.03 => ( c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2)
% 10.88/11.03 => c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln_OIfFalse,axiom,
% 10.88/11.03 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 10.88/11.03 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.03 => ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2)
% 10.88/11.03 => c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_WTs__elim__cases_I3_J,axiom,
% 10.88/11.03 ! [V_c_2,V_a_2,V_Y_2] :
% 10.88/11.03 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)))
% 10.88/11.03 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I68_J,axiom,
% 10.88/11.03 ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_OIfFalse,axiom,
% 10.88/11.03 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 10.88/11.03 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.03 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 10.88/11.03 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_OIfTrue,axiom,
% 10.88/11.03 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 10.88/11.03 ( hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.03 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 10.88/11.03 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc__elim__cases_I5_J,axiom,
% 10.88/11.03 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2))
% 10.88/11.03 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.03 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 10.88/11.03 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.03 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_OSemi,axiom,
% 10.88/11.03 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 10.88/11.03 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 10.88/11.03 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc__elim__cases_I1_J,axiom,
% 10.88/11.03 ! [V_t,V_s] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 10.88/11.03 => V_t = V_s ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_OSkip,axiom,
% 10.88/11.03 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_Oequations_I4_J,axiom,
% 10.88/11.03 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 10.88/11.03 <=> ? [B_s1] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 10.88/11.03 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_Oequations_I5_J,axiom,
% 10.88/11.03 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2))
% 10.88/11.03 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.03 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 10.88/11.03 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.03 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_Oequations_I6_J,axiom,
% 10.88/11.03 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2))
% 10.88/11.03 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.03 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 10.88/11.03 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.03 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com__det,axiom,
% 10.88/11.03 ! [V_u,V_t,V_s,V_c] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 10.88/11.03 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 10.88/11.03 => V_u = V_t ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I44_J,axiom,
% 10.88/11.03 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I35_J,axiom,
% 10.88/11.03 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I45_J,axiom,
% 10.88/11.03 ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I34_J,axiom,
% 10.88/11.03 ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I37_J,axiom,
% 10.88/11.03 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I36_J,axiom,
% 10.88/11.03 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I3_J,axiom,
% 10.88/11.03 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 10.88/11.03 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 10.88/11.03 <=> ( V_com1_2 = V_com1_H_2
% 10.88/11.03 & V_com2_2 = V_com2_H_2 ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I4_J,axiom,
% 10.88/11.03 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 10.88/11.03 ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)
% 10.88/11.03 <=> ( V_fun_2 = V_fun_H_2
% 10.88/11.03 & V_com1_2 = V_com1_H_2
% 10.88/11.03 & V_com2_2 = V_com2_H_2 ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I2_J,axiom,
% 10.88/11.03 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 10.88/11.03 ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)
% 10.88/11.03 <=> ( V_loc_2 = V_loc_H_2
% 10.88/11.03 & V_fun_2 = V_fun_H_2
% 10.88/11.03 & V_com_2 = V_com_H_2 ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_eval__eq,axiom,
% 10.88/11.03 ! [V_t_2,V_s_2,V_c_2] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2))
% 10.88/11.03 <=> ? [B_n] : c_Natural_Oevaln(V_c_2,V_s_2,B_n,V_t_2) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln__evalc,axiom,
% 10.88/11.03 ! [V_t,V_n,V_s,V_c] :
% 10.88/11.03 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 10.88/11.03 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_Oequations_I1_J,axiom,
% 10.88/11.03 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_WT_Oequations_I3_J,axiom,
% 10.88/11.03 ! [V_a1_2,V_a3_2,V_a2_2] :
% 10.88/11.03 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 10.88/11.03 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_WT_OLocal,axiom,
% 10.88/11.03 ! [V_a_2,V_Y_2,V_c_2] :
% 10.88/11.03 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 10.88/11.03 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln_Oequations_I5_J,axiom,
% 10.88/11.03 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 10.88/11.03 ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2),V_a2_2,V_a4_2,V_a5_2)
% 10.88/11.03 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.03 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) )
% 10.88/11.03 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.03 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln_Oequations_I6_J,axiom,
% 10.88/11.03 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 10.88/11.03 ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2),V_a2_2,V_a4_2,V_a5_2)
% 10.88/11.03 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.03 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) )
% 10.88/11.03 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.03 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I41_J,axiom,
% 10.88/11.03 ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I40_J,axiom,
% 10.88/11.03 ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_WT_Oequations_I5_J,axiom,
% 10.88/11.03 ! [V_a2_2,V_a1_2,V_a3_2] :
% 10.88/11.03 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 10.88/11.03 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 10.88/11.03 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_WT_OIf,axiom,
% 10.88/11.03 ! [V_b_2,V_c1_2,V_c0_2] :
% 10.88/11.03 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 10.88/11.03 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 10.88/11.03 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I55_J,axiom,
% 10.88/11.03 ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I54_J,axiom,
% 10.88/11.03 ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln_Oequations_I4_J,axiom,
% 10.88/11.03 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 10.88/11.03 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2)
% 10.88/11.03 <=> ? [B_s1] :
% 10.88/11.03 ( c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1)
% 10.88/11.03 & c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I22_J,axiom,
% 10.88/11.03 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I23_J,axiom,
% 10.88/11.03 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I43_J,axiom,
% 10.88/11.03 ! [V_com_2,V_fun_2,V_loc_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I42_J,axiom,
% 10.88/11.03 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I10_J,axiom,
% 10.88/11.03 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I11_J,axiom,
% 10.88/11.03 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 10.88/11.03
% 10.88/11.03 fof(fact_WT_Oequations_I4_J,axiom,
% 10.88/11.03 ! [V_a2_2,V_a1_2] :
% 10.88/11.03 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 10.88/11.03 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 10.88/11.03 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_WT_OSemi,axiom,
% 10.88/11.03 ! [V_c1,V_c0] :
% 10.88/11.03 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 10.88/11.03 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 10.88/11.03 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I26_J,axiom,
% 10.88/11.03 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I27_J,axiom,
% 10.88/11.03 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I57_J,axiom,
% 10.88/11.03 ! [V_com2_2,V_com1_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I56_J,axiom,
% 10.88/11.03 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I14_J,axiom,
% 10.88/11.03 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I15_J,axiom,
% 10.88/11.03 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I49_J,axiom,
% 10.88/11.03 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I48_J,axiom,
% 10.88/11.03 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I24_J,axiom,
% 10.88/11.03 ! [V_com2_H_2,V_com1_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I25_J,axiom,
% 10.88/11.03 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I50_J,axiom,
% 10.88/11.03 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I51_J,axiom,
% 10.88/11.03 ! [V_com2_2,V_com1_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I12_J,axiom,
% 10.88/11.03 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I13_J,axiom,
% 10.88/11.03 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Orecs_I3_J,axiom,
% 10.88/11.03 ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com_2)) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Orecs_I5_J,axiom,
% 10.88/11.03 ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com1_2)),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com2_2)) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Orecs_I4_J,axiom,
% 10.88/11.03 ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com1_2)),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com2_2)) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_com_Osimps_I66_J,axiom,
% 10.88/11.03 ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc__elim__cases_I4_J,axiom,
% 10.88/11.03 ! [V_t,V_s,V_c2,V_c1] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t))
% 10.88/11.03 => ~ ! [B_s1] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1))
% 10.88/11.03 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln__elim__cases_I4_J,axiom,
% 10.88/11.03 ! [V_t,V_n,V_s,V_c2,V_c1] :
% 10.88/11.03 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c1,V_c2),V_s,V_n,V_t)
% 10.88/11.03 => ~ ! [B_s1] :
% 10.88/11.03 ( c_Natural_Oevaln(V_c1,V_s,V_n,B_s1)
% 10.88/11.03 => ~ c_Natural_Oevaln(V_c2,B_s1,V_n,V_t) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc__evaln,axiom,
% 10.88/11.03 ! [V_t,V_s,V_c] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 10.88/11.03 => ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_OLocal,axiom,
% 10.88/11.03 ! [V_s1_2,V_a_2,V_Y_2,V_s0_2,V_c_2] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2))),V_s1_2))
% 10.88/11.03 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2)))) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln_OLocal,axiom,
% 10.88/11.03 ! [V_s1_2,V_n_2,V_a_2,V_Y_2,V_s0_2,V_c_2] :
% 10.88/11.03 ( c_Natural_Oevaln(V_c_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2)),V_n_2,V_s1_2)
% 10.88/11.03 => c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2),V_s0_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2))) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_Oequations_I3_J,axiom,
% 10.88/11.03 ! [V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))))
% 10.88/11.03 <=> ? [B_s1] :
% 10.88/11.03 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))
% 10.88/11.03 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),B_s1)) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evaln_Oequations_I3_J,axiom,
% 10.88/11.03 ! [V_a6_2,V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
% 10.88/11.03 ( c_Natural_Oevaln(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2),V_a2_2,V_a5_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)))
% 10.88/11.03 <=> ? [B_s1] :
% 10.88/11.03 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))
% 10.88/11.03 & c_Natural_Oevaln(V_a1_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2)),V_a5_2,B_s1) ) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_OBody,axiom,
% 10.88/11.03 ! [V_s1,V_s0,V_pn] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 10.88/11.03 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc__elim__cases_I6_J,axiom,
% 10.88/11.03 ! [V_s1,V_s,V_P] :
% 10.88/11.03 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 10.88/11.03 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_WTs__elim__cases_I6_J,axiom,
% 10.88/11.03 ! [V_c_2,V_b_2] :
% 10.88/11.03 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2)))
% 10.88/11.03 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_OWhileFalse,axiom,
% 10.88/11.03 ! [V_c_2,V_s_2,V_b_2] :
% 10.88/11.03 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.03 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ).
% 10.88/11.03
% 10.88/11.03 fof(fact_evalc_OWhileTrue,axiom,
% 10.88/11.03 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
% 10.88/11.03 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 10.88/11.03 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s0_2),V_s1_2))
% 10.88/11.04 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
% 10.88/11.04 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln_OWhileTrue,axiom,
% 10.88/11.04 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] :
% 10.88/11.04 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 10.88/11.04 => ( c_Natural_Oevaln(V_c_2,V_s0_2,V_n_2,V_s1_2)
% 10.88/11.04 => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s1_2,V_n_2,V_s2_2)
% 10.88/11.04 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s0_2,V_n_2,V_s2_2) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln_OWhileFalse,axiom,
% 10.88/11.04 ! [V_n_2,V_c_2,V_s_2,V_b_2] :
% 10.88/11.04 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.04 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_s_2) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I5_J,axiom,
% 10.88/11.04 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 10.88/11.04 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 10.88/11.04 <=> ( V_fun_2 = V_fun_H_2
% 10.88/11.04 & V_com_2 = V_com_H_2 ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Osimps_I2_J,axiom,
% 10.88/11.04 ! [V_loc_H_2,V_loc_2] :
% 10.88/11.04 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2)
% 10.88/11.04 <=> V_loc_2 = V_loc_H_2 ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln_Oequations_I8_J,axiom,
% 10.88/11.04 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 10.88/11.04 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2)
% 10.88/11.04 <=> ( ( V_a6_2 = V_a2_2
% 10.88/11.04 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 10.88/11.04 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.04 & ? [B_s1] :
% 10.88/11.04 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 10.88/11.04 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2) ) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln_Oequations_I7_J,axiom,
% 10.88/11.04 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 10.88/11.04 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2)
% 10.88/11.04 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.04 => ? [B_s1] :
% 10.88/11.04 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 10.88/11.04 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evalc_Oequations_I8_J,axiom,
% 10.88/11.04 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 10.88/11.04 <=> ( ( V_a5_2 = V_a2_2
% 10.88/11.04 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 10.88/11.04 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.04 & ? [B_s1] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 10.88/11.04 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evalc_Oequations_I7_J,axiom,
% 10.88/11.04 ! [V_a2_2,V_a3_2,V_a1_2] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 10.88/11.04 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 10.88/11.04 => ? [B_s1] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 10.88/11.04 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_While,axiom,
% 10.88/11.04 ! [V_b_2,V_c_2] :
% 10.88/11.04 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 10.88/11.04 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_WT_Oequations_I6_J,axiom,
% 10.88/11.04 ! [V_a1_2,V_a2_2] :
% 10.88/11.04 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 10.88/11.04 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I58_J,axiom,
% 10.88/11.04 ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I59_J,axiom,
% 10.88/11.04 ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I52_J,axiom,
% 10.88/11.04 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I53_J,axiom,
% 10.88/11.04 ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I29_J,axiom,
% 10.88/11.04 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I28_J,axiom,
% 10.88/11.04 ! [V_com_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I61_J,axiom,
% 10.88/11.04 ! [V_com_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I60_J,axiom,
% 10.88/11.04 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I38_J,axiom,
% 10.88/11.04 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I39_J,axiom,
% 10.88/11.04 ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I47_J,axiom,
% 10.88/11.04 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I46_J,axiom,
% 10.88/11.04 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I17_J,axiom,
% 10.88/11.04 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I16_J,axiom,
% 10.88/11.04 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Orecs_I6_J,axiom,
% 10.88/11.04 ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f6_2,V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com_2)) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evalc_Oequations_I9_J,axiom,
% 10.88/11.04 ! [V_a3_2,V_a2_2,V_a1_2] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 10.88/11.04 <=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2)) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osimps_I69_J,axiom,
% 10.88/11.04 ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(V_f6_2,V_fun_2),V_com_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Osize_I2_J,axiom,
% 10.88/11.04 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evalc__elim__cases_I3_J,axiom,
% 10.88/11.04 ! [V_t_2,V_s_2,V_c_2,V_a_2,V_Y_2] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)),V_s_2),V_t_2))
% 10.88/11.04 => ~ ! [B_s1] :
% 10.88/11.04 ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2))
% 10.88/11.04 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2))),B_s1)) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln__elim__cases_I3_J,axiom,
% 10.88/11.04 ! [V_t_2,V_n_2,V_s_2,V_c_2,V_a_2,V_Y_2] :
% 10.88/11.04 ( c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2),V_s_2,V_n_2,V_t_2)
% 10.88/11.04 => ~ ! [B_s1] :
% 10.88/11.04 ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2))
% 10.88/11.04 => ~ c_Natural_Oevaln(V_c_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2)),V_n_2,B_s1) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Osize_I4_J,axiom,
% 10.88/11.04 ! [V_loc] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln_OBody,axiom,
% 10.88/11.04 ! [V_s1,V_n,V_s0,V_pn] :
% 10.88/11.04 ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1)
% 10.88/11.04 => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Osimps_I6_J,axiom,
% 10.88/11.04 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Orecs_I2_J,axiom,
% 10.88/11.04 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln_Oequations_I9_J,axiom,
% 10.88/11.04 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 10.88/11.04 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2)
% 10.88/11.04 <=> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2)),V_a2_2,V_a3_2,V_a4_2) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_WT_OBody,axiom,
% 10.88/11.04 ! [V_pn] :
% 10.88/11.04 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 10.88/11.04 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_WT_Oequations_I7_J,axiom,
% 10.88/11.04 ! [V_a_2] :
% 10.88/11.04 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 10.88/11.04 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evalc_OCall,axiom,
% 10.88/11.04 ! [V_X_2,V_s1_2,V_a_2,V_s0_2,V_pna_2] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pna_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2))),V_s1_2))
% 10.88/11.04 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_pna_2,V_a_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes)))) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln_OCall,axiom,
% 10.88/11.04 ! [V_X_2,V_s1_2,V_n_2,V_a_2,V_s0_2,V_pna_2] :
% 10.88/11.04 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pna_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2)),V_n_2,V_s1_2)
% 10.88/11.04 => c_Natural_Oevaln(c_Com_Ocom_OCall(V_X_2,V_pna_2,V_a_2),V_s0_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes))) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln__Suc,axiom,
% 10.88/11.04 ! [V_s_H,V_n,V_s,V_c] :
% 10.88/11.04 ( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
% 10.88/11.04 => c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln_Oequations_I10_J,axiom,
% 10.88/11.04 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a6_2] :
% 10.88/11.04 ( c_Natural_Oevaln(c_Com_Ocom_OCall(V_a6_2,V_a1_2,V_a3_2),V_a2_2,V_a4_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)))
% 10.88/11.04 <=> ? [B_s1] :
% 10.88/11.04 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 10.88/11.04 & c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2)),V_a4_2,B_s1) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evalc_Oequations_I10_J,axiom,
% 10.88/11.04 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a5_2] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_a5_2,V_a1_2,V_a3_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes))))
% 10.88/11.04 <=> ? [B_s1] :
% 10.88/11.04 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 10.88/11.04 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2))),B_s1)) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evalc__elim__cases_I7_J,axiom,
% 10.88/11.04 ! [V_s1_2,V_s_2,V_a_2,V_Pa_2,V_X_2] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2)),V_s_2),V_s1_2))
% 10.88/11.04 => ~ ! [B_s1] :
% 10.88/11.04 ( V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 10.88/11.04 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_Pa_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2))),B_s1)) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln__elim__cases_I7_J,axiom,
% 10.88/11.04 ! [V_s1_2,V_n_2,V_s_2,V_a_2,V_Pa_2,V_X_2] :
% 10.88/11.04 ( c_Natural_Oevaln(c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2),V_s_2,V_n_2,V_s1_2)
% 10.88/11.04 => ~ ! [B_s1] :
% 10.88/11.04 ( V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 10.88/11.04 => ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_Pa_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2)),V_n_2,B_s1) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_WT__bodiesD,axiom,
% 10.88/11.04 ! [V_b,V_pn] :
% 10.88/11.04 ( c_Com_OWT__bodies
% 10.88/11.04 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 10.88/11.04 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln__elim__cases_I6_J,axiom,
% 10.88/11.04 ! [V_s1,V_n,V_s,V_P] :
% 10.88/11.04 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
% 10.88/11.04 => ~ ! [B_n] :
% 10.88/11.04 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 10.88/11.04 => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Osize_I1_J,axiom,
% 10.88/11.04 ! [V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,c_Option_Ooption_ONone(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_WTs__elim__cases_I7_J,axiom,
% 10.88/11.04 ! [V_P] :
% 10.88/11.04 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 10.88/11.04 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_the_Osimps,axiom,
% 10.88/11.04 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 10.88/11.04
% 10.88/11.04 fof(fact_not__None__eq,axiom,
% 10.88/11.04 ! [T_b,V_x_2] :
% 10.88/11.04 ( V_x_2 != c_Option_Ooption_ONone(T_b)
% 10.88/11.04 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_not__Some__eq,axiom,
% 10.88/11.04 ! [T_b,V_x_2] :
% 10.88/11.04 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
% 10.88/11.04 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Osimps_I3_J,axiom,
% 10.88/11.04 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Oinject,axiom,
% 10.88/11.04 ! [V_a_H_2,V_a_2,T_b] :
% 10.88/11.04 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
% 10.88/11.04 <=> V_a_2 = V_a_H_2 ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Osimps_I2_J,axiom,
% 10.88/11.04 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Osize_I4_J,axiom,
% 10.88/11.04 ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Osize_I3_J,axiom,
% 10.88/11.04 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_Suc__neq__Zero,axiom,
% 10.88/11.04 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_Zero__neq__Suc,axiom,
% 10.88/11.04 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat_Osimps_I3_J,axiom,
% 10.88/11.04 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_Suc__not__Zero,axiom,
% 10.88/11.04 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat_Osimps_I2_J,axiom,
% 10.88/11.04 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_Zero__not__Suc,axiom,
% 10.88/11.04 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Osize_I1_J,axiom,
% 10.88/11.04 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Osize_I3_J,axiom,
% 10.88/11.04 ! [V_glb] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Osize_I2_J,axiom,
% 10.88/11.04 ! [V_a_2,V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 10.88/11.04 ! [V_c,V_b,V_a,T_a] :
% 10.88/11.04 ( class_Groups_Oab__semigroup__add(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__left__cancel,axiom,
% 10.88/11.04 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 10.88/11.04 ( class_Groups_Ocancel__semigroup__add(T_b)
% 10.88/11.04 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
% 10.88/11.04 <=> V_b_2 = V_c_2 ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__right__cancel,axiom,
% 10.88/11.04 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 10.88/11.04 ( class_Groups_Ocancel__semigroup__add(T_b)
% 10.88/11.04 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
% 10.88/11.04 <=> V_b_2 = V_c_2 ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__left__imp__eq,axiom,
% 10.88/11.04 ! [V_c,V_b,V_a,T_a] :
% 10.88/11.04 ( class_Groups_Ocancel__semigroup__add(T_a)
% 10.88/11.04 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
% 10.88/11.04 => V_b = V_c ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__imp__eq,axiom,
% 10.88/11.04 ! [V_c,V_b,V_a,T_a] :
% 10.88/11.04 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 10.88/11.04 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
% 10.88/11.04 => V_b = V_c ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__right__imp__eq,axiom,
% 10.88/11.04 ! [V_c,V_a,V_b,T_a] :
% 10.88/11.04 ( class_Groups_Ocancel__semigroup__add(T_a)
% 10.88/11.04 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
% 10.88/11.04 => V_b = V_c ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat__add__right__cancel,axiom,
% 10.88/11.04 ! [V_n_2,V_k_2,V_m_2] :
% 10.88/11.04 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)
% 10.88/11.04 <=> V_m_2 = V_n_2 ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat__add__left__cancel,axiom,
% 10.88/11.04 ! [V_n_2,V_m_2,V_k_2] :
% 10.88/11.04 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)
% 10.88/11.04 <=> V_m_2 = V_n_2 ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat__add__assoc,axiom,
% 10.88/11.04 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat__add__left__commute,axiom,
% 10.88/11.04 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat__add__commute,axiom,
% 10.88/11.04 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Osimps_I1_J,axiom,
% 10.88/11.04 ! [V_glb_H_2,V_glb_2] :
% 10.88/11.04 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2)
% 10.88/11.04 <=> V_glb_2 = V_glb_H_2 ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_plus__nat_Oadd__0,axiom,
% 10.88/11.04 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 10.88/11.04
% 10.88/11.04 fof(fact_Nat_Oadd__0__right,axiom,
% 10.88/11.04 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__is__0,axiom,
% 10.88/11.04 ! [V_n_2,V_m_2] :
% 10.88/11.04 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 10.88/11.04 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 10.88/11.04 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__eq__self__zero,axiom,
% 10.88/11.04 ! [V_n,V_m] :
% 10.88/11.04 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 10.88/11.04 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__Suc__shift,axiom,
% 10.88/11.04 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__Suc,axiom,
% 10.88/11.04 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__Suc__right,axiom,
% 10.88/11.04 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__0__left,axiom,
% 10.88/11.04 ! [V_a,T_a] :
% 10.88/11.04 ( class_Groups_Omonoid__add(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__0,axiom,
% 10.88/11.04 ! [V_a,T_a] :
% 10.88/11.04 ( class_Groups_Ocomm__monoid__add(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_double__zero__sym,axiom,
% 10.88/11.04 ! [V_a_2,T_b] :
% 10.88/11.04 ( class_Groups_Olinordered__ab__group__add(T_b)
% 10.88/11.04 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 10.88/11.04 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__0__right,axiom,
% 10.88/11.04 ! [V_a,T_a] :
% 10.88/11.04 ( class_Groups_Omonoid__add(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add_Ocomm__neutral,axiom,
% 10.88/11.04 ! [V_a,T_a] :
% 10.88/11.04 ( class_Groups_Ocomm__monoid__add(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_one__is__add,axiom,
% 10.88/11.04 ! [V_n_2,V_m_2] :
% 10.88/11.04 ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
% 10.88/11.04 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 10.88/11.04 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 10.88/11.04 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 10.88/11.04 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__is__1,axiom,
% 10.88/11.04 ! [V_n_2,V_m_2] :
% 10.88/11.04 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 10.88/11.04 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 10.88/11.04 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 10.88/11.04 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 10.88/11.04 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Osimps_I3_J,axiom,
% 10.88/11.04 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Osimps_I4_J,axiom,
% 10.88/11.04 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_Suc__inject,axiom,
% 10.88/11.04 ! [V_y,V_x] :
% 10.88/11.04 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 10.88/11.04 => V_x = V_y ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat_Oinject,axiom,
% 10.88/11.04 ! [V_nat_H_2,V_nat_2] :
% 10.88/11.04 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 10.88/11.04 <=> V_nat_2 = V_nat_H_2 ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_Suc__n__not__n,axiom,
% 10.88/11.04 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 10.88/11.04
% 10.88/11.04 fof(fact_n__not__Suc__n,axiom,
% 10.88/11.04 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat_Osize_I4_J,axiom,
% 10.88/11.04 ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat_Osize_I2_J,axiom,
% 10.88/11.04 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Orecs_I1_J,axiom,
% 10.88/11.04 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_vname_Osimps_I5_J,axiom,
% 10.88/11.04 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osize_I14_J,axiom,
% 10.88/11.04 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osize_I6_J,axiom,
% 10.88/11.04 ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osize_I13_J,axiom,
% 10.88/11.04 ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osize_I5_J,axiom,
% 10.88/11.04 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osize_I11_J,axiom,
% 10.88/11.04 ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osize_I3_J,axiom,
% 10.88/11.04 ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osize_I12_J,axiom,
% 10.88/11.04 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_com_Osize_I4_J,axiom,
% 10.88/11.04 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 10.88/11.04 ! [V_a,T_a] :
% 10.88/11.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 10.88/11.04 ! [V_a,T_a] :
% 10.88/11.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__0__iff,axiom,
% 10.88/11.04 ! [V_a_2,V_b_2,T_b] :
% 10.88/11.04 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 10.88/11.04 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 10.88/11.04 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_double__eq__0__iff,axiom,
% 10.88/11.04 ! [V_a_2,T_b] :
% 10.88/11.04 ( class_Groups_Olinordered__ab__group__add(T_b)
% 10.88/11.04 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 10.88/11.04 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Osimps_I5_J,axiom,
% 10.88/11.04 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Orecs_I2_J,axiom,
% 10.88/11.04 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Osimps_I4_J,axiom,
% 10.88/11.04 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_c)) = V_f1_2 ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Orecs_I1_J,axiom,
% 10.88/11.04 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_c)) = V_f1_2 ).
% 10.88/11.04
% 10.88/11.04 fof(fact_is__none__code_I2_J,axiom,
% 10.88/11.04 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_is__none__def,axiom,
% 10.88/11.04 ! [V_x_2,T_b] :
% 10.88/11.04 ( c_Option_Ois__none(T_b,V_x_2)
% 10.88/11.04 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_is__none__code_I1_J,axiom,
% 10.88/11.04 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 10.88/11.04 ! [V_c,V_a,T_a] :
% 10.88/11.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 10.88/11.04 ! [V_d,V_c,V_a,T_a] :
% 10.88/11.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 10.88/11.04 ! [V_d,V_c,V_a,T_a] :
% 10.88/11.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 10.88/11.04 ! [V_c,V_b,V_a,T_a] :
% 10.88/11.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 10.88/11.04 ! [V_c,V_b,V_a,T_a] :
% 10.88/11.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 10.88/11.04 ! [V_d,V_c,V_b,V_a,T_a] :
% 10.88/11.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 10.88/11.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 10.88/11.04 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 10.88/11.04 ( class_Rings_Osemiring__1(T_b)
% 10.88/11.04 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 10.88/11.04 ! [V_i_2,V_inc_2,T_b] :
% 10.88/11.04 ( class_Rings_Osemiring__1(T_b)
% 10.88/11.04 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evalc__WHILE__case,axiom,
% 10.88/11.04 ! [V_t_2,V_s_2,V_c_2,V_b_2] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_t_2))
% 10.88/11.04 => ( ( V_t_2 = V_s_2
% 10.88/11.04 => hBOOL(hAPP(V_b_2,V_s_2)) )
% 10.88/11.04 => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.04 => ! [B_s1] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),B_s1))
% 10.88/11.04 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),B_s1),V_t_2)) ) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_evaln__WHILE__case,axiom,
% 10.88/11.04 ! [V_t_2,V_n_2,V_s_2,V_c_2,V_b_2] :
% 10.88/11.04 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_t_2)
% 10.88/11.04 => ( ( V_t_2 = V_s_2
% 10.88/11.04 => hBOOL(hAPP(V_b_2,V_s_2)) )
% 10.88/11.04 => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
% 10.88/11.04 => ! [B_s1] :
% 10.88/11.04 ( c_Natural_Oevaln(V_c_2,V_s_2,V_n_2,B_s1)
% 10.88/11.04 => ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),B_s1,V_n_2,V_t_2) ) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_pair__box_Osize_I1_J,axiom,
% 10.88/11.04 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_sum_Osize_I2_J,axiom,
% 10.88/11.04 ! [V_b_2,V_fb_2,V_fa_2,T_c,T_b] : c_Sum__Type_Osum_Osum__size(T_b,T_c,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fb_2,V_b_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_sum_Osize_I1_J,axiom,
% 10.88/11.04 ! [V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Sum__Type_Osum_Osum__size(T_b,T_c,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_option_Oexhaust,axiom,
% 10.88/11.04 ! [T_a,V_y] :
% 10.88/11.04 ( V_y != c_Option_Ooption_ONone(T_a)
% 10.88/11.04 => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_zero__less__Suc,axiom,
% 10.88/11.04 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat_Oexhaust,axiom,
% 10.88/11.04 ! [V_y] :
% 10.88/11.04 ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 10.88/11.04 => ~ ! [B_nat] : V_y != hAPP(c_Nat_OSuc,B_nat) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_zero__induct,axiom,
% 10.88/11.04 ! [V_k_2,V_Pa_2] :
% 10.88/11.04 ( hBOOL(hAPP(V_Pa_2,V_k_2))
% 10.88/11.04 => ( ! [B_n] :
% 10.88/11.04 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_OSuc,B_n)))
% 10.88/11.04 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 10.88/11.04 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_less__zeroE,axiom,
% 10.88/11.04 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_Suc__mono,axiom,
% 10.88/11.04 ! [V_n,V_m] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 10.88/11.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_lessI,axiom,
% 10.88/11.04 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_pair__box_Oinject,axiom,
% 10.88/11.04 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 10.88/11.04 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
% 10.88/11.04 <=> ( V_a_2 = V_a_H_2
% 10.88/11.04 & V_b_2 = V_b_H_2 ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_less__not__refl,axiom,
% 10.88/11.04 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat__neq__iff,axiom,
% 10.88/11.04 ! [V_n_2,V_m_2] :
% 10.88/11.04 ( V_m_2 != V_n_2
% 10.88/11.04 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 10.88/11.04 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_linorder__neqE__nat,axiom,
% 10.88/11.04 ! [V_y,V_x] :
% 10.88/11.04 ( V_x != V_y
% 10.88/11.04 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 10.88/11.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_less__irrefl__nat,axiom,
% 10.88/11.04 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_less__not__refl2,axiom,
% 10.88/11.04 ! [V_m,V_n] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 10.88/11.04 => V_m != V_n ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_less__not__refl3,axiom,
% 10.88/11.04 ! [V_t,V_s] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 10.88/11.04 => V_s != V_t ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_nat__less__cases,axiom,
% 10.88/11.04 ! [V_Pa_2,V_n_2,V_m_2] :
% 10.88/11.04 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 10.88/11.04 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 10.88/11.04 => ( ( V_m_2 = V_n_2
% 10.88/11.04 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 10.88/11.04 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 10.88/11.04 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 10.88/11.04 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__less__cancel__right,axiom,
% 10.88/11.04 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 10.88/11.04 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 10.88/11.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 10.88/11.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__less__cancel__left,axiom,
% 10.88/11.04 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 10.88/11.04 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 10.88/11.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 10.88/11.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__strict__right__mono,axiom,
% 10.88/11.04 ! [V_c,V_b,V_a,T_a] :
% 10.88/11.04 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 10.88/11.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 10.88/11.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__strict__left__mono,axiom,
% 10.88/11.04 ! [V_c,V_b,V_a,T_a] :
% 10.88/11.04 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 10.88/11.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 10.88/11.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__strict__mono,axiom,
% 10.88/11.04 ! [V_d,V_c,V_b,V_a,T_a] :
% 10.88/11.04 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 10.88/11.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 10.88/11.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 10.88/11.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__less__imp__less__right,axiom,
% 10.88/11.04 ! [V_b,V_c,V_a,T_a] :
% 10.88/11.04 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 10.88/11.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 10.88/11.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_add__less__imp__less__left,axiom,
% 10.88/11.04 ! [V_b,V_a,V_c,T_a] :
% 10.88/11.04 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 10.88/11.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 10.88/11.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_not__less0,axiom,
% 10.88/11.04 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_neq0__conv,axiom,
% 10.88/11.04 ! [V_n_2] :
% 10.88/11.04 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 10.88/11.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_less__nat__zero__code,axiom,
% 10.88/11.04 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_gr__implies__not0,axiom,
% 10.88/11.04 ! [V_n,V_m] :
% 10.88/11.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 10.88/11.04 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 10.88/11.04
% 10.88/11.04 fof(fact_gr0I,axiom,
% 10.88/11.04 ! [V_n] :
% 10.88/11.05 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_Suc__less__SucD,axiom,
% 10.88/11.05 ! [V_n,V_m] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_Suc__lessD,axiom,
% 10.88/11.05 ! [V_n,V_m] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_less__SucE,axiom,
% 10.88/11.05 ! [V_n,V_m] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 10.88/11.05 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 10.88/11.05 => V_m = V_n ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_less__trans__Suc,axiom,
% 10.88/11.05 ! [V_k,V_j,V_i] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_Suc__lessI,axiom,
% 10.88/11.05 ! [V_n,V_m] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 10.88/11.05 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_less__SucI,axiom,
% 10.88/11.05 ! [V_n,V_m] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_less__antisym,axiom,
% 10.88/11.05 ! [V_m,V_n] :
% 10.88/11.05 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 10.88/11.05 => V_m = V_n ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_not__less__less__Suc__eq,axiom,
% 10.88/11.05 ! [V_m_2,V_n_2] :
% 10.88/11.05 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 10.88/11.05 <=> V_n_2 = V_m_2 ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_Suc__less__eq,axiom,
% 10.88/11.05 ! [V_n_2,V_m_2] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 10.88/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_less__Suc__eq,axiom,
% 10.88/11.05 ! [V_n_2,V_m_2] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 10.88/11.05 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 10.88/11.05 | V_m_2 = V_n_2 ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_not__less__eq,axiom,
% 10.88/11.05 ! [V_n_2,V_m_2] :
% 10.88/11.05 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 10.88/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_add__lessD1,axiom,
% 10.88/11.05 ! [V_k,V_j,V_i] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_less__add__eq__less,axiom,
% 10.88/11.05 ! [V_n,V_m,V_l,V_k] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 10.88/11.05 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_add__less__mono,axiom,
% 10.88/11.05 ! [V_l,V_k,V_j,V_i] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_add__less__mono1,axiom,
% 10.88/11.05 ! [V_k,V_j,V_i] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_trans__less__add2,axiom,
% 10.88/11.05 ! [V_m,V_j,V_i] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_trans__less__add1,axiom,
% 10.88/11.05 ! [V_m,V_j,V_i] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_nat__add__left__cancel__less,axiom,
% 10.88/11.05 ! [V_n_2,V_m_2,V_k_2] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 10.88/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_not__add__less2,axiom,
% 10.88/11.05 ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_not__add__less1,axiom,
% 10.88/11.05 ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_add__neg__neg,axiom,
% 10.88/11.05 ! [V_b,V_a,T_a] :
% 10.88/11.05 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_add__pos__pos,axiom,
% 10.88/11.05 ! [V_b,V_a,T_a] :
% 10.88/11.05 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 10.88/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 10.88/11.05 ! [V_a_2,T_b] :
% 10.88/11.05 ( class_Groups_Olinordered__ab__group__add(T_b)
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 10.88/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 10.88/11.05 ! [V_a_2,T_b] :
% 10.88/11.05 ( class_Groups_Olinordered__ab__group__add(T_b)
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 10.88/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_even__less__0__iff,axiom,
% 10.88/11.05 ! [V_a_2,T_b] :
% 10.88/11.05 ( class_Rings_Olinordered__idom(T_b)
% 10.88/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 10.88/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_gr0__conv__Suc,axiom,
% 10.88/11.05 ! [V_n_2] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 10.88/11.05 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 10.88/11.05
% 10.88/11.05 fof(fact_less__Suc0,axiom,
% 10.88/11.05 ! [V_n_2] :
% 10.88/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 11.05/11.05 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__Suc__eq__0__disj,axiom,
% 11.05/11.05 ! [V_n_2,V_m_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 11.05/11.05 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.05 | ? [B_j] :
% 11.05/11.05 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 11.05/11.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_add__gr__0,axiom,
% 11.05/11.05 ! [V_n_2,V_m_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
% 11.05/11.05 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 11.05/11.05 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__add__Suc1,axiom,
% 11.05/11.05 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__add__Suc2,axiom,
% 11.05/11.05 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__iff__Suc__add,axiom,
% 11.05/11.05 ! [V_n_2,V_m_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 11.05/11.05 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_pair__box_Osize_I2_J,axiom,
% 11.05/11.05 ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_pair__box_Osimps_I2_J,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_pair__box_Orecs,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_pos__add__strict,axiom,
% 11.05/11.05 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_sum_Osimps_I4_J,axiom,
% 11.05/11.05 ! [V_a_1,V_b_H_1,T_a_1,T_b_1] : hAPP(c_Sum__Type_OInr(T_b_1,T_a_1),V_b_H_1) != hAPP(c_Sum__Type_OInl(T_a_1,T_b_1),V_a_1) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Inr__not__Inl,axiom,
% 11.05/11.05 ! [V_a,V_b,T_a,T_b] : hAPP(c_Sum__Type_OInr(T_b,T_a),V_b) != hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_sum_Osimps_I3_J,axiom,
% 11.05/11.05 ! [V_b_H,V_a,T_b,T_a] : hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_b_H) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Inl__not__Inr,axiom,
% 11.05/11.05 ! [V_b,V_a,T_b,T_a] : hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_b) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_sum_Osize_I3_J,axiom,
% 11.05/11.05 ! [V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInl(T_a,T_b),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_sum_Osize_I4_J,axiom,
% 11.05/11.05 ! [V_b,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_a),V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_termination__basic__simps_I2_J,axiom,
% 11.05/11.05 ! [V_y,V_z,V_x] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_linorder__neqE__linordered__idom,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.05 => ( V_x != V_y
% 11.05/11.05 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_sum_Osimps_I2_J,axiom,
% 11.05/11.05 ! [V_b_H_2,V_b_2,T_b,T_c] :
% 11.05/11.05 ( hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2) = hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_H_2)
% 11.05/11.05 <=> V_b_2 = V_b_H_2 ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Inr__inject,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a,T_b] :
% 11.05/11.05 ( hAPP(c_Sum__Type_OInr(T_b,T_a),V_x) = hAPP(c_Sum__Type_OInr(T_b,T_a),V_y)
% 11.05/11.05 => V_x = V_y ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_sum_Osimps_I1_J,axiom,
% 11.05/11.05 ! [V_a_H_2,V_a_2,T_c,T_b] :
% 11.05/11.05 ( hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2) = hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_H_2)
% 11.05/11.05 <=> V_a_2 = V_a_H_2 ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Inl__inject,axiom,
% 11.05/11.05 ! [V_y,V_x,T_b,T_a] :
% 11.05/11.05 ( hAPP(c_Sum__Type_OInl(T_a,T_b),V_x) = hAPP(c_Sum__Type_OInl(T_a,T_b),V_y)
% 11.05/11.05 => V_x = V_y ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_termination__basic__simps_I1_J,axiom,
% 11.05/11.05 ! [V_z,V_y,V_x] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Projl_Osimps,axiom,
% 11.05/11.05 ! [V_x,T_b,T_a] : c_Sum__Type_OProjl(T_a,T_b,hAPP(c_Sum__Type_OInl(T_a,T_b),V_x)) = V_x ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Projr_Osimps,axiom,
% 11.05/11.05 ! [V_x,T_b,T_a] : c_Sum__Type_OProjr(T_a,T_b,hAPP(c_Sum__Type_OInr(T_b,T_a),V_x)) = V_x ).
% 11.05/11.05
% 11.05/11.05 fof(fact_sum_Orecs_I1_J,axiom,
% 11.05/11.05 ! [V_a_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : c_Sum__Type_Osum_Osum__rec(T_c,T_b,T_d,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInl(T_c,T_d),V_a_2)) = hAPP(V_f1_2,V_a_2) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_sum_Orecs_I2_J,axiom,
% 11.05/11.05 ! [V_b_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : c_Sum__Type_Osum_Osum__rec(T_c,T_b,T_d,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInr(T_d,T_c),V_b_2)) = hAPP(V_f2_2,V_b_2) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Suml_Osimps,axiom,
% 11.05/11.05 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_OSuml(T_c,T_b,T_d,V_f_2),hAPP(c_Sum__Type_OInl(T_c,T_d),V_x_2)) = hAPP(V_f_2,V_x_2) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Sumr_Osimps,axiom,
% 11.05/11.05 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_OSumr(T_c,T_b,T_d,V_f_2),hAPP(c_Sum__Type_OInr(T_c,T_d),V_x_2)) = hAPP(V_f_2,V_x_2) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__nat__0__less__iff,axiom,
% 11.05/11.05 ! [V_n_2,T_b] :
% 11.05/11.05 ( class_Rings_Olinordered__semidom(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__imp__Suc__add,axiom,
% 11.05/11.05 ! [V_n,V_m] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.05 => ? [B_k] : V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),B_k)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__imp__add__positive,axiom,
% 11.05/11.05 ! [V_j,V_i] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 11.05/11.05 => ? [B_k] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_k))
% 11.05/11.05 & hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),B_k) = V_j ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_gr0__implies__Suc,axiom,
% 11.05/11.05 ! [V_n] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.05 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__nat__eq__iff,axiom,
% 11.05/11.05 ! [V_n_2,V_m_2,T_b] :
% 11.05/11.05 ( class_Nat_Osemiring__char__0(T_b)
% 11.05/11.05 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)
% 11.05/11.05 <=> V_m_2 = V_n_2 ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Sumr__inject,axiom,
% 11.05/11.05 ! [V_g_2,V_f_2,T_b,T_d,T_c] :
% 11.05/11.05 ( c_Sum__Type_OSumr(T_c,T_d,T_b,V_f_2) = c_Sum__Type_OSumr(T_c,T_d,T_b,V_g_2)
% 11.05/11.05 => V_f_2 = V_g_2 ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Suml__inject,axiom,
% 11.05/11.05 ! [V_g_2,V_f_2,T_c,T_d,T_b] :
% 11.05/11.05 ( c_Sum__Type_OSuml(T_b,T_d,T_c,V_f_2) = c_Sum__Type_OSuml(T_b,T_d,T_c,V_g_2)
% 11.05/11.05 => V_f_2 = V_g_2 ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_int__eq__0__conv,axiom,
% 11.05/11.05 ! [V_n_2] :
% 11.05/11.05 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.05 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_int__0,axiom,
% 11.05/11.05 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zless__iff__Suc__zadd,axiom,
% 11.05/11.05 ! [V_z_2,V_w_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 11.05/11.05 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zless__int,axiom,
% 11.05/11.05 ! [V_n_2,V_m_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zadd__int,axiom,
% 11.05/11.05 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zadd__int__left,axiom,
% 11.05/11.05 ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zero__less__int__conv,axiom,
% 11.05/11.05 ! [V_n_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__nat__less__0__iff,axiom,
% 11.05/11.05 ! [V_m,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.05 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__nat__0,axiom,
% 11.05/11.05 ! [T_a] :
% 11.05/11.05 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.05 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__nat__less__iff,axiom,
% 11.05/11.05 ! [V_n_2,V_m_2,T_b] :
% 11.05/11.05 ( class_Rings_Olinordered__semidom(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__imp__of__nat__less,axiom,
% 11.05/11.05 ! [V_n,V_m,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__nat__less__imp__less,axiom,
% 11.05/11.05 ! [V_n,V_m,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__nat__add,axiom,
% 11.05/11.05 ! [V_n,V_m,T_a] :
% 11.05/11.05 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.05 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_lift__Suc__mono__less,axiom,
% 11.05/11.05 ! [V_n_H_2,V_n_2,V_f_2,T_b] :
% 11.05/11.05 ( class_Orderings_Oorder(T_b)
% 11.05/11.05 => ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_n_H_2))) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_lift__Suc__mono__less__iff,axiom,
% 11.05/11.05 ! [V_m_2,V_n_2,V_f_2,T_b] :
% 11.05/11.05 ( class_Orderings_Oorder(T_b)
% 11.05/11.05 => ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 11.05/11.05 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 11.05/11.05 ! [V_y_2,V_x_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 11.05/11.05 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_linorder__cases,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Olinorder(T_a)
% 11.05/11.05 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 => ( V_x != V_y
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_order__less__asym,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Opreorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_xt1_I10_J,axiom,
% 11.05/11.05 ! [V_z,V_x,V_y,T_a] :
% 11.05/11.05 ( class_Orderings_Oorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_order__less__trans,axiom,
% 11.05/11.05 ! [V_z,V_y,V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Opreorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_xt1_I2_J,axiom,
% 11.05/11.05 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.05 ( class_Orderings_Oorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 11.05/11.05 => ( V_b = V_c
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_int__less__0__conv,axiom,
% 11.05/11.05 ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_int__int__eq,axiom,
% 11.05/11.05 ! [V_n_2,V_m_2] :
% 11.05/11.05 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
% 11.05/11.05 <=> V_m_2 = V_n_2 ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 11.05/11.05 ! [V_y_2,V_x_2] :
% 11.05/11.05 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
% 11.05/11.05 <=> V_x_2 = V_y_2 ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zadd__commute,axiom,
% 11.05/11.05 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zadd__left__commute,axiom,
% 11.05/11.05 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zadd__assoc,axiom,
% 11.05/11.05 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zadd__0__right,axiom,
% 11.05/11.05 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zadd__0,axiom,
% 11.05/11.05 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zless__linear,axiom,
% 11.05/11.05 ! [V_y,V_x] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 11.05/11.05 | V_x = V_y
% 11.05/11.05 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zadd__strict__right__mono,axiom,
% 11.05/11.05 ! [V_k,V_j,V_i] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_order__less__irrefl,axiom,
% 11.05/11.05 ! [V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Opreorder(T_a)
% 11.05/11.05 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_linorder__neq__iff,axiom,
% 11.05/11.05 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.05 ( class_Orderings_Olinorder(T_b)
% 11.05/11.05 => ( V_x_2 != V_y_2
% 11.05/11.05 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 11.05/11.05 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_not__less__iff__gr__or__eq,axiom,
% 11.05/11.05 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.05 ( class_Orderings_Olinorder(T_b)
% 11.05/11.05 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 11.05/11.05 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 11.05/11.05 | V_x_2 = V_y_2 ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_linorder__less__linear,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Olinorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 | V_x = V_y
% 11.05/11.05 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_linorder__antisym__conv3,axiom,
% 11.05/11.05 ! [V_x_2,V_y_2,T_b] :
% 11.05/11.05 ( class_Orderings_Olinorder(T_b)
% 11.05/11.05 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 11.05/11.05 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 11.05/11.05 <=> V_x_2 = V_y_2 ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_linorder__neqE,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Olinorder(T_a)
% 11.05/11.05 => ( V_x != V_y
% 11.05/11.05 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__imp__neq,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Oorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 => V_x != V_y ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_order__less__not__sym,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Opreorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_order__less__imp__not__less,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Opreorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_order__less__imp__not__eq,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Oorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 => V_x != V_y ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_order__less__imp__not__eq2,axiom,
% 11.05/11.05 ! [V_y,V_x,T_a] :
% 11.05/11.05 ( class_Orderings_Oorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.05 => V_y != V_x ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_order__less__asym_H,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Orderings_Opreorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.05 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_xt1_I9_J,axiom,
% 11.05/11.05 ! [V_a,V_b,T_a] :
% 11.05/11.05 ( class_Orderings_Oorder(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 11.05/11.05 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_ord__eq__less__trans,axiom,
% 11.05/11.05 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.05 ( class_Orderings_Oord(T_a)
% 11.05/11.05 => ( V_a = V_b
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_xt1_I1_J,axiom,
% 11.05/11.05 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.05 ( class_Orderings_Oorder(T_a)
% 11.05/11.05 => ( V_a = V_b
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_ord__less__eq__trans,axiom,
% 11.05/11.05 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.05 ( class_Orderings_Oord(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.05 => ( V_b = V_c
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zero__less__imp__eq__int,axiom,
% 11.05/11.05 ! [V_k] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 11.05/11.05 => ? [B_n] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 11.05/11.05 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__int__0__less__iff,axiom,
% 11.05/11.05 ! [V_z_2,T_b] :
% 11.05/11.05 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__int__less__0__iff,axiom,
% 11.05/11.05 ! [V_z_2,T_b] :
% 11.05/11.05 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zmult__zless__mono2__lemma,axiom,
% 11.05/11.05 ! [V_k,V_j,V_i] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_negative__zless__0,axiom,
% 11.05/11.05 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_split__nat,axiom,
% 11.05/11.05 ! [V_i_2,V_Pa_2] :
% 11.05/11.05 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
% 11.05/11.05 <=> ( ! [B_n] :
% 11.05/11.05 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 11.05/11.05 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 11.05/11.05 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.05 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zero__less__nat__eq,axiom,
% 11.05/11.05 ! [V_z_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_negative__zless,axiom,
% 11.05/11.05 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_int__Suc,axiom,
% 11.05/11.05 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_odd__less__0,axiom,
% 11.05/11.05 ! [V_z_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 11.05/11.05 ! [V_m,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 11.05/11.05 ! [V_a,V_m,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 11.05/11.05 ! [V_m,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__1__mult,axiom,
% 11.05/11.05 ! [V_n,V_m,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__mult__right,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Oring(T_a)
% 11.05/11.05 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__mult__left,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Oring(T_a)
% 11.05/11.05 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__mult__commute,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Oring(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__mult__minus,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Oring(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_square__eq__1__iff,axiom,
% 11.05/11.05 ! [V_x_2,T_b] :
% 11.05/11.05 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 11.05/11.05 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 11.05/11.05 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 11.05/11.05 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_square__eq__iff,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.05 ( class_Rings_Oidom(T_b)
% 11.05/11.05 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
% 11.05/11.05 <=> ( V_a_2 = V_b_2
% 11.05/11.05 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__int__1,axiom,
% 11.05/11.05 ! [T_a] :
% 11.05/11.05 ( class_Rings_Oring__1(T_a)
% 11.05/11.05 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 11.05/11.05 ! [V_x,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__ring__1(T_a)
% 11.05/11.05 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zminus__zminus,axiom,
% 11.05/11.05 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__int__minus,axiom,
% 11.05/11.05 ! [V_z,T_a] :
% 11.05/11.05 ( class_Rings_Oring__1(T_a)
% 11.05/11.05 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__int__mult,axiom,
% 11.05/11.05 ! [V_z,V_w,T_a] :
% 11.05/11.05 ( class_Rings_Oring__1(T_a)
% 11.05/11.05 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zmult__1,axiom,
% 11.05/11.05 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zmult__1__right,axiom,
% 11.05/11.05 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zmult__commute,axiom,
% 11.05/11.05 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 11.05/11.05 ! [V_ry,V_rx,V_lx,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 11.05/11.05 ! [V_ry,V_rx,V_lx,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zmult__zminus,axiom,
% 11.05/11.05 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__int__eq__iff,axiom,
% 11.05/11.05 ! [V_z_2,V_w_2,T_b] :
% 11.05/11.05 ( class_Int_Oring__char__0(T_b)
% 11.05/11.05 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 11.05/11.05 <=> V_w_2 = V_z_2 ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 11.05/11.05 ! [V_rx,V_ly,V_lx,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zmult__assoc,axiom,
% 11.05/11.05 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 11.05/11.05 ! [V_rx,V_ly,V_lx,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 11.05/11.05 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 11.05/11.05 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 11.05/11.05 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__minus,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.05 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__1__left,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__1,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Groups_Ocomm__monoid__mult(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_one__reorient,axiom,
% 11.05/11.05 ! [V_x_2,T_b] :
% 11.05/11.05 ( class_Groups_Oone(T_b)
% 11.05/11.05 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 11.05/11.05 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__1__right,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult_Ocomm__neutral,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Groups_Ocomm__monoid__mult(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_equation__minus__iff,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_b)
% 11.05/11.05 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 11.05/11.05 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__equation__iff,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_b)
% 11.05/11.05 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 11.05/11.05 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_neg__equal__iff__equal,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_b)
% 11.05/11.05 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 11.05/11.05 <=> V_a_2 = V_b_2 ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 11.05/11.05 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.05 ( class_Groups_Oab__semigroup__mult(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__nat__mult,axiom,
% 11.05/11.05 ! [V_n,V_m,T_a] :
% 11.05/11.05 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.05 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__nat__1,axiom,
% 11.05/11.05 ! [T_a] :
% 11.05/11.05 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.05 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__int__of__nat,axiom,
% 11.05/11.05 ! [V_k,T_a] :
% 11.05/11.05 ( class_Rings_Oring__1(T_a)
% 11.05/11.05 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.05 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) )
% 11.05/11.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.05 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_nat__zminus__int,axiom,
% 11.05/11.05 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_nat__1,axiom,
% 11.05/11.05 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_pos__zmult__eq__1__iff,axiom,
% 11.05/11.05 ! [V_n_2,V_m_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 11.05/11.05 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 11.05/11.05 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 11.05/11.05 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__zero,axiom,
% 11.05/11.05 ! [T_a] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.05 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_neg__0__equal__iff__equal,axiom,
% 11.05/11.05 ! [V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_b)
% 11.05/11.05 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 11.05/11.05 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_equal__neg__zero,axiom,
% 11.05/11.05 ! [V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Olinordered__ab__group__add(T_b)
% 11.05/11.05 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 11.05/11.05 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_neg__equal__0__iff__equal,axiom,
% 11.05/11.05 ! [V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_b)
% 11.05/11.05 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.05 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_neg__equal__zero,axiom,
% 11.05/11.05 ! [V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Olinordered__ab__group__add(T_b)
% 11.05/11.05 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 11.05/11.05 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__minus__iff,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__less__iff,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_neg__less__iff__less,axiom,
% 11.05/11.05 ! [V_a_2,V_b_2,T_b] :
% 11.05/11.05 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__add__distrib,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Groups_Oab__group__add(T_a)
% 11.05/11.05 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__add,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.05 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_add__minus__cancel,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__add__cancel,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__zero__left,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Rings_Omult__zero(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__zero__right,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Rings_Omult__zero(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__eq__0__iff,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.05 ( class_Rings_Oring__no__zero__divisors(T_b)
% 11.05/11.05 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.05 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.05 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_no__zero__divisors,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ono__zero__divisors(T_a)
% 11.05/11.05 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.05 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_divisors__zero,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ono__zero__divisors(T_a)
% 11.05/11.05 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.05 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.05 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_one__neq__zero,axiom,
% 11.05/11.05 ! [T_a] :
% 11.05/11.05 ( class_Rings_Ozero__neq__one(T_a)
% 11.05/11.05 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zero__neq__one,axiom,
% 11.05/11.05 ! [T_a] :
% 11.05/11.05 ( class_Rings_Ozero__neq__one(T_a)
% 11.05/11.05 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zminus__0,axiom,
% 11.05/11.05 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_nat__int,axiom,
% 11.05/11.05 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 11.05/11.05
% 11.05/11.05 fof(fact_crossproduct__eq,axiom,
% 11.05/11.05 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 11.05/11.05 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 11.05/11.05 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
% 11.05/11.05 <=> ( V_w_2 = V_x_2
% 11.05/11.05 | V_y_2 = V_z_2 ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 11.05/11.05 ! [V_b,V_m,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 11.05/11.05 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_crossproduct__noteq,axiom,
% 11.05/11.05 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.05/11.05 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 11.05/11.05 => ( ( V_a_2 != V_b_2
% 11.05/11.05 & V_c_2 != V_d_2 )
% 11.05/11.05 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 11.05/11.05 ! [V_z,V_y,V_x,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_combine__common__factor,axiom,
% 11.05/11.05 ! [V_c,V_b,V_e,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Osemiring(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_comm__semiring__class_Odistrib,axiom,
% 11.05/11.05 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Ocomm__semiring(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zminus__zadd__distrib,axiom,
% 11.05/11.05 ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zadd__zmult__distrib,axiom,
% 11.05/11.05 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zadd__zmult__distrib2,axiom,
% 11.05/11.05 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_int__0__neq__1,axiom,
% 11.05/11.05 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_of__int__int__eq,axiom,
% 11.05/11.05 ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_one__less__nat__eq,axiom,
% 11.05/11.05 ! [V_z_2] :
% 11.05/11.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_neg__0__less__iff__less,axiom,
% 11.05/11.05 ! [V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_neg__less__0__iff__less,axiom,
% 11.05/11.05 ! [V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_neg__less__nonneg,axiom,
% 11.05/11.05 ! [V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Olinordered__ab__group__add(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_less__minus__self__iff,axiom,
% 11.05/11.05 ! [V_a_2,T_b] :
% 11.05/11.05 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_minus__unique,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.05 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.05 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_ab__left__minus,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Groups_Oab__group__add(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_left__minus,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_b)
% 11.05/11.05 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 11.05/11.05 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_right__minus,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.05 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_nat__0,axiom,
% 11.05/11.05 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 11.05/11.05 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_not__square__less__zero,axiom,
% 11.05/11.05 ! [V_a,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__ring(T_a)
% 11.05/11.05 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__less__cancel__right__disj,axiom,
% 11.05/11.05 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 11.05/11.05 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 11.05/11.05 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 11.05/11.05 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__less__cancel__left__disj,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.05 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 11.05/11.05 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 11.05/11.05 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__less__cancel__left__pos,axiom,
% 11.05/11.05 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.05 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 11.05/11.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__pos__pos,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__pos__neg,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_mult__pos__neg2,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.05
% 11.05/11.05 fof(fact_zero__less__mult__pos,axiom,
% 11.05/11.05 ! [V_b,V_a,T_a] :
% 11.05/11.05 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 11.05/11.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zero__less__mult__pos2,axiom,
% 11.05/11.06 ! [V_a,V_b,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__less__cancel__left__neg,axiom,
% 11.05/11.06 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__neg__pos,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__neg__neg,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__ring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__strict__right__mono,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__strict__left__mono,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_comm__mult__strict__left__mono,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__strict__right__mono__neg,axiom,
% 11.05/11.06 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__ring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__strict__left__mono__neg,axiom,
% 11.05/11.06 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__ring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_not__one__less__zero,axiom,
% 11.05/11.06 ! [T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zero__less__one,axiom,
% 11.05/11.06 ! [T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_sum__squares__eq__zero__iff,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.06 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.06 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.06 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__scale__eq__noteq,axiom,
% 11.05/11.06 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 11.05/11.06 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 11.05/11.06 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.06 => ( ( V_a = V_b
% 11.05/11.06 & V_c != V_d )
% 11.05/11.06 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_less__add__one,axiom,
% 11.05/11.06 ! [V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zadd__zminus__inverse2,axiom,
% 11.05/11.06 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_negative__eq__positive,axiom,
% 11.05/11.06 ! [V_m_2,V_n_2] :
% 11.05/11.06 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
% 11.05/11.06 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.06 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_not__int__zless__negative,axiom,
% 11.05/11.06 ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zmult__zless__mono2,axiom,
% 11.05/11.06 ! [V_k,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_int__0__less__1,axiom,
% 11.05/11.06 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_odd__nonzero,axiom,
% 11.05/11.06 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zless__add1__eq,axiom,
% 11.05/11.06 ! [V_z_2,V_w_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 11.05/11.06 | V_w_2 = V_z_2 ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__int__0,axiom,
% 11.05/11.06 ! [T_a] :
% 11.05/11.06 ( class_Rings_Oring__1(T_a)
% 11.05/11.06 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__int__0__eq__iff,axiom,
% 11.05/11.06 ! [V_z_2,T_b] :
% 11.05/11.06 ( class_Int_Oring__char__0(T_b)
% 11.05/11.06 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 11.05/11.06 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__int__eq__0__iff,axiom,
% 11.05/11.06 ! [V_z_2,T_b] :
% 11.05/11.06 ( class_Int_Oring__char__0(T_b)
% 11.05/11.06 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.06 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__int__less__iff,axiom,
% 11.05/11.06 ! [V_z_2,V_w_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__int__add,axiom,
% 11.05/11.06 ! [V_z,V_w,T_a] :
% 11.05/11.06 ( class_Rings_Oring__1(T_a)
% 11.05/11.06 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__int__of__nat__eq,axiom,
% 11.05/11.06 ! [V_n,T_a] :
% 11.05/11.06 ( class_Rings_Oring__1(T_a)
% 11.05/11.06 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__mono__iff,axiom,
% 11.05/11.06 ! [V_w_2,V_z_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zless__nat__conj,axiom,
% 11.05/11.06 ! [V_z_2,V_w_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zless__nat__eq__int__zless,axiom,
% 11.05/11.06 ! [V_z_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_sum__squares__gt__zero__iff,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
% 11.05/11.06 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.06 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_not__sum__squares__lt__zero,axiom,
% 11.05/11.06 ! [V_y,V_x,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__ring(T_a)
% 11.05/11.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zero__less__two,axiom,
% 11.05/11.06 ! [T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__nat__Suc,axiom,
% 11.05/11.06 ! [V_m,T_a] :
% 11.05/11.06 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.06 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_int__Suc0__eq__1,axiom,
% 11.05/11.06 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__aux__def,axiom,
% 11.05/11.06 ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_negD,axiom,
% 11.05/11.06 ! [V_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.06 => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_sgn__if,axiom,
% 11.05/11.06 ! [V_x,T_a] :
% 11.05/11.06 ( class_Groups_Osgn__if(T_a)
% 11.05/11.06 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.06 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 11.05/11.06 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.06 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.06 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 11.05/11.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.06 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_sgn__neg,axiom,
% 11.05/11.06 ! [V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_sgn__1__neg,axiom,
% 11.05/11.06 ! [V_a_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.06 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zsgn__def,axiom,
% 11.05/11.06 ! [V_i] :
% 11.05/11.06 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.06 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 11.05/11.06 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.06 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 11.05/11.06 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 11.05/11.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 11.05/11.06 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 11.05/11.06 ! [V_z] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 11.05/11.06 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__less__iff,axiom,
% 11.05/11.06 ! [V_m_2,V_w_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_convex__bound__lt,axiom,
% 11.05/11.06 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 11.05/11.06 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_sgn__1__pos,axiom,
% 11.05/11.06 ! [V_a_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.06 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__refl,axiom,
% 11.05/11.06 ! [V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Opreorder(T_a)
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le0,axiom,
% 11.05/11.06 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_negative__zle,axiom,
% 11.05/11.06 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__eq__self__implies__10,axiom,
% 11.05/11.06 ! [V_n,V_m] :
% 11.05/11.06 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 11.05/11.06 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 11.05/11.06 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__mult__le__cancel1,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__square,axiom,
% 11.05/11.06 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__cube,axiom,
% 11.05/11.06 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__mult__1,axiom,
% 11.05/11.06 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__1__eq__mult__iff,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 11.05/11.06 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 11.05/11.06 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__mult__1__right,axiom,
% 11.05/11.06 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__mult__commute,axiom,
% 11.05/11.06 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__mult__eq__1__iff,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 11.05/11.06 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 11.05/11.06 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__mult__assoc,axiom,
% 11.05/11.06 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__le__mono1,axiom,
% 11.05/11.06 ! [V_k,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__le__mono2,axiom,
% 11.05/11.06 ! [V_k,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__le__mono,axiom,
% 11.05/11.06 ! [V_l,V_k,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zle__antisym,axiom,
% 11.05/11.06 ! [V_w,V_z] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 11.05/11.06 => V_z = V_w ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zle__trans,axiom,
% 11.05/11.06 ! [V_k,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zle__linear,axiom,
% 11.05/11.06 ! [V_w,V_z] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 11.05/11.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zle__refl,axiom,
% 11.05/11.06 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_sgn__sgn,axiom,
% 11.05/11.06 ! [V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.06 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_linorder__le__cases,axiom,
% 11.05/11.06 ! [V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Olinorder(T_a)
% 11.05/11.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__funE,axiom,
% 11.05/11.06 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 11.05/11.06 ( class_Orderings_Oord(T_c)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_xt1_I6_J,axiom,
% 11.05/11.06 ! [V_z,V_x,V_y,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_xt1_I5_J,axiom,
% 11.05/11.06 ! [V_x,V_y,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.06 => V_x = V_y ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__trans,axiom,
% 11.05/11.06 ! [V_z,V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Opreorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__antisym,axiom,
% 11.05/11.06 ! [V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.05/11.06 => V_x = V_y ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_xt1_I4_J,axiom,
% 11.05/11.06 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 11.05/11.06 => ( V_b = V_c
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_ord__le__eq__trans,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Orderings_Oord(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => ( V_b = V_c
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_xt1_I3_J,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( V_a = V_b
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_ord__eq__le__trans,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Orderings_Oord(T_a)
% 11.05/11.06 => ( V_a = V_b
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__antisym__conv,axiom,
% 11.05/11.06 ! [V_x_2,V_y_2,T_b] :
% 11.05/11.06 ( class_Orderings_Oorder(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.05/11.06 <=> V_x_2 = V_y_2 ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__funD,axiom,
% 11.05/11.06 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 11.05/11.06 ( class_Orderings_Oord(T_c)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__eq__refl,axiom,
% 11.05/11.06 ! [V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Opreorder(T_a)
% 11.05/11.06 => ( V_x = V_y
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__eq__iff,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Orderings_Oorder(T_b)
% 11.05/11.06 => ( V_x_2 = V_y_2
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_linorder__linear,axiom,
% 11.05/11.06 ! [V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Olinorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__fun__def,axiom,
% 11.05/11.06 ! [V_g_2,V_f_2,T_b,T_c] :
% 11.05/11.06 ( class_Orderings_Oord(T_c)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 11.05/11.06 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__nat__le__iff,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__semidom(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zle__int,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__int__le__iff,axiom,
% 11.05/11.06 ! [V_z_2,V_w_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_one__le__mult__iff,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__le__cancel1,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__le__cancel2,axiom,
% 11.05/11.06 ! [V_n_2,V_k_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_linorder__not__less,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Orderings_Olinorder(T_b)
% 11.05/11.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_linorder__not__le,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Orderings_Olinorder(T_b)
% 11.05/11.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_linorder__le__less__linear,axiom,
% 11.05/11.06 ! [V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Olinorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__less__le,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Orderings_Oorder(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.05/11.06 & V_x_2 != V_y_2 ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_less__le__not__le,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Orderings_Opreorder(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.05/11.06 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__le__less,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Orderings_Oorder(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 11.05/11.06 | V_x_2 = V_y_2 ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_leI,axiom,
% 11.05/11.06 ! [V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Olinorder(T_a)
% 11.05/11.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_not__leE,axiom,
% 11.05/11.06 ! [V_x,V_y,T_a] :
% 11.05/11.06 ( class_Orderings_Olinorder(T_a)
% 11.05/11.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_linorder__antisym__conv1,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Orderings_Olinorder(T_b)
% 11.05/11.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.05/11.06 <=> V_x_2 = V_y_2 ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__neq__le__trans,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( V_a != V_b
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_xt1_I12_J,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( V_a != V_b
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_leD,axiom,
% 11.05/11.06 ! [V_x,V_y,T_a] :
% 11.05/11.06 ( class_Orderings_Olinorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.05/11.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__less__imp__le,axiom,
% 11.05/11.06 ! [V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Opreorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_linorder__antisym__conv2,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Orderings_Olinorder(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.05/11.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 11.05/11.06 <=> V_x_2 = V_y_2 ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__le__imp__less__or__eq,axiom,
% 11.05/11.06 ! [V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.06 | V_x = V_y ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__le__neq__trans,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => ( V_a != V_b
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_xt1_I11_J,axiom,
% 11.05/11.06 ! [V_a,V_b,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 11.05/11.06 => ( V_a != V_b
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__less__le__trans,axiom,
% 11.05/11.06 ! [V_z,V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Opreorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_xt1_I7_J,axiom,
% 11.05/11.06 ! [V_z,V_x,V_y,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_order__le__less__trans,axiom,
% 11.05/11.06 ! [V_z,V_y,V_x,T_a] :
% 11.05/11.06 ( class_Orderings_Opreorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_xt1_I8_J,axiom,
% 11.05/11.06 ! [V_z,V_x,V_y,T_a] :
% 11.05/11.06 ( class_Orderings_Oorder(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__le__imp__le__left,axiom,
% 11.05/11.06 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__le__imp__le__right,axiom,
% 11.05/11.06 ! [V_b,V_c,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__mono,axiom,
% 11.05/11.06 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__left__mono,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__right__mono,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__le__cancel__left,axiom,
% 11.05/11.06 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.06 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__le__cancel__right,axiom,
% 11.05/11.06 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 11.05/11.06 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__cancel2,axiom,
% 11.05/11.06 ! [V_n_2,V_k_2,V_m_2] :
% 11.05/11.06 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
% 11.05/11.06 <=> ( V_m_2 = V_n_2
% 11.05/11.06 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__cancel1,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.06 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 11.05/11.06 <=> ( V_m_2 = V_n_2
% 11.05/11.06 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__is__0,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.06 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.06 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__0__right,axiom,
% 11.05/11.06 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__0,axiom,
% 11.05/11.06 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__mult__cancel1,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.06 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)
% 11.05/11.06 <=> V_m_2 = V_n_2 ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__0__eq,axiom,
% 11.05/11.06 ! [V_n_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 11.05/11.06 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 11.05/11.06 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__imp__neg__le,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__ab__group__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_neg__le__iff__le,axiom,
% 11.05/11.06 ! [V_a_2,V_b_2,T_b] :
% 11.05/11.06 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_minus__le__iff,axiom,
% 11.05/11.06 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.06 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__minus__iff,axiom,
% 11.05/11.06 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.06 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__mult__distrib2,axiom,
% 11.05/11.06 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__mult__distrib,axiom,
% 11.05/11.06 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__n__not__le__n,axiom,
% 11.05/11.06 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_not__less__eq__eq,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__Suc__eq,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.05/11.06 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__le__mono,axiom,
% 11.05/11.06 ! [V_m_2,V_n_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__SucI,axiom,
% 11.05/11.06 ! [V_n,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__SucE,axiom,
% 11.05/11.06 ! [V_n,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 11.05/11.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.06 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__leD,axiom,
% 11.05/11.06 ! [V_n,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 11.05/11.06 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_termination__basic__simps_I5_J,axiom,
% 11.05/11.06 ! [V_y,V_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_less__or__eq__imp__le,axiom,
% 11.05/11.06 ! [V_n,V_m] :
% 11.05/11.06 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.06 | V_m = V_n )
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__neq__implies__less,axiom,
% 11.05/11.06 ! [V_n,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.06 => ( V_m != V_n
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_less__imp__le__nat,axiom,
% 11.05/11.06 ! [V_n,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__eq__less__or__eq,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 11.05/11.06 | V_m_2 = V_n_2 ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__less__le,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.05/11.06 & V_m_2 != V_n_2 ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_termination__basic__simps_I3_J,axiom,
% 11.05/11.06 ! [V_z,V_y,V_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_termination__basic__simps_I4_J,axiom,
% 11.05/11.06 ! [V_y,V_z,V_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__add2,axiom,
% 11.05/11.06 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__add1,axiom,
% 11.05/11.06 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__iff__add,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.05/11.06 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__add__left__cancel__le,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_trans__le__add1,axiom,
% 11.05/11.06 ! [V_m,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_trans__le__add2,axiom,
% 11.05/11.06 ! [V_m,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__le__mono1,axiom,
% 11.05/11.06 ! [V_k,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__le__mono,axiom,
% 11.05/11.06 ! [V_l,V_k,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__leD2,axiom,
% 11.05/11.06 ! [V_n,V_k,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__leD1,axiom,
% 11.05/11.06 ! [V_n,V_k,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__leE,axiom,
% 11.05/11.06 ! [V_n,V_k,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 11.05/11.06 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zless__le,axiom,
% 11.05/11.06 ! [V_w_2,V_z_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 11.05/11.06 & V_z_2 != V_w_2 ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zadd__left__mono,axiom,
% 11.05/11.06 ! [V_k,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_evaln__nonstrict,axiom,
% 11.05/11.06 ! [V_m,V_t,V_n,V_s,V_c] :
% 11.05/11.06 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.06 => c_Natural_Oevaln(V_c,V_s,V_m,V_t) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__le__eq__zle,axiom,
% 11.05/11.06 ! [V_z_2,V_w_2] :
% 11.05/11.06 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 11.05/11.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__mult__distrib,axiom,
% 11.05/11.06 ! [V_z_H,V_z] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 11.05/11.06 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 11.05/11.06 ! [V_y,V_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__int__0__le__iff,axiom,
% 11.05/11.06 ! [V_z_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__int__le__0__iff,axiom,
% 11.05/11.06 ! [V_z_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_sgn__0__0,axiom,
% 11.05/11.06 ! [V_a_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.06 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.06 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_sgn0,axiom,
% 11.05/11.06 ! [T_a] :
% 11.05/11.06 ( class_Groups_Osgn__if(T_a)
% 11.05/11.06 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_sgn__times,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.06 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__mult__distrib__neg,axiom,
% 11.05/11.06 ! [V_z_H,V_z] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.06 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 11.05/11.06 ! [V_a_2,T_b] :
% 11.05/11.06 ( class_Groups_Olinordered__ab__group__add(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 11.05/11.06 ! [V_a_2,T_b] :
% 11.05/11.06 ( class_Groups_Olinordered__ab__group__add(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__nonneg__nonneg,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__nonneg__eq__0__iff,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 11.05/11.06 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.06 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.06 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__increasing,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__increasing2,axiom,
% 11.05/11.06 ! [V_a,V_b,V_c,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__nonpos__nonpos,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_split__mult__neg__le,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__cancel__semiring(T_a)
% 11.05/11.06 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 11.05/11.06 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_split__mult__pos__le,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__ring(T_a)
% 11.05/11.06 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 11.05/11.06 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__mono,axiom,
% 11.05/11.06 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__mono_H,axiom,
% 11.05/11.06 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__left__mono__neg,axiom,
% 11.05/11.06 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__ring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__right__mono__neg,axiom,
% 11.05/11.06 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__ring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_comm__mult__left__mono,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__comm__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__left__mono,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__right__mono,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__nonpos__nonpos,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__ring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__nonpos__nonneg,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__cancel__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__nonneg__nonpos2,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__cancel__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__nonneg__nonpos,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__cancel__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__nonneg__nonneg,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Oordered__cancel__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__le__0__iff,axiom,
% 11.05/11.06 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.06 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 11.05/11.06 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zero__le__mult__iff,axiom,
% 11.05/11.06 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.06 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
% 11.05/11.06 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 11.05/11.06 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zero__le__square,axiom,
% 11.05/11.06 ! [V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__ring(T_a)
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__le__less__mono,axiom,
% 11.05/11.06 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__less__le__mono,axiom,
% 11.05/11.06 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zero__le__one,axiom,
% 11.05/11.06 ! [T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_not__one__le__zero,axiom,
% 11.05/11.06 ! [T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_neg__0__le__iff__le,axiom,
% 11.05/11.06 ! [V_a_2,T_b] :
% 11.05/11.06 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__minus__self__iff,axiom,
% 11.05/11.06 ! [V_a_2,T_b] :
% 11.05/11.06 ( class_Groups_Olinordered__ab__group__add(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_neg__le__0__iff__le,axiom,
% 11.05/11.06 ! [V_a_2,T_b] :
% 11.05/11.06 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_minus__le__self__iff,axiom,
% 11.05/11.06 ! [V_a_2,T_b] :
% 11.05/11.06 ( class_Groups_Olinordered__ab__group__add(T_b)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__eq__1__iff,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 11.05/11.06 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 11.05/11.06 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zero__le__imp__of__nat,axiom,
% 11.05/11.06 ! [V_m,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_of__nat__0__le__iff,axiom,
% 11.05/11.06 ! [V_n,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__less__mono2,axiom,
% 11.05/11.06 ! [V_k,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__less__mono1,axiom,
% 11.05/11.06 ! [V_k,V_j,V_i] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__less__cancel2,axiom,
% 11.05/11.06 ! [V_n_2,V_k_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__less__cancel1,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_nat__0__less__mult__iff,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
% 11.05/11.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 11.05/11.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__mult__less__cancel1,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__Suc,axiom,
% 11.05/11.06 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__Suc__right,axiom,
% 11.05/11.06 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_One__nat__def,axiom,
% 11.05/11.06 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__le__lessD,axiom,
% 11.05/11.06 ! [V_n,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__less__Suc__eq,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 11.05/11.06 <=> V_n_2 = V_m_2 ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__leI,axiom,
% 11.05/11.06 ! [V_n,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_le__imp__less__Suc,axiom,
% 11.05/11.06 ! [V_n,V_m] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__le__eq,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_less__Suc__eq__le,axiom,
% 11.05/11.06 ! [V_n_2,V_m_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_less__eq__Suc__le,axiom,
% 11.05/11.06 ! [V_m_2,V_n_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 11.05/11.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__eq__plus1,axiom,
% 11.05/11.06 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Suc__eq__plus1__left,axiom,
% 11.05/11.06 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 11.05/11.06 ! [V_y,V_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zero__zle__int,axiom,
% 11.05/11.06 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 11.05/11.06 ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 11.05/11.06 ! [V_Pa_2] :
% 11.05/11.06 ( ? [B_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 11.05/11.06 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 11.05/11.06 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 11.05/11.06 ! [V_Pa_2] :
% 11.05/11.06 ( ! [B_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 11.05/11.06 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 11.05/11.06 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 11.05/11.06 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_eq__nat__nat__iff,axiom,
% 11.05/11.06 ! [V_z_H_2,V_z_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 11.05/11.06 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 11.05/11.06 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_ex__nat,axiom,
% 11.05/11.06 ! [V_Pa_2] :
% 11.05/11.06 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 11.05/11.06 <=> ? [B_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 11.05/11.06 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_all__nat,axiom,
% 11.05/11.06 ! [V_Pa_2] :
% 11.05/11.06 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 11.05/11.06 <=> ! [B_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 11.05/11.06 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 11.05/11.06 ! [V_y_2,V_x_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 11.05/11.06 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 11.05/11.06 <=> V_x_2 = V_y_2 ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zadd__zless__mono,axiom,
% 11.05/11.06 ! [V_z,V_z_H,V_w,V_w_H] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 11.05/11.06 ! [V_y,V_x] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_int__mult,axiom,
% 11.05/11.06 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zmult__int,axiom,
% 11.05/11.06 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 11.05/11.06 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_zle__iff__zadd,axiom,
% 11.05/11.06 ! [V_z_2,V_w_2] :
% 11.05/11.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 11.05/11.06 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_int__1,axiom,
% 11.05/11.06 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 11.05/11.06 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 11.05/11.06 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__nonpos__neg,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__neg__nonpos,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__strict__increasing2,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__strict__increasing,axiom,
% 11.05/11.06 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__nonneg__pos,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_add__pos__nonneg,axiom,
% 11.05/11.06 ! [V_b,V_a,T_a] :
% 11.05/11.06 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__left__le__imp__le,axiom,
% 11.05/11.06 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__right__le__imp__le,axiom,
% 11.05/11.06 ! [V_b,V_c,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__less__imp__less__left,axiom,
% 11.05/11.06 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__left__less__imp__less,axiom,
% 11.05/11.06 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__less__imp__less__right,axiom,
% 11.05/11.06 ! [V_b,V_c,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__right__less__imp__less,axiom,
% 11.05/11.06 ! [V_b,V_c,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__le__less__imp__less,axiom,
% 11.05/11.06 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__less__le__imp__less,axiom,
% 11.05/11.06 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.06 fof(fact_mult__strict__mono_H,axiom,
% 11.05/11.06 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.05/11.06 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 11.05/11.06
% 11.05/11.07 fof(fact_mult__strict__mono,axiom,
% 11.05/11.07 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Rings_Olinordered__semiring__strict(T_a)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mult__le__cancel__left__neg,axiom,
% 11.05/11.07 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.07 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mult__le__cancel__left__pos,axiom,
% 11.05/11.07 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.07 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_sum__squares__ge__zero,axiom,
% 11.05/11.07 ! [V_y,V_x,T_a] :
% 11.05/11.07 ( class_Rings_Olinordered__ring(T_a)
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_sum__squares__le__zero__iff,axiom,
% 11.05/11.07 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.07 ( class_Rings_Olinordered__ring__strict(T_b)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.07 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.07 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mult__left__le__one__le,axiom,
% 11.05/11.07 ! [V_y,V_x,T_a] :
% 11.05/11.07 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mult__right__le__one__le,axiom,
% 11.05/11.07 ! [V_y,V_x,T_a] :
% 11.05/11.07 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_sgn__less,axiom,
% 11.05/11.07 ! [V_a_2,T_b] :
% 11.05/11.07 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_sgn__greater,axiom,
% 11.05/11.07 ! [V_a_2,T_b] :
% 11.05/11.07 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_one__less__mult,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_n__less__n__mult__m,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_n__less__m__mult__n,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_int__le__0__conv,axiom,
% 11.05/11.07 ! [V_n_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__0__iff,axiom,
% 11.05/11.07 ! [V_i_2] :
% 11.05/11.07 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__le__0,axiom,
% 11.05/11.07 ! [V_z] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_int__one__le__iff__zero__less,axiom,
% 11.05/11.07 ! [V_z_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__0__le,axiom,
% 11.05/11.07 ! [V_z] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 11.05/11.07 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_int__eq__iff,axiom,
% 11.05/11.07 ! [V_z_2,V_m_2] :
% 11.05/11.07 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 11.05/11.07 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_int__nat__eq,axiom,
% 11.05/11.07 ! [V_z] :
% 11.05/11.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 11.05/11.07 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 11.05/11.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 11.05/11.07 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zle__add1__eq__le,axiom,
% 11.05/11.07 ! [V_z_2,V_w_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_add1__zle__eq,axiom,
% 11.05/11.07 ! [V_z_2,V_w_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zless__imp__add1__zle,axiom,
% 11.05/11.07 ! [V_z,V_w] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_int__zle__neg,axiom,
% 11.05/11.07 ! [V_m_2,V_n_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))
% 11.05/11.07 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_negative__zle__0,axiom,
% 11.05/11.07 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_convex__bound__le,axiom,
% 11.05/11.07 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 11.05/11.07 ( class_Rings_Olinordered__semiring__1(T_a)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 11.05/11.07 ! [V_y_2,V_x_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__less__eq__zless,axiom,
% 11.05/11.07 ! [V_z_2,V_w_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__eq__iff,axiom,
% 11.05/11.07 ! [V_m_2,V_w_2] :
% 11.05/11.07 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 11.05/11.07 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 11.05/11.07 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 11.05/11.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 11.05/11.07 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__eq__iff2,axiom,
% 11.05/11.07 ! [V_w_2,V_m_2] :
% 11.05/11.07 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 11.05/11.07 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 11.05/11.07 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 11.05/11.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 11.05/11.07 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 11.05/11.07 ! [V_y,V_x] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__add__distrib,axiom,
% 11.05/11.07 ! [V_z_H,V_z] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 11.05/11.07 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__imp__0__less,axiom,
% 11.05/11.07 ! [V_z] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_not__zle__0__negative,axiom,
% 11.05/11.07 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_of__nat__nat,axiom,
% 11.05/11.07 ! [V_z,T_a] :
% 11.05/11.07 ( class_Rings_Oring__1(T_a)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 11.05/11.07 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_sgn__pos,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.07 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_self__quotient__aux1,axiom,
% 11.05/11.07 ! [V_q,V_r,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.07 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_self__quotient__aux2,axiom,
% 11.05/11.07 ! [V_q,V_r,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.07 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 11.05/11.07 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 11.05/11.07 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_unique__quotient__lemma__neg,axiom,
% 11.05/11.07 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__mono2__lemma,axiom,
% 11.05/11.07 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 11.05/11.07 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_unique__quotient__lemma,axiom,
% 11.05/11.07 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_q__neg__lemma,axiom,
% 11.05/11.07 ! [V_r_H,V_q_H,V_b_H] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_q__pos__lemma,axiom,
% 11.05/11.07 ! [V_r_H,V_q_H,V_b_H] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__mult__le__cancel1,axiom,
% 11.05/11.07 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__antisym,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.07 => V_m = V_n ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__trans,axiom,
% 11.05/11.07 ! [V_k,V_j,V_i] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_eq__imp__le,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( V_m = V_n
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__le__linear,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__refl,axiom,
% 11.05/11.07 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_less__fun__def,axiom,
% 11.05/11.07 ! [V_g_2,V_f_2,T_b,T_c] :
% 11.05/11.07 ( class_Orderings_Oord(T_c)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 11.05/11.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 11.05/11.07 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 11.05/11.07 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.07 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 11.05/11.07 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 | V_m_2 = V_n_2 ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_left__add__mult__distrib,axiom,
% 11.05/11.07 ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__mult__eq__cancel1,axiom,
% 11.05/11.07 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 11.05/11.07 <=> V_m_2 = V_n_2 ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__mult__less__cancel1,axiom,
% 11.05/11.07 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_transfer__morphism__nat__int,axiom,
% 11.05/11.07 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_compl__mono,axiom,
% 11.05/11.07 ! [V_y,V_x,T_a] :
% 11.05/11.07 ( class_Lattices_Oboolean__algebra(T_a)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_compl__le__compl__iff,axiom,
% 11.05/11.07 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.07 ( class_Lattices_Oboolean__algebra(T_b)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_ex__least__nat__less,axiom,
% 11.05/11.07 ! [V_n_2,V_Pa_2] :
% 11.05/11.07 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 11.05/11.07 => ( hBOOL(hAPP(V_Pa_2,V_n_2))
% 11.05/11.07 => ? [B_k] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 11.05/11.07 & ! [B_i] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 11.05/11.07 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 11.05/11.07 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_split__zmod,axiom,
% 11.05/11.07 ! [V_k_2,V_n_2,V_Pa_2] :
% 11.05/11.07 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 11.05/11.07 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 11.05/11.07 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 11.05/11.07 => ! [B_i,B_j] :
% 11.05/11.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 11.05/11.07 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,B_j)) ) )
% 11.05/11.07 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ! [B_i,B_j] :
% 11.05/11.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmult2__lemma__aux3,axiom,
% 11.05/11.07 ! [V_q,V_b,V_r,V_c] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmult2__lemma__aux4,axiom,
% 11.05/11.07 ! [V_q,V_b,V_r,V_c] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmult2__lemma__aux1,axiom,
% 11.05/11.07 ! [V_q,V_r,V_b,V_c] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mod__trivial,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__0,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__by__0,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__self,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__add__cong,axiom,
% 11.05/11.07 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 11.05/11.07 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__simps_I1_J,axiom,
% 11.05/11.07 ! [V_b,V_c,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__simps_I2_J,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__add__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__add__left__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__add__right__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__add__self1,axiom,
% 11.05/11.07 ! [V_a,V_b,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__add__self2,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__cong,axiom,
% 11.05/11.07 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 11.05/11.07 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__simps_I4_J,axiom,
% 11.05/11.07 ! [V_b,V_c,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__mult2,axiom,
% 11.05/11.07 ! [V_b,V_c,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__mult1,axiom,
% 11.05/11.07 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__left__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__right__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__minus__cong,axiom,
% 11.05/11.07 ! [V_a_H,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Oring__div(T_a)
% 11.05/11.07 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__minus__eq,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Oring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__zero,axiom,
% 11.05/11.07 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__self,axiom,
% 11.05/11.07 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__zmult1__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__simps_I3_J,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__zminus2,axiom,
% 11.05/11.07 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__zminus__zminus,axiom,
% 11.05/11.07 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zminus__zmod,axiom,
% 11.05/11.07 ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__self2__is__0,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__self1__is__0,axiom,
% 11.05/11.07 ! [V_a,V_b,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__self1,axiom,
% 11.05/11.07 ! [V_b,V_c,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__self2,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__by__1,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__le__nonneg__dividend,axiom,
% 11.05/11.07 ! [V_k,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 11.05/11.07 ! [V_y,V_x] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_neg__mod__bound,axiom,
% 11.05/11.07 ! [V_a,V_b] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_pos__mod__bound,axiom,
% 11.05/11.07 ! [V_a,V_b] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__eq__0__iff,axiom,
% 11.05/11.07 ! [V_d_2,V_m_2] :
% 11.05/11.07 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__zminus2__not__zero,axiom,
% 11.05/11.07 ! [V_l,V_k] :
% 11.05/11.07 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__zminus1__not__zero,axiom,
% 11.05/11.07 ! [V_l,V_k] :
% 11.05/11.07 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__neg__neg__trivial,axiom,
% 11.05/11.07 ! [V_b,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_neg__mod__conj,axiom,
% 11.05/11.07 ! [V_a,V_b] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_neg__mod__sign,axiom,
% 11.05/11.07 ! [V_a,V_b] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__pos__pos__trivial,axiom,
% 11.05/11.07 ! [V_b,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_pos__mod__conj,axiom,
% 11.05/11.07 ! [V_a,V_b] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_pos__mod__sign,axiom,
% 11.05/11.07 ! [V_a,V_b] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_times_Oidem,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mult__idem,axiom,
% 11.05/11.07 ! [V_x,T_a] :
% 11.05/11.07 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mult__left__idem,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_double__compl,axiom,
% 11.05/11.07 ! [V_x,T_a] :
% 11.05/11.07 ( class_Lattices_Oboolean__algebra(T_a)
% 11.05/11.07 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_uminus__apply,axiom,
% 11.05/11.07 ! [V_x_2,V_A_2,T_c,T_b] :
% 11.05/11.07 ( class_Groups_Ouminus(T_b)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_compl__eq__compl__iff,axiom,
% 11.05/11.07 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.07 ( class_Lattices_Oboolean__algebra(T_b)
% 11.05/11.07 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 11.05/11.07 <=> V_x_2 = V_y_2 ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__pos__neg__trivial,axiom,
% 11.05/11.07 ! [V_b,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_divmod__int__rel__mod__eq,axiom,
% 11.05/11.07 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 11.05/11.07 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y)
% 11.05/11.07 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 11.05/11.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 11.05/11.07 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmult2__lemma__aux2,axiom,
% 11.05/11.07 ! [V_q,V_r,V_b,V_c] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_z3mod__def,axiom,
% 11.05/11.07 ! [V_k,V_l] :
% 11.05/11.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 11.05/11.07 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 11.05/11.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 11.05/11.07 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_split__pos__lemma,axiom,
% 11.05/11.07 ! [V_n_2,V_Pa_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 11.05/11.07 <=> ! [B_i,B_j] :
% 11.05/11.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 11.05/11.07 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 11.05/11.07 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_split__neg__lemma,axiom,
% 11.05/11.07 ! [V_n_2,V_Pa_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 11.05/11.07 <=> ! [B_i,B_j] :
% 11.05/11.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 11.05/11.07 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__zmult2__eq,axiom,
% 11.05/11.07 ! [V_b,V_a,V_c] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 11.05/11.07 ! [V_y,V_x] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_divmod__int__rel__div__eq,axiom,
% 11.05/11.07 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 11.05/11.07 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
% 11.05/11.07 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 11.05/11.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 11.05/11.07 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_split__zdiv,axiom,
% 11.05/11.07 ! [V_k_2,V_n_2,V_Pa_2] :
% 11.05/11.07 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 11.05/11.07 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.05/11.07 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 11.05/11.07 => ! [B_i] :
% 11.05/11.07 ( ? [B_j] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 11.05/11.07 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,B_i)) ) )
% 11.05/11.07 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ! [B_i] :
% 11.05/11.07 ( ? [B_j] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_split__div_H,axiom,
% 11.05/11.07 ! [V_n_2,V_m_2,V_Pa_2] :
% 11.05/11.07 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 11.05/11.07 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 11.05/11.07 | ? [B_q] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
% 11.05/11.07 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__add1__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__int,axiom,
% 11.05/11.07 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 11.05/11.07 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult1__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult2__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__le__dividend,axiom,
% 11.05/11.07 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__le__mono,axiom,
% 11.05/11.07 ! [V_k,V_n,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__zero,axiom,
% 11.05/11.07 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 11.05/11.07 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult2__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__less,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__less__eq__dividend,axiom,
% 11.05/11.07 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__distrib2,axiom,
% 11.05/11.07 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__distrib,axiom,
% 11.05/11.07 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__zminus__zminus,axiom,
% 11.05/11.07 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__zminus2,axiom,
% 11.05/11.07 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__0,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__by__0,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__by__1,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__div__distrib,axiom,
% 11.05/11.07 ! [V_y,V_x] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.07 => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 11.05/11.07 ! [V_y,V_x] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__1,axiom,
% 11.05/11.07 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__less,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__mult__div__cancel__disj,axiom,
% 11.05/11.07 ! [V_n,V_m,V_k] :
% 11.05/11.07 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.05/11.07 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__1,axiom,
% 11.05/11.07 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__Suc,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.05/11.07 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 11.05/11.07 ! [V_y,V_x] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__less__divisor,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 11.05/11.07 ! [V_a_2,V_b_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 11.05/11.07 ! [V_a_2,V_b_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__neg__pos__less0,axiom,
% 11.05/11.07 ! [V_b,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__self,axiom,
% 11.05/11.07 ! [V_a] :
% 11.05/11.07 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__eq__0__iff,axiom,
% 11.05/11.07 ! [V_d_2,V_m_2] :
% 11.05/11.07 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_DIVISION__BY__ZERO,axiom,
% 11.05/11.07 ! [V_a] :
% 11.05/11.07 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__zdiv__trivial,axiom,
% 11.05/11.07 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__self3,axiom,
% 11.05/11.07 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__zadd1__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__int,axiom,
% 11.05/11.07 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 11.05/11.07 ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult__mult1,axiom,
% 11.05/11.07 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult__mult2,axiom,
% 11.05/11.07 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult__self1__is__id,axiom,
% 11.05/11.07 ! [V_a,V_b,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult__self2__is__id,axiom,
% 11.05/11.07 ! [V_a,V_b,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult__mult1__if,axiom,
% 11.05/11.07 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) )
% 11.05/11.07 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__self,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__div__trivial,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__le__mono2,axiom,
% 11.05/11.07 ! [V_k,V_n,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult__self__is__m,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult__self1__is__m,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__mult__div__cancel1,axiom,
% 11.05/11.07 ! [V_n,V_m,V_k] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__less__dividend,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__eq__0__iff,axiom,
% 11.05/11.07 ! [V_k_2,V_i_2] :
% 11.05/11.07 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 11.05/11.07 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 11.05/11.07 ! [V_a_2,V_b_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 11.05/11.07 ! [V_i_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 11.05/11.07 ! [V_b_2,V_a_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 11.05/11.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__mono2,axiom,
% 11.05/11.07 ! [V_b,V_b_H,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__nonneg__neg__le0,axiom,
% 11.05/11.07 ! [V_b,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__pos__pos__trivial,axiom,
% 11.05/11.07 ! [V_b,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 11.05/11.07 ! [V_a_2,V_b_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__nonpos__pos__le0,axiom,
% 11.05/11.07 ! [V_b,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__mono2__neg,axiom,
% 11.05/11.07 ! [V_b,V_b_H,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__neg__neg__trivial,axiom,
% 11.05/11.07 ! [V_b,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__mono1,axiom,
% 11.05/11.07 ! [V_b,V_a_H,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__mono1__neg,axiom,
% 11.05/11.07 ! [V_b,V_a_H,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__le__divisor,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_int__div__less__self,axiom,
% 11.05/11.07 ! [V_k,V_x] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__zmult2__eq,axiom,
% 11.05/11.07 ! [V_b,V_a,V_c] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__mult__self4,axiom,
% 11.05/11.07 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zmod__zdiv__equality,axiom,
% 11.05/11.07 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__zmult1__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__zmod__equality,axiom,
% 11.05/11.07 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__zmod__equality2,axiom,
% 11.05/11.07 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult__self2,axiom,
% 11.05/11.07 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mult__self1,axiom,
% 11.05/11.07 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__add__self2,axiom,
% 11.05/11.07 ! [V_a,V_b,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__add__self1,axiom,
% 11.05/11.07 ! [V_a,V_b,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__div__equality2,axiom,
% 11.05/11.07 ! [V_a,V_b,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__div__equality,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mod__equality2,axiom,
% 11.05/11.07 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mod__equality,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_split__div,axiom,
% 11.05/11.07 ! [V_k_2,V_n_2,V_Pa_2] :
% 11.05/11.07 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 11.05/11.07 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 11.05/11.07 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 => ! [B_i,B_j] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 11.05/11.07 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_split__mod,axiom,
% 11.05/11.07 ! [V_k_2,V_n_2,V_Pa_2] :
% 11.05/11.07 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 11.05/11.07 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 11.05/11.07 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 => ! [B_i,B_j] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 11.05/11.07 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__lemma,axiom,
% 11.05/11.07 ! [V_q,V_b,V_r,V_c] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Suc__times__mod__eq,axiom,
% 11.05/11.07 ! [V_m,V_k] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__mod__distrib,axiom,
% 11.05/11.07 ! [V_y,V_x] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.07 => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 11.05/11.07 ! [V_y,V_x] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_split__div__lemma,axiom,
% 11.05/11.07 ! [V_m_2,V_q_2,V_n_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 11.05/11.07 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))
% 11.05/11.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2)))) )
% 11.05/11.07 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_z3div__def,axiom,
% 11.05/11.07 ! [V_k,V_l] :
% 11.05/11.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 11.05/11.07 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 11.05/11.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 11.05/11.07 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__zminus1__eq__if,axiom,
% 11.05/11.07 ! [V_a,V_b] :
% 11.05/11.07 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) )
% 11.05/11.07 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiv__zminus2__eq__if,axiom,
% 11.05/11.07 ! [V_a,V_b] :
% 11.05/11.07 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) )
% 11.05/11.07 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__div__geq,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.07 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__div__decomp,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Osemiring__div(T_a)
% 11.05/11.07 => V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 11.05/11.07 ! [V_y,V_x] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_incr__mult__lemma,axiom,
% 11.05/11.07 ! [V_k_2,V_Pa_2,V_d_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 11.05/11.07 => ( ! [B_x] :
% 11.05/11.07 ( hBOOL(hAPP(V_Pa_2,B_x))
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 11.05/11.07 => ! [B_x] :
% 11.05/11.07 ( hBOOL(hAPP(V_Pa_2,B_x))
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_field__le__mult__one__interval,axiom,
% 11.05/11.07 ! [V_y,V_x,T_a] :
% 11.05/11.07 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 11.05/11.07 => ( ! [B_z] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y)) ) )
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__commute,axiom,
% 11.05/11.07 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__eq__diff__eq,axiom,
% 11.05/11.07 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.05/11.07 ( class_Groups_Oab__group__add(T_b)
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 11.05/11.07 => ( V_a_2 = V_b_2
% 11.05/11.07 <=> V_c_2 = V_d_2 ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_of__int__diff,axiom,
% 11.05/11.07 ! [V_z,V_w,T_a] :
% 11.05/11.07 ( class_Rings_Oring__1(T_a)
% 11.05/11.07 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_minus__apply,axiom,
% 11.05/11.07 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 11.05/11.07 ( class_Groups_Ominus(T_b)
% 11.05/11.07 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_of__nat__diff,axiom,
% 11.05/11.07 ! [V_m,V_n,T_a] :
% 11.05/11.07 ( class_Rings_Oring__1(T_a)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.07 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiff__int,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__eq__diff__less__eq,axiom,
% 11.05/11.07 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.05/11.07 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_right__minus__eq,axiom,
% 11.05/11.07 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.07 ( class_Groups_Ogroup__add(T_b)
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.07 <=> V_a_2 = V_b_2 ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_eq__iff__diff__eq__0,axiom,
% 11.05/11.07 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.07 ( class_Groups_Oab__group__add(T_b)
% 11.05/11.07 => ( V_a_2 = V_b_2
% 11.05/11.07 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__self,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__0__right,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__eq__diff__less,axiom,
% 11.05/11.07 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.05/11.07 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_add__diff__cancel,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__add__cancel,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_minus__diff__eq,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Groups_Oab__group__add(T_a)
% 11.05/11.07 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__diff__cong,axiom,
% 11.05/11.07 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Oring__div(T_a)
% 11.05/11.07 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 11.05/11.07 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__diff__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Oring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__diff__left__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Oring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__diff__right__eq,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.07 ( class_Divides_Oring__div(T_a)
% 11.05/11.07 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diffs0__imp__equal,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 => V_m = V_n ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__self__eq__0,axiom,
% 11.05/11.07 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_minus__nat_Odiff__0,axiom,
% 11.05/11.07 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__0__eq__0,axiom,
% 11.05/11.07 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__Suc__Suc,axiom,
% 11.05/11.07 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Suc__diff__diff,axiom,
% 11.05/11.07 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__less__mono2,axiom,
% 11.05/11.07 ! [V_l,V_n,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_less__imp__diff__less,axiom,
% 11.05/11.07 ! [V_n,V_k,V_j] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__geq,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mod__if,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 11.05/11.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__add__inverse2,axiom,
% 11.05/11.07 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__add__inverse,axiom,
% 11.05/11.07 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__diff__left,axiom,
% 11.05/11.07 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__cancel,axiom,
% 11.05/11.07 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__cancel2,axiom,
% 11.05/11.07 ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__le__self,axiom,
% 11.05/11.07 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__le__mono2,axiom,
% 11.05/11.07 ! [V_l,V_n,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__le__mono,axiom,
% 11.05/11.07 ! [V_l,V_n,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__diff__cancel,axiom,
% 11.05/11.07 ! [V_n,V_i] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_eq__diff__iff,axiom,
% 11.05/11.07 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)
% 11.05/11.07 <=> V_m_2 = V_n_2 ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Nat_Odiff__diff__eq,axiom,
% 11.05/11.07 ! [V_n,V_m,V_k] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__diff__iff,axiom,
% 11.05/11.07 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__mod__geq,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.07 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiff__zmult__distrib,axiom,
% 11.05/11.07 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiff__zmult__distrib2,axiom,
% 11.05/11.07 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__mult__distrib2,axiom,
% 11.05/11.07 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__mult__distrib,axiom,
% 11.05/11.07 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiff__zmod__left,axiom,
% 11.05/11.07 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiff__zmod__right,axiom,
% 11.05/11.07 ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_nat__diff__distrib,axiom,
% 11.05/11.07 ! [V_z,V_z_H] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 11.05/11.07 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zdiff__int__split,axiom,
% 11.05/11.07 ! [V_y_2,V_x_2,V_Pa_2] :
% 11.05/11.07 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
% 11.05/11.07 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 11.05/11.07 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 11.05/11.07 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__iff__diff__le__0,axiom,
% 11.05/11.07 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.07 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_less__iff__diff__less__0,axiom,
% 11.05/11.07 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.07 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_eq__add__iff2,axiom,
% 11.05/11.07 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 11.05/11.07 ( class_Rings_Oring(T_b)
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 11.05/11.07 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_eq__add__iff1,axiom,
% 11.05/11.07 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 11.05/11.07 ( class_Rings_Oring(T_b)
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 11.05/11.07 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__0,axiom,
% 11.05/11.07 ! [V_a,T_a] :
% 11.05/11.07 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__def,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_ab__diff__minus,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Groups_Oab__group__add(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__minus__eq__add,axiom,
% 11.05/11.07 ! [V_b,V_a,T_a] :
% 11.05/11.07 ( class_Groups_Ogroup__add(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 11.05/11.07 ! [V_y,V_x,T_a] :
% 11.05/11.07 ( class_Rings_Ocomm__ring__1(T_a)
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_less__bin__lemma,axiom,
% 11.05/11.07 ! [V_l_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__less,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_zero__less__diff,axiom,
% 11.05/11.07 ! [V_m_2,V_n_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__less__Suc,axiom,
% 11.05/11.07 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__add__0,axiom,
% 11.05/11.07 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__is__0__eq_H,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__is__0__eq,axiom,
% 11.05/11.07 ! [V_n_2,V_m_2] :
% 11.05/11.07 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_less__diff__conv,axiom,
% 11.05/11.07 ! [V_k_2,V_j_2,V_i_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_add__diff__inverse,axiom,
% 11.05/11.07 ! [V_n,V_m] :
% 11.05/11.07 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Suc__diff__le,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_less__diff__iff,axiom,
% 11.05/11.07 ! [V_n_2,V_m_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__less__mono,axiom,
% 11.05/11.07 ! [V_c,V_b,V_a] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__add__assoc2,axiom,
% 11.05/11.07 ! [V_i,V_j,V_k] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_add__diff__assoc2,axiom,
% 11.05/11.07 ! [V_i,V_j,V_k] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__add__assoc,axiom,
% 11.05/11.07 ! [V_i,V_j,V_k] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__imp__diff__is__add,axiom,
% 11.05/11.07 ! [V_k_2,V_j_2,V_i_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 11.05/11.07 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 11.05/11.07 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__add__diff__inverse2,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__diff__conv2,axiom,
% 11.05/11.07 ! [V_i_2,V_j_2,V_k_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_add__diff__assoc,axiom,
% 11.05/11.07 ! [V_i,V_j,V_k] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__add__diff__inverse,axiom,
% 11.05/11.07 ! [V_m,V_n] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__add__diff,axiom,
% 11.05/11.07 ! [V_m,V_n,V_k] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 11.05/11.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__diff__conv,axiom,
% 11.05/11.07 ! [V_i_2,V_k_2,V_j_2] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2))
% 11.05/11.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__diff__right,axiom,
% 11.05/11.07 ! [V_i,V_j,V_k] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 11.05/11.07 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__int__def__symmetric,axiom,
% 11.05/11.07 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__int__def,axiom,
% 11.05/11.07 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 11.05/11.07 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_diff__Suc__1,axiom,
% 11.05/11.07 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Divides_Omod__div__equality_H,axiom,
% 11.05/11.07 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_mult__div__cancel,axiom,
% 11.05/11.07 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_div__mod__equality_H,axiom,
% 11.05/11.07 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_tsub__eq,axiom,
% 11.05/11.07 ! [V_x,V_y] :
% 11.05/11.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 11.05/11.07 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 11.05/11.07 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)) ).
% 11.05/11.07
% 11.05/11.07 fof(fact_le__add__iff2,axiom,
% 11.05/11.07 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 11.05/11.07 ( class_Rings_Oordered__ring(T_b)
% 11.05/11.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_le__add__iff1,axiom,
% 11.05/11.08 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 11.05/11.08 ( class_Rings_Oordered__ring(T_b)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__add__iff2,axiom,
% 11.05/11.08 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 11.05/11.08 ( class_Rings_Oordered__ring(T_b)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__add__iff1,axiom,
% 11.05/11.08 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 11.05/11.08 ( class_Rings_Oordered__ring(T_b)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_diff__Suc__less,axiom,
% 11.05/11.08 ! [V_i,V_n] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__pred,axiom,
% 11.05/11.08 ! [V_n] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.08 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__diff__split,axiom,
% 11.05/11.08 ! [V_b_2,V_a_2,V_Pa_2] :
% 11.05/11.08 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 11.05/11.08 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 11.05/11.08 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 11.05/11.08 & ! [B_d] :
% 11.05/11.08 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 11.05/11.08 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__diff__split__asm,axiom,
% 11.05/11.08 ! [V_b_2,V_a_2,V_Pa_2] :
% 11.05/11.08 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 11.05/11.08 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 11.05/11.08 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 11.05/11.08 | ? [B_d] :
% 11.05/11.08 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 11.05/11.08 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zle__diff1__eq,axiom,
% 11.05/11.08 ! [V_z_2,V_w_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_diff__Suc__diff__eq2,axiom,
% 11.05/11.08 ! [V_m,V_j,V_k] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_diff__Suc__diff__eq1,axiom,
% 11.05/11.08 ! [V_m,V_j,V_k] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__eq__add__iff2,axiom,
% 11.05/11.08 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 11.05/11.08 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 11.05/11.08 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__diff__add__eq2,axiom,
% 11.05/11.08 ! [V_n,V_m,V_u,V_j,V_i] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__le__add__iff2,axiom,
% 11.05/11.08 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__eq__add__iff1,axiom,
% 11.05/11.08 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 11.05/11.08 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 11.05/11.08 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__diff__add__eq1,axiom,
% 11.05/11.08 ! [V_n,V_m,V_u,V_i,V_j] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__le__add__iff1,axiom,
% 11.05/11.08 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zmod__zminus2__eq__if,axiom,
% 11.05/11.08 ! [V_b,V_a] :
% 11.05/11.08 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 11.05/11.08 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zmod__zminus1__eq__if,axiom,
% 11.05/11.08 ! [V_b,V_a] :
% 11.05/11.08 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 11.05/11.08 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zmult__div__cancel,axiom,
% 11.05/11.08 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zmod__zdiv__equality_H,axiom,
% 11.05/11.08 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_tsub__def,axiom,
% 11.05/11.08 ! [V_x,V_y] :
% 11.05/11.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 11.05/11.08 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 11.05/11.08 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__pred_H,axiom,
% 11.05/11.08 ! [V_n] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.08 => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__diff__1,axiom,
% 11.05/11.08 ! [V_n] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.08 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__less__add__iff2,axiom,
% 11.05/11.08 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__less__add__iff1,axiom,
% 11.05/11.08 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__eq__if,axiom,
% 11.05/11.08 ! [V_n,V_m] :
% 11.05/11.08 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 11.05/11.08 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_div__if,axiom,
% 11.05/11.08 ! [V_m,V_n] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.08 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.08 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.08 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_div__geq,axiom,
% 11.05/11.08 ! [V_m,V_n] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.08 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.08 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mult__eq__if,axiom,
% 11.05/11.08 ! [V_n,V_m] :
% 11.05/11.08 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.05/11.08 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_int__power__div__base,axiom,
% 11.05/11.08 ! [V_k,V_m] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 11.05/11.08 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_decr__mult__lemma,axiom,
% 11.05/11.08 ! [V_k_2,V_Pa_2,V_d_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 11.05/11.08 => ( ! [B_x] :
% 11.05/11.08 ( hBOOL(hAPP(V_Pa_2,B_x))
% 11.05/11.08 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 11.05/11.08 => ! [B_x] :
% 11.05/11.08 ( hBOOL(hAPP(V_Pa_2,B_x))
% 11.05/11.08 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_decr__lemma,axiom,
% 11.05/11.08 ! [V_z,V_x,V_d] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_incr__lemma,axiom,
% 11.05/11.08 ! [V_x,V_z,V_d] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__mod__eq__lemma,axiom,
% 11.05/11.08 ! [V_y,V_n,V_x] :
% 11.05/11.08 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 11.05/11.08 => ? [B_q] : V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mod__induct__0,axiom,
% 11.05/11.08 ! [V_i_2,V_Pa_2,V_p_2] :
% 11.05/11.08 ( ! [B_i] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 11.05/11.08 => ( hBOOL(hAPP(V_Pa_2,B_i))
% 11.05/11.08 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 11.05/11.08 => ( hBOOL(hAPP(V_Pa_2,V_i_2))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 11.05/11.08 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_expand__Suc,axiom,
% 11.05/11.08 ! [V_v] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)))
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__gcd_Osimps,axiom,
% 11.05/11.08 ! [V_x,V_y] :
% 11.05/11.08 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 11.05/11.08 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 => c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_of__int__power,axiom,
% 11.05/11.08 ! [V_n,V_z,T_a] :
% 11.05/11.08 ( class_Rings_Oring__1(T_a)
% 11.05/11.08 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_of__int__number__of__eq,axiom,
% 11.05/11.08 ! [V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__reorient,axiom,
% 11.05/11.08 ! [V_x_2,V_w_2,T_b] :
% 11.05/11.08 ( class_Int_Onumber(T_b)
% 11.05/11.08 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 11.05/11.08 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_eq__number__of,axiom,
% 11.05/11.08 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Int_Oring__char__0(T_b) )
% 11.05/11.08 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 11.05/11.08 <=> V_x_2 = V_y_2 ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__idempotent,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zero__le__zpower__abs,axiom,
% 11.05/11.08 ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__ge__self,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__le__D1,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__zero,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__eq__0,axiom,
% 11.05/11.08 ! [V_a_2,T_b] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 11.05/11.08 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.08 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__add__abs,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__mult,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__mult__self,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__minus__commute,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__one,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__minus__cancel,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 11.05/11.08 ! [V_q,V_y,V_x,T_a] :
% 11.05/11.08 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__of__nat,axiom,
% 11.05/11.08 ! [V_n,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__int__eq,axiom,
% 11.05/11.08 ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 11.05/11.08 ! [V_q,V_p,V_x,T_a] :
% 11.05/11.08 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zpower__zpower,axiom,
% 11.05/11.08 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 11.05/11.08 ! [V_x,T_a] :
% 11.05/11.08 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zpower__zmod,axiom,
% 11.05/11.08 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_of__nat__number__of__lemma,axiom,
% 11.05/11.08 ! [V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__eq,axiom,
% 11.05/11.08 ! [V_k,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__number__of,axiom,
% 11.05/11.08 ! [V_x,T_a] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_a) )
% 11.05/11.08 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zero__less__zpower__abs__iff,axiom,
% 11.05/11.08 ! [V_n_2,V_x_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2)))
% 11.05/11.08 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.08 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__of__nonneg,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__le__zero__iff,axiom,
% 11.05/11.08 ! [V_a_2,T_b] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.08 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__ge__zero,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__not__less__zero,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zero__less__abs__iff,axiom,
% 11.05/11.08 ! [V_a_2,T_b] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
% 11.05/11.08 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__of__pos,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__triangle__ineq,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__mult__less,axiom,
% 11.05/11.08 ! [V_d,V_b,V_c,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__triangle__ineq3,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__triangle__ineq2,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__triangle__ineq2__sym,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__le__D2,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__leI,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__le__iff,axiom,
% 11.05/11.08 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 11.05/11.08 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 11.05/11.08 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__ge__minus__self,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__less__iff,axiom,
% 11.05/11.08 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 11.05/11.08 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 11.05/11.08 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_le__number__of__eq__not__less,axiom,
% 11.05/11.08 ! [V_w_2,V_v_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber(T_b)
% 11.05/11.08 & class_Orderings_Olinorder(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.08 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_right__distrib__number__of,axiom,
% 11.05/11.08 ! [V_c,V_b,V_v,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber(T_b)
% 11.05/11.08 & class_Rings_Osemiring(T_b) )
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_left__distrib__number__of,axiom,
% 11.05/11.08 ! [V_v,V_b,V_a,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber(T_b)
% 11.05/11.08 & class_Rings_Osemiring(T_b) )
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 11.05/11.08 ! [V_q,V_x,T_a] :
% 11.05/11.08 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 11.05/11.08 ! [V_q,V_x,T_a] :
% 11.05/11.08 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 11.05/11.08 ! [V_q,V_x,T_a] :
% 11.05/11.08 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_right__diff__distrib__number__of,axiom,
% 11.05/11.08 ! [V_c,V_b,V_v,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber(T_b)
% 11.05/11.08 & class_Rings_Oring(T_b) )
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_left__diff__distrib__number__of,axiom,
% 11.05/11.08 ! [V_v,V_b,V_a,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber(T_b)
% 11.05/11.08 & class_Rings_Oring(T_b) )
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_le__number__of,axiom,
% 11.05/11.08 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 11.05/11.08 ! [V_x,T_a] :
% 11.05/11.08 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 11.05/11.08 ! [V_q,V_p,V_x,T_a] :
% 11.05/11.08 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__number__of,axiom,
% 11.05/11.08 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__number__of__left,axiom,
% 11.05/11.08 ! [V_z,V_w,V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__number__of__eq,axiom,
% 11.05/11.08 ! [V_w,V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__add,axiom,
% 11.05/11.08 ! [V_w,V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 11.05/11.08 ! [V_n,V_x] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__mult,axiom,
% 11.05/11.08 ! [V_w,V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_arith__simps_I32_J,axiom,
% 11.05/11.08 ! [V_w,V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mult__number__of__left,axiom,
% 11.05/11.08 ! [V_z,V_w,V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__zmult__eq__1,axiom,
% 11.05/11.08 ! [V_n,V_m] :
% 11.05/11.08 ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__diff,axiom,
% 11.05/11.08 ! [V_w,V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zpower__zadd__distrib,axiom,
% 11.05/11.08 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_arith__simps_I30_J,axiom,
% 11.05/11.08 ! [V_w,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__minus,axiom,
% 11.05/11.08 ! [V_w,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__sgn,axiom,
% 11.05/11.08 ! [V_k,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mult__sgn__abs,axiom,
% 11.05/11.08 ! [V_x,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__mult__pos,axiom,
% 11.05/11.08 ! [V_y,V_x,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__eq__mult,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Oordered__ring__abs(T_a)
% 11.05/11.08 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 11.05/11.08 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.08 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__diff__triangle__ineq,axiom,
% 11.05/11.08 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__triangle__ineq4,axiom,
% 11.05/11.08 ! [V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__of__nonpos,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__minus__le__zero,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__if,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oabs__if(T_a)
% 11.05/11.08 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__of__neg,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zabs__less__one__iff,axiom,
% 11.05/11.08 ! [V_z_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 11.05/11.08 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__number__of__diff1,axiom,
% 11.05/11.08 ! [V_c,V_w,V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zabs__def,axiom,
% 11.05/11.08 ! [V_i] :
% 11.05/11.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_minus__number__of__mult,axiom,
% 11.05/11.08 ! [V_z,V_w,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__abs__mult__distrib,axiom,
% 11.05/11.08 ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_diff__number__of__eq,axiom,
% 11.05/11.08 ! [V_w,V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__number__of__diff2,axiom,
% 11.05/11.08 ! [V_w,V_c,V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__strict__mono,axiom,
% 11.05/11.08 ! [V_n,V_b,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_one__less__power,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__le__imp__le__exp,axiom,
% 11.05/11.08 ! [V_n,V_m,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__increasing__iff,axiom,
% 11.05/11.08 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_b)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__decreasing,axiom,
% 11.05/11.08 ! [V_a,V_N,V_n,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__strict__decreasing,axiom,
% 11.05/11.08 ! [V_a,V_N,V_n,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__Suc__less__one,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__is__id,axiom,
% 11.05/11.08 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__eq__number__of__int__code,axiom,
% 11.05/11.08 ! [V_l_2,V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__number__of__int__code,axiom,
% 11.05/11.08 ! [V_l_2,V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_plus__numeral__code_I9_J,axiom,
% 11.05/11.08 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_times__numeral__code_I5_J,axiom,
% 11.05/11.08 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_minus__numeral__code_I5_J,axiom,
% 11.05/11.08 ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 11.05/11.08 ! [V_m_2,V_x_2] :
% 11.05/11.08 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 11.05/11.08 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__Suc__0,axiom,
% 11.05/11.08 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__power__less__imp__less,axiom,
% 11.05/11.08 ! [V_n,V_m,V_i] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__zero__less__power__iff,axiom,
% 11.05/11.08 ! [V_n_2,V_x_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
% 11.05/11.08 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 11.05/11.08 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_int__number__of__def,axiom,
% 11.05/11.08 ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__one__le__power,axiom,
% 11.05/11.08 ! [V_n,V_i] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__number__of__def,axiom,
% 11.05/11.08 ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__number__of,axiom,
% 11.05/11.08 ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 11.05/11.08 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zpower__int,axiom,
% 11.05/11.08 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_int__power,axiom,
% 11.05/11.08 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_minus__numeral__code_I6_J,axiom,
% 11.05/11.08 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__eq__if,axiom,
% 11.05/11.08 ! [V_p,V_m] :
% 11.05/11.08 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 11.05/11.08 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_int__eq__iff__number__of,axiom,
% 11.05/11.08 ! [V_v_2,V_m_2] :
% 11.05/11.08 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)
% 11.05/11.08 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 11.05/11.08 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__power__eq,axiom,
% 11.05/11.08 ! [V_n,V_z] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 11.05/11.08 => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 11.05/11.08 ! [V_n,V_x] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_field__power__not__zero,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 11.05/11.08 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__mult__distrib,axiom,
% 11.05/11.08 ! [V_n,V_b,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Ocomm__monoid__mult(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__commutes,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__one,axiom,
% 11.05/11.08 ! [V_n,T_a] :
% 11.05/11.08 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_of__nat__power,axiom,
% 11.05/11.08 ! [V_n,V_m,T_a] :
% 11.05/11.08 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.08 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__mult,axiom,
% 11.05/11.08 ! [V_n,V_m,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_one__div__nat__number__of,axiom,
% 11.05/11.08 ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__abs,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__one__right,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zero__le__power,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__mono,axiom,
% 11.05/11.08 ! [V_n,V_b,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zero__less__power,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__eq__0__iff,axiom,
% 11.05/11.08 ! [V_n_2,V_a_2,T_b] :
% 11.05/11.08 ( ( class_Power_Opower(T_b)
% 11.05/11.08 & class_Rings_Omult__zero(T_b)
% 11.05/11.08 & class_Rings_Ono__zero__divisors(T_b)
% 11.05/11.08 & class_Rings_Ozero__neq__one(T_b) )
% 11.05/11.08 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.08 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.08 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_one__le__power,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__0__Suc,axiom,
% 11.05/11.08 ! [V_n,T_a] :
% 11.05/11.08 ( ( class_Power_Opower(T_a)
% 11.05/11.08 & class_Rings_Osemiring__0(T_a) )
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__inject__exp,axiom,
% 11.05/11.08 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_b)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 11.05/11.08 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
% 11.05/11.08 <=> V_m_2 = V_n_2 ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__Suc2,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__Suc,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Power_Opower(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__0,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Power_Opower(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__add,axiom,
% 11.05/11.08 ! [V_n,V_m,V_a,T_a] :
% 11.05/11.08 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__power__minus,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__less__imp__less__base,axiom,
% 11.05/11.08 ! [V_b,V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__inject__base,axiom,
% 11.05/11.08 ! [V_b,V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.08 => V_a = V_b ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__le__imp__le__base,axiom,
% 11.05/11.08 ! [V_b,V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__less__power__Suc,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__gt1__lemma,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__0__left,axiom,
% 11.05/11.08 ! [V_n,T_a] :
% 11.05/11.08 ( ( class_Power_Opower(T_a)
% 11.05/11.08 & class_Rings_Osemiring__0(T_a) )
% 11.05/11.08 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 11.05/11.08 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__gt1,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__strict__increasing__iff,axiom,
% 11.05/11.08 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_b)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__less__imp__less__exp,axiom,
% 11.05/11.08 ! [V_n,V_m,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__strict__increasing,axiom,
% 11.05/11.08 ! [V_a,V_N,V_n,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zero__le__power__abs,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__increasing,axiom,
% 11.05/11.08 ! [V_a,V_N,V_n,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__minus,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Oring__1(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__Suc__less,axiom,
% 11.05/11.08 ! [V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__eq__imp__eq__base,axiom,
% 11.05/11.08 ! [V_b,V_n,V_a,T_a] :
% 11.05/11.08 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.08 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.08 => V_a = V_b ) ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 11.05/11.08 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 11.05/11.08 ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_one__mod__nat__number__of,axiom,
% 11.05/11.08 ! [V_v_H] :
% 11.05/11.08 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__power__power,axiom,
% 11.05/11.08 ! [T_b] :
% 11.05/11.08 ( class_Power_Opower(T_b)
% 11.05/11.08 => c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_div__nat__number__of,axiom,
% 11.05/11.08 ! [V_v_H,V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mod__nat__number__of,axiom,
% 11.05/11.08 ! [V_v_H,V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 11.05/11.08 ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_not__neg__0,axiom,
% 11.05/11.08 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_not__neg__int,axiom,
% 11.05/11.08 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_not__neg__1,axiom,
% 11.05/11.08 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_not__neg__eq__ge__0,axiom,
% 11.05/11.08 ! [V_x_2] :
% 11.05/11.08 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_neg__def,axiom,
% 11.05/11.08 ! [V_Z_2] :
% 11.05/11.08 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_neg__nat,axiom,
% 11.05/11.08 ! [V_z] :
% 11.05/11.08 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 11.05/11.08 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_not__neg__nat,axiom,
% 11.05/11.08 ! [V_z] :
% 11.05/11.08 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 11.05/11.08 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power_Opower_Opower__0,axiom,
% 11.05/11.08 ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power_Opower_Opower__Suc,axiom,
% 11.05/11.08 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_neg__imp__number__of__eq__0,axiom,
% 11.05/11.08 ! [V_v] :
% 11.05/11.08 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_neg__zminus__int,axiom,
% 11.05/11.08 ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_eq__nat__number__of,axiom,
% 11.05/11.08 ! [V_v_H_2,V_v_2] :
% 11.05/11.08 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)
% 11.05/11.08 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 11.05/11.08 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 11.05/11.08 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__number__of__add__left,axiom,
% 11.05/11.08 ! [V_k,V_v_H,V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_int__nat__number__of,axiom,
% 11.05/11.08 ! [V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_of__nat__number__of__eq,axiom,
% 11.05/11.08 ! [V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__nat__number__of__number__of,axiom,
% 11.05/11.08 ! [V_w,V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power__nat__number__of,axiom,
% 11.05/11.08 ! [V_n,V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__nat__number__of__add,axiom,
% 11.05/11.08 ! [V_n,V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__nat__number__of,axiom,
% 11.05/11.08 ! [V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.08 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zmod__minus1,axiom,
% 11.05/11.08 ! [V_b] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_div__pos__neg__trivial,axiom,
% 11.05/11.08 ! [V_b,V_a] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.08 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_int__val__lemma,axiom,
% 11.05/11.08 ! [V_k_2,V_f_2,V_n_2] :
% 11.05/11.08 ( ! [B_i] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 11.05/11.08 => ? [B_i] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 11.05/11.08 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat0__intermed__int__val,axiom,
% 11.05/11.08 ! [V_k_2,V_f_2,V_n_2] :
% 11.05/11.08 ( ! [B_i] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 11.05/11.08 => ? [B_i] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 11.05/11.08 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_eq__number__of__eq,axiom,
% 11.05/11.08 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 11.05/11.08 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_diff__bin__simps_I2_J,axiom,
% 11.05/11.08 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nonzero__number__of__Min,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I24_J,axiom,
% 11.05/11.08 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I7_J,axiom,
% 11.05/11.08 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_iszero__def,axiom,
% 11.05/11.08 ! [V_z_2,T_b] :
% 11.05/11.08 ( class_Rings_Osemiring__1(T_b)
% 11.05/11.08 => ( c_Int_Oiszero(T_b,V_z_2)
% 11.05/11.08 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_iszero__0,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.08 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_not__iszero__1,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.08 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_bin__less__0__simps_I2_J,axiom,
% 11.05/11.08 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Int_OMin__def,axiom,
% 11.05/11.08 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mult__Min,axiom,
% 11.05/11.08 ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_neg__number__of__Min,axiom,
% 11.05/11.08 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mult__minus1,axiom,
% 11.05/11.08 ! [V_z,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mult__minus1__right,axiom,
% 11.05/11.08 ! [V_z,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__Min,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_arith__simps_I31_J,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__minus__one,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_a) )
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zmod__minus1__right,axiom,
% 11.05/11.08 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 11.05/11.08 ! [V_n,V_m] :
% 11.05/11.08 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 11.05/11.08 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 11.05/11.08 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zmult__eq__1__iff,axiom,
% 11.05/11.08 ! [V_n_2,V_m_2] :
% 11.05/11.08 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 11.05/11.08 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 11.05/11.08 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 11.05/11.08 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 11.05/11.08 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_of__int__m1,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zdiv__minus1__right,axiom,
% 11.05/11.08 ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_succ__def,axiom,
% 11.05/11.08 ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_abs__power__minus__one,axiom,
% 11.05/11.08 ! [V_n,T_a] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_a) )
% 11.05/11.08 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_div__eq__minus1,axiom,
% 11.05/11.08 ! [V_b] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.08 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__succ,axiom,
% 11.05/11.08 ! [V_k,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__number__of__add__1,axiom,
% 11.05/11.08 ! [V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__1__add__number__of,axiom,
% 11.05/11.08 ! [V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_eq__special_I1_J,axiom,
% 11.05/11.08 ! [V_y_2,T_b] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 11.05/11.08 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_eq__special_I3_J,axiom,
% 11.05/11.08 ! [V_x_2,T_b] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.08 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_neg__number__of__pred__iff__0,axiom,
% 11.05/11.08 ! [V_v_2] :
% 11.05/11.08 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 11.05/11.08 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__number__of__mult__left,axiom,
% 11.05/11.08 ! [V_k,V_v_H,V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mult__nat__number__of,axiom,
% 11.05/11.08 ! [V_v_H,V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_pred__Pls,axiom,
% 11.05/11.08 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Pls__def,axiom,
% 11.05/11.08 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I19_J,axiom,
% 11.05/11.08 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I2_J,axiom,
% 11.05/11.08 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__Pls__right,axiom,
% 11.05/11.08 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__Pls,axiom,
% 11.05/11.08 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mult__Pls,axiom,
% 11.05/11.08 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 11.05/11.08
% 11.05/11.08 fof(fact_diff__bin__simps_I1_J,axiom,
% 11.05/11.08 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 11.05/11.08
% 11.05/11.08 fof(fact_minus__Pls,axiom,
% 11.05/11.08 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I40_J,axiom,
% 11.05/11.08 c_Int_OMin != c_Int_OPls ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I37_J,axiom,
% 11.05/11.08 c_Int_OPls != c_Int_OMin ).
% 11.05/11.08
% 11.05/11.08 fof(fact_succ__pred,axiom,
% 11.05/11.08 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 11.05/11.08
% 11.05/11.08 fof(fact_semiring__norm_I112_J,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__Pls,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__numeral__0__right,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__numeral__0,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_bin__less__0__simps_I1_J,axiom,
% 11.05/11.08 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_semiring__norm_I113_J,axiom,
% 11.05/11.08 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__number__of__Pls,axiom,
% 11.05/11.08 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zero__is__num__zero,axiom,
% 11.05/11.08 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__diff__number__of,axiom,
% 11.05/11.08 ! [V_m,V_v] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I23_J,axiom,
% 11.05/11.08 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I20_J,axiom,
% 11.05/11.08 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I6_J,axiom,
% 11.05/11.08 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I3_J,axiom,
% 11.05/11.08 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_eq__number__of__Pls__Min,axiom,
% 11.05/11.08 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_not__neg__number__of__Pls,axiom,
% 11.05/11.08 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_iszero__Numeral0,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_succ__Min,axiom,
% 11.05/11.08 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 11.05/11.08
% 11.05/11.08 fof(fact_le__iff__pred__less,axiom,
% 11.05/11.08 ! [V_l_2,V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_pred__def,axiom,
% 11.05/11.08 ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__Min,axiom,
% 11.05/11.08 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__Min__right,axiom,
% 11.05/11.08 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__number__of__diff__1,axiom,
% 11.05/11.08 ! [V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_eq__0__number__of,axiom,
% 11.05/11.08 ! [V_v_2] :
% 11.05/11.08 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_eq__number__of__0,axiom,
% 11.05/11.08 ! [V_v_2] :
% 11.05/11.08 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of2,axiom,
% 11.05/11.08 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__nat__number__of,axiom,
% 11.05/11.08 ! [V_v_H_2,V_v_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
% 11.05/11.08 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 11.05/11.08 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_le__nat__number__of,axiom,
% 11.05/11.08 ! [V_v_H_2,V_v_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
% 11.05/11.08 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 11.05/11.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_le__special_I1_J,axiom,
% 11.05/11.08 ! [V_y_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_le__special_I3_J,axiom,
% 11.05/11.08 ! [V_x_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__special_I3_J,axiom,
% 11.05/11.08 ! [V_x_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__special_I1_J,axiom,
% 11.05/11.08 ! [V_y_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__0__number__of,axiom,
% 11.05/11.08 ! [V_v_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__nat__number__of,axiom,
% 11.05/11.08 ! [V_v_H,V_v] :
% 11.05/11.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 11.05/11.08 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) )
% 11.05/11.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) ) ) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__pred,axiom,
% 11.05/11.08 ! [V_w,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_eq__special_I2_J,axiom,
% 11.05/11.08 ! [V_y_2,T_b] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 11.05/11.08 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_eq__special_I4_J,axiom,
% 11.05/11.08 ! [V_x_2,T_b] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 11.05/11.08 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_diff__special_I1_J,axiom,
% 11.05/11.08 ! [V_w,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_diff__special_I2_J,axiom,
% 11.05/11.08 ! [V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_div__Suc__eq__div__add3,axiom,
% 11.05/11.08 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__div__eq__add3__div,axiom,
% 11.05/11.08 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I51_J,axiom,
% 11.05/11.08 ! [V_l_2,V_k_2] :
% 11.05/11.08 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 11.05/11.08 <=> V_k_2 = V_l_2 ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__eq__int__code_I16_J,axiom,
% 11.05/11.08 ! [V_k2_2,V_k1_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I34_J,axiom,
% 11.05/11.08 ! [V_l_2,V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__int__code_I16_J,axiom,
% 11.05/11.08 ! [V_k2_2,V_k1_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I17_J,axiom,
% 11.05/11.08 ! [V_l_2,V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I46_J,axiom,
% 11.05/11.08 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I39_J,axiom,
% 11.05/11.08 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I47_J,axiom,
% 11.05/11.08 ! [V_k_2] :
% 11.05/11.08 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 11.05/11.08 <=> V_k_2 = c_Int_OMin ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I43_J,axiom,
% 11.05/11.08 ! [V_l_2] :
% 11.05/11.08 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 11.05/11.08 <=> c_Int_OMin = V_l_2 ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Bit1__Min,axiom,
% 11.05/11.08 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 11.05/11.08
% 11.05/11.08 fof(fact_bin__less__0__simps_I4_J,axiom,
% 11.05/11.08 ! [V_w_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I22_J,axiom,
% 11.05/11.08 ! [V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I12_J,axiom,
% 11.05/11.08 ! [V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Bit1__def,axiom,
% 11.05/11.08 ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I30_J,axiom,
% 11.05/11.08 ! [V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I26_J,axiom,
% 11.05/11.08 ! [V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I13_J,axiom,
% 11.05/11.08 ! [V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I9_J,axiom,
% 11.05/11.08 ! [V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_neg__number__of__Bit1,axiom,
% 11.05/11.08 ! [V_w_2] :
% 11.05/11.08 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 11.05/11.08 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_minus__Bit1,axiom,
% 11.05/11.08 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_iszero__number__of__Bit1,axiom,
% 11.05/11.08 ! [V_w,T_a] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 & class_Int_Oring__char__0(T_a) )
% 11.05/11.08 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_succ__Pls,axiom,
% 11.05/11.08 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_number__of__Bit1,axiom,
% 11.05/11.08 ! [V_w,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mult__numeral__1,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mult__numeral__1__right,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_semiring__norm_I110_J,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_numeral__1__eq__1,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I5_J,axiom,
% 11.05/11.08 ! [V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_rel__simps_I29_J,axiom,
% 11.05/11.08 ! [V_k_2] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_one__is__num__one,axiom,
% 11.05/11.08 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_nat__numeral__1__eq__1,axiom,
% 11.05/11.08 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Numeral1__eq1__nat,axiom,
% 11.05/11.08 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_diff__bin__simps_I4_J,axiom,
% 11.05/11.08 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_minus__Min,axiom,
% 11.05/11.08 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_not__iszero__Numeral1,axiom,
% 11.05/11.08 ! [T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_numeral__3__eq__3,axiom,
% 11.05/11.08 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_numeral__1__eq__Suc__0,axiom,
% 11.05/11.08 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_power3__eq__cube,axiom,
% 11.05/11.08 ! [V_a,T_a] :
% 11.05/11.08 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 11.05/11.08 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc3__eq__add__3,axiom,
% 11.05/11.08 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 11.05/11.08 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 11.05/11.08 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_le__special_I2_J,axiom,
% 11.05/11.08 ! [V_y_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_le__special_I4_J,axiom,
% 11.05/11.08 ! [V_x_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__special_I2_J,axiom,
% 11.05/11.08 ! [V_y_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_less__special_I4_J,axiom,
% 11.05/11.08 ! [V_x_2,T_b] :
% 11.05/11.08 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.08 & class_Rings_Olinordered__idom(T_b) )
% 11.05/11.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
% 11.05/11.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__special_I3_J,axiom,
% 11.05/11.08 ! [V_v,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_add__special_I2_J,axiom,
% 11.05/11.08 ! [V_w,T_a] :
% 11.05/11.08 ( class_Int_Onumber__ring(T_a)
% 11.05/11.08 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 11.05/11.08 ! [V_m,V_n] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
% 11.05/11.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 11.05/11.08 ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 11.05/11.08 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 11.05/11.08 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 11.05/11.08 ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_neg__zmod__mult__2,axiom,
% 11.05/11.08 ! [V_b,V_a] :
% 11.05/11.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.08 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 11.05/11.08
% 11.05/11.08 fof(fact_zmod__number__of__Bit1,axiom,
% 11.05/11.08 ! [V_v,V_w] :
% 11.05/11.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 11.05/11.09 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 11.05/11.09 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_neg__zdiv__mult__2,axiom,
% 11.05/11.09 ! [V_b,V_a] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.09 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_pos__zdiv__mult__2,axiom,
% 11.05/11.09 ! [V_b,V_a] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.09 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_pos__zmod__mult__2,axiom,
% 11.05/11.09 ! [V_b,V_a] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.09 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_of__nat__double,axiom,
% 11.05/11.09 ! [V_x,T_a] :
% 11.05/11.09 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 11.05/11.09 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I48_J,axiom,
% 11.05/11.09 ! [V_l_2,V_k_2] :
% 11.05/11.09 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 11.05/11.09 <=> V_k_2 = V_l_2 ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I31_J,axiom,
% 11.05/11.09 ! [V_l_2,V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__eq__int__code_I13_J,axiom,
% 11.05/11.09 ! [V_k2_2,V_k1_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I14_J,axiom,
% 11.05/11.09 ! [V_l_2,V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__int__code_I13_J,axiom,
% 11.05/11.09 ! [V_k2_2,V_k1_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Bit0__Pls,axiom,
% 11.05/11.09 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I38_J,axiom,
% 11.05/11.09 ! [V_l_2] :
% 11.05/11.09 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 11.05/11.09 <=> c_Int_OPls = V_l_2 ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I44_J,axiom,
% 11.05/11.09 ! [V_k_2] :
% 11.05/11.09 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 11.05/11.09 <=> V_k_2 = c_Int_OPls ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I49_J,axiom,
% 11.05/11.09 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I50_J,axiom,
% 11.05/11.09 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__Bit0__Bit0,axiom,
% 11.05/11.09 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Bit0__def,axiom,
% 11.05/11.09 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mult__Bit0,axiom,
% 11.05/11.09 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__bin__simps_I7_J,axiom,
% 11.05/11.09 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_minus__Bit0,axiom,
% 11.05/11.09 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I42_J,axiom,
% 11.05/11.09 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I45_J,axiom,
% 11.05/11.09 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 11.05/11.09
% 11.05/11.09 fof(fact_bin__less__0__simps_I3_J,axiom,
% 11.05/11.09 ! [V_w_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I21_J,axiom,
% 11.05/11.09 ! [V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I27_J,axiom,
% 11.05/11.09 ! [V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I32_J,axiom,
% 11.05/11.09 ! [V_l_2,V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__eq__int__code_I14_J,axiom,
% 11.05/11.09 ! [V_k2_2,V_k1_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I4_J,axiom,
% 11.05/11.09 ! [V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I10_J,axiom,
% 11.05/11.09 ! [V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I16_J,axiom,
% 11.05/11.09 ! [V_l_2,V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__int__code_I15_J,axiom,
% 11.05/11.09 ! [V_k2_2,V_k1_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__Bit0__Bit1,axiom,
% 11.05/11.09 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__Bit1__Bit0,axiom,
% 11.05/11.09 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__bin__simps_I3_J,axiom,
% 11.05/11.09 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__bin__simps_I9_J,axiom,
% 11.05/11.09 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__bin__simps_I10_J,axiom,
% 11.05/11.09 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I28_J,axiom,
% 11.05/11.09 ! [V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I8_J,axiom,
% 11.05/11.09 ! [V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zdiv__number__of__Bit0,axiom,
% 11.05/11.09 ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_neg__number__of__Bit0,axiom,
% 11.05/11.09 ! [V_w_2] :
% 11.05/11.09 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 11.05/11.09 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_pred__Bit0,axiom,
% 11.05/11.09 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_pred__Bit1,axiom,
% 11.05/11.09 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_pred__Min,axiom,
% 11.05/11.09 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_iszero__number__of__Bit0,axiom,
% 11.05/11.09 ! [V_w_2,T_b] :
% 11.05/11.09 ( ( class_Int_Onumber__ring(T_b)
% 11.05/11.09 & class_Int_Oring__char__0(T_b) )
% 11.05/11.09 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 11.05/11.09 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_succ__Bit1,axiom,
% 11.05/11.09 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_succ__Bit0,axiom,
% 11.05/11.09 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_number__of__Bit0,axiom,
% 11.05/11.09 ! [V_w,T_a] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_a)
% 11.05/11.09 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__eq__int__code_I15_J,axiom,
% 11.05/11.09 ! [V_k2_2,V_k1_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I33_J,axiom,
% 11.05/11.09 ! [V_l_2,V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__int__code_I14_J,axiom,
% 11.05/11.09 ! [V_k2_2,V_k1_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I15_J,axiom,
% 11.05/11.09 ! [V_l_2,V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mult__Bit1,axiom,
% 11.05/11.09 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I11_J,axiom,
% 11.05/11.09 ! [V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_rel__simps_I25_J,axiom,
% 11.05/11.09 ! [V_k_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__bin__simps_I5_J,axiom,
% 11.05/11.09 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__bin__simps_I6_J,axiom,
% 11.05/11.09 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__bin__simps_I8_J,axiom,
% 11.05/11.09 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__Bit1__Bit1,axiom,
% 11.05/11.09 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_double__number__of__Bit0,axiom,
% 11.05/11.09 ! [V_w,T_a] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_number__of1,axiom,
% 11.05/11.09 ! [V_n] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n))))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mult__2,axiom,
% 11.05/11.09 ! [V_z,T_a] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mult__2__right,axiom,
% 11.05/11.09 ! [V_z,T_a] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_one__add__one__is__two,axiom,
% 11.05/11.09 ! [T_a] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zero__power2,axiom,
% 11.05/11.09 ! [T_a] :
% 11.05/11.09 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zero__eq__power2,axiom,
% 11.05/11.09 ! [V_a_2,T_b] :
% 11.05/11.09 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 11.05/11.09 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_numeral__2__eq__2,axiom,
% 11.05/11.09 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_semiring__norm_I115_J,axiom,
% 11.05/11.09 hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 11.05/11.09 ! [V_x,T_a] :
% 11.05/11.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__eq__square,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 11.05/11.09 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__2__eq__Suc_H,axiom,
% 11.05/11.09 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__2__eq__Suc,axiom,
% 11.05/11.09 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_one__power2,axiom,
% 11.05/11.09 ! [T_a] :
% 11.05/11.09 ( class_Rings_Osemiring__1(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__minus,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Rings_Oring__1(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__mult__2,axiom,
% 11.05/11.09 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__mult__2__right,axiom,
% 11.05/11.09 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__even__eq,axiom,
% 11.05/11.09 ! [V_n,V_a,T_a] :
% 11.05/11.09 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 11.05/11.09 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 11.05/11.09 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_abs__power2,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.09 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__abs,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__1__add__1,axiom,
% 11.05/11.09 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mod2__Suc__Suc,axiom,
% 11.05/11.09 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_div2__Suc__Suc,axiom,
% 11.05/11.09 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zmod__number__of__Bit0,axiom,
% 11.05/11.09 ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__self__div__2,axiom,
% 11.05/11.09 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zero__le__power2,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__le__imp__le,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__eq__imp__eq,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.09 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => V_x = V_y ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zero__less__power2,axiom,
% 11.05/11.09 ! [V_a_2,T_b] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 11.05/11.09 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__less__0,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.09 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_sum__power2__eq__zero__iff,axiom,
% 11.05/11.09 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.09 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__eq__square__number__of,axiom,
% 11.05/11.09 ! [V_w,T_b] :
% 11.05/11.09 ( ( class_Groups_Omonoid__mult(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__2__cases,axiom,
% 11.05/11.09 ! [V_n] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 11.05/11.09 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.05/11.09 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__2,axiom,
% 11.05/11.09 hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__eq__1__iff,axiom,
% 11.05/11.09 ! [V_a_2,T_b] :
% 11.05/11.09 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 11.05/11.09 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
% 11.05/11.09 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 11.05/11.09 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 11.05/11.09 ! [V_n,V_x,T_a] :
% 11.05/11.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__minus__even,axiom,
% 11.05/11.09 ! [V_n,V_a,T_a] :
% 11.05/11.09 ( class_Rings_Oring__1(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__less__imp__less,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__semidom(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_sum__power2__ge__zero,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_sum__power2__le__zero__iff,axiom,
% 11.05/11.09 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_sum__power2__gt__zero__iff,axiom,
% 11.05/11.09 ! [V_y_2,V_x_2,T_b] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
% 11.05/11.09 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_not__sum__power2__lt__zero,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.09 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__sum,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zero__le__even__power_H,axiom,
% 11.05/11.09 ! [V_n,V_a,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 11.05/11.09 ! [V_n,V_x,T_a] :
% 11.05/11.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__odd__eq,axiom,
% 11.05/11.09 ! [V_n,V_a,T_a] :
% 11.05/11.09 ( class_Groups_Omonoid__mult(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__minus1__even,axiom,
% 11.05/11.09 ! [V_n,T_a] :
% 11.05/11.09 ( class_Rings_Oring__1(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zdiv__number__of__Bit1,axiom,
% 11.05/11.09 ! [V_v,V_w] :
% 11.05/11.09 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 11.05/11.09 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 11.05/11.09 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mod2__gr__0,axiom,
% 11.05/11.09 ! [V_m_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 11.05/11.09 <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_div__2__gt__zero,axiom,
% 11.05/11.09 ! [V_n] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power2__diff,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 11.05/11.09 ! [V_n,V_a,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_odd__power__less__zero,axiom,
% 11.05/11.09 ! [V_n,V_a,T_a] :
% 11.05/11.09 ( class_Rings_Olinordered__idom(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__minus1__odd,axiom,
% 11.05/11.09 ! [V_n,T_a] :
% 11.05/11.09 ( class_Rings_Oring__1(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__m1__even,axiom,
% 11.05/11.09 ! [V_n,T_a] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__m1__odd,axiom,
% 11.05/11.09 ! [V_n,T_a] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 11.05/11.09 ! [V_n] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_int__of__code,axiom,
% 11.05/11.09 ! [V_k] :
% 11.05/11.09 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.05/11.09 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 11.05/11.09 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.05/11.09 => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.05/11.09 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
% 11.05/11.09 & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.05/11.09 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_one__code__numeral__code,axiom,
% 11.05/11.09 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_half__gt__zero,axiom,
% 11.05/11.09 ! [V_r,T_a] :
% 11.05/11.09 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 11.05/11.09 & class_Int_Onumber__ring(T_a) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_half__gt__zero__iff,axiom,
% 11.05/11.09 ! [V_r_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber__ring(T_b) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 11.05/11.09 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__intermed__int__val,axiom,
% 11.05/11.09 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 11.05/11.09 ( ! [B_i] :
% 11.05/11.09 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 11.05/11.09 => ? [B_i] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 11.05/11.09 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral__zero__minus__one,axiom,
% 11.05/11.09 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__zero,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__zero__left,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__divide__distrib,axiom,
% 11.05/11.09 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_times__divide__times__eq,axiom,
% 11.05/11.09 ! [V_w,V_z,V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_times__divide__eq__right,axiom,
% 11.05/11.09 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__divide__distrib,axiom,
% 11.05/11.09 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__1,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_minus__divide__right,axiom,
% 11.05/11.09 ! [V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_minus__divide__divide,axiom,
% 11.05/11.09 ! [V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_minus__divide__left,axiom,
% 11.05/11.09 ! [V_b,V_a,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__divide,axiom,
% 11.05/11.09 ! [V_n,V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_abs__divide,axiom,
% 11.05/11.09 ! [V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 11.05/11.09 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 11.05/11.09 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 11.05/11.09 ! [V_y,V_x] :
% 11.05/11.09 ( c_Nat__Transfer_Ois__nat(V_x)
% 11.05/11.09 => ( c_Nat__Transfer_Ois__nat(V_y)
% 11.05/11.09 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 11.05/11.09 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 11.05/11.09 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 11.05/11.09 ! [V_y,V_x] :
% 11.05/11.09 ( c_Nat__Transfer_Ois__nat(V_x)
% 11.05/11.09 => ( c_Nat__Transfer_Ois__nat(V_y)
% 11.05/11.09 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 11.05/11.09 ! [V_y,V_x] :
% 11.05/11.09 ( c_Nat__Transfer_Ois__nat(V_x)
% 11.05/11.09 => ( c_Nat__Transfer_Ois__nat(V_y)
% 11.05/11.09 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 11.05/11.09 ! [V_y,V_x] :
% 11.05/11.09 ( c_Nat__Transfer_Ois__nat(V_x)
% 11.05/11.09 => ( c_Nat__Transfer_Ois__nat(V_y)
% 11.05/11.09 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 11.05/11.09 ! [V_n,V_x] :
% 11.05/11.09 ( c_Nat__Transfer_Ois__nat(V_x)
% 11.05/11.09 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zero__le__divide__iff,axiom,
% 11.05/11.09 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 11.05/11.09 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__le__0__iff,axiom,
% 11.05/11.09 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 11.05/11.09 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__right__mono,axiom,
% 11.05/11.09 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__right__mono__neg,axiom,
% 11.05/11.09 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__strict__right__mono__neg,axiom,
% 11.05/11.09 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__strict__right__mono,axiom,
% 11.05/11.09 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__neg__neg,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__neg__pos,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__pos__neg,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__pos__pos,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__less__0__iff,axiom,
% 11.05/11.09 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 11.05/11.09 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zero__less__divide__iff,axiom,
% 11.05/11.09 ! [V_b_2,V_a_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 11.05/11.09 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_eq__divide__eq,axiom,
% 11.05/11.09 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_b)
% 11.05/11.09 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 11.05/11.09 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 11.05/11.09 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__eq__eq,axiom,
% 11.05/11.09 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_b)
% 11.05/11.09 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 11.05/11.09 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 11.05/11.09 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mult__divide__mult__cancel__right,axiom,
% 11.05/11.09 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mult__divide__mult__cancel__left,axiom,
% 11.05/11.09 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_frac__eq__eq,axiom,
% 11.05/11.09 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 11.05/11.09 ( class_Fields_Ofield(T_b)
% 11.05/11.09 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
% 11.05/11.09 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_eq__divide__imp,axiom,
% 11.05/11.09 ! [V_b,V_a,V_c,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 11.05/11.09 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__eq__imp,axiom,
% 11.05/11.09 ! [V_a,V_b,V_c,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nonzero__divide__eq__eq,axiom,
% 11.05/11.09 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_b)
% 11.05/11.09 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 11.05/11.09 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nonzero__eq__divide__eq,axiom,
% 11.05/11.09 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_b)
% 11.05/11.09 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 11.05/11.09 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_right__inverse__eq,axiom,
% 11.05/11.09 ! [V_a_2,V_b_2,T_b] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_b)
% 11.05/11.09 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 11.05/11.09 <=> V_a_2 = V_b_2 ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__self,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__self__if,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 11.05/11.09 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 11.05/11.09 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nonzero__minus__divide__divide,axiom,
% 11.05/11.09 ! [V_a,V_b,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nonzero__minus__divide__right,axiom,
% 11.05/11.09 ! [V_a,V_b,T_a] :
% 11.05/11.09 ( class_Rings_Odivision__ring(T_a)
% 11.05/11.09 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nonzero__power__divide,axiom,
% 11.05/11.09 ! [V_n,V_a,V_b,T_a] :
% 11.05/11.09 ( class_Fields_Ofield(T_a)
% 11.05/11.09 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nonzero__abs__divide,axiom,
% 11.05/11.09 ! [V_a,V_b,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__one__over,axiom,
% 11.05/11.09 ! [V_n,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 11.05/11.09 ! [V_y,V_x] :
% 11.05/11.09 ( c_Nat__Transfer_Ois__nat(V_x)
% 11.05/11.09 => ( c_Nat__Transfer_Ois__nat(V_y)
% 11.05/11.09 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__nonpos__neg,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__nonpos__pos,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_frac__le,axiom,
% 11.05/11.09 ! [V_z,V_w,V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_frac__less,axiom,
% 11.05/11.09 ! [V_z,V_w,V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_frac__less2,axiom,
% 11.05/11.09 ! [V_z,V_w,V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__nonneg__neg,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__nonneg__pos,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__strict__left__mono__neg,axiom,
% 11.05/11.09 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__strict__left__mono,axiom,
% 11.05/11.09 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_neg__divide__less__eq,axiom,
% 11.05/11.09 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_neg__less__divide__eq,axiom,
% 11.05/11.09 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mult__imp__less__div__pos,axiom,
% 11.05/11.09 ! [V_x,V_z,V_y,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mult__imp__div__pos__less,axiom,
% 11.05/11.09 ! [V_z,V_x,V_y,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_pos__divide__less__eq,axiom,
% 11.05/11.09 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_pos__less__divide__eq,axiom,
% 11.05/11.09 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__less__eq,axiom,
% 11.05/11.09 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__divide__eq,axiom,
% 11.05/11.09 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_is__nat__def,axiom,
% 11.05/11.09 ! [V_x_2] :
% 11.05/11.09 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__frac__eq,axiom,
% 11.05/11.09 ! [V_w,V_x,V_z,V_y,T_a] :
% 11.05/11.09 ( class_Fields_Ofield(T_a)
% 11.05/11.09 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__add__eq__iff,axiom,
% 11.05/11.09 ! [V_y,V_x,V_z,T_a] :
% 11.05/11.09 ( class_Fields_Ofield(T_a)
% 11.05/11.09 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__frac__num,axiom,
% 11.05/11.09 ! [V_z,V_x,V_y,T_a] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__divide__eq__iff,axiom,
% 11.05/11.09 ! [V_y,V_x,V_z,T_a] :
% 11.05/11.09 ( class_Fields_Ofield(T_a)
% 11.05/11.09 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_add__num__frac,axiom,
% 11.05/11.09 ! [V_x,V_z,V_y,T_a] :
% 11.05/11.09 ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__frac__eq,axiom,
% 11.05/11.09 ! [V_w,V_x,V_z,V_y,T_a] :
% 11.05/11.09 ( class_Fields_Ofield(T_a)
% 11.05/11.09 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__diff__eq__iff,axiom,
% 11.05/11.09 ! [V_y,V_x,V_z,T_a] :
% 11.05/11.09 ( class_Fields_Ofield(T_a)
% 11.05/11.09 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__divide__eq__iff,axiom,
% 11.05/11.09 ! [V_y,V_x,V_z,T_a] :
% 11.05/11.09 ( class_Fields_Ofield(T_a)
% 11.05/11.09 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__eq__eq__number__of1,axiom,
% 11.05/11.09 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
% 11.05/11.09 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) )
% 11.05/11.09 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__eq__eq__number__of,axiom,
% 11.05/11.09 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
% 11.05/11.09 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) )
% 11.05/11.09 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_eq__divide__eq__number__of,axiom,
% 11.05/11.09 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 11.05/11.09 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 )
% 11.05/11.09 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_eq__divide__eq__number__of1,axiom,
% 11.05/11.09 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
% 11.05/11.09 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 )
% 11.05/11.09 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.05/11.09 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__half__sum,axiom,
% 11.05/11.09 ! [V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_gt__half__sum,axiom,
% 11.05/11.09 ! [V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__Numeral0,axiom,
% 11.05/11.09 ! [V_x,T_a] :
% 11.05/11.09 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 & class_Int_Onumber__ring(T_a) )
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_abs__div__pos,axiom,
% 11.05/11.09 ! [V_x,V_y,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__Numeral1,axiom,
% 11.05/11.09 ! [V_x,T_a] :
% 11.05/11.09 ( ( class_Fields_Ofield(T_a)
% 11.05/11.09 & class_Int_Onumber__ring(T_a) )
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__numeral__1,axiom,
% 11.05/11.09 ! [V_a,T_a] :
% 11.05/11.09 ( ( class_Fields_Ofield(T_a)
% 11.05/11.09 & class_Int_Onumber__ring(T_a) )
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__minus1,axiom,
% 11.05/11.09 ! [V_x,T_a] :
% 11.05/11.09 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 & class_Int_Onumber__ring(T_a) )
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zero__code__numeral__code,axiom,
% 11.05/11.09 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_le__divide__eq,axiom,
% 11.05/11.09 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__le__eq,axiom,
% 11.05/11.09 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_pos__le__divide__eq,axiom,
% 11.05/11.09 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_pos__divide__le__eq,axiom,
% 11.05/11.09 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mult__imp__div__pos__le,axiom,
% 11.05/11.09 ! [V_z,V_x,V_y,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_mult__imp__le__div__pos,axiom,
% 11.05/11.09 ! [V_x,V_z,V_y,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_neg__le__divide__eq,axiom,
% 11.05/11.09 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_neg__divide__le__eq,axiom,
% 11.05/11.09 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_b)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__left__mono,axiom,
% 11.05/11.09 ! [V_c,V_a,V_b,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__left__mono__neg,axiom,
% 11.05/11.09 ! [V_c,V_b,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__divide__eq__number__of1,axiom,
% 11.05/11.09 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__divide__eq__number__of,axiom,
% 11.05/11.09 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__less__eq__number__of,axiom,
% 11.05/11.09 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__less__eq__number__of1,axiom,
% 11.05/11.09 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__diff,axiom,
% 11.05/11.09 ! [V_m,V_n,V_a,T_a] :
% 11.05/11.09 ( class_Fields_Ofield(T_a)
% 11.05/11.09 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_minus1__divide,axiom,
% 11.05/11.09 ! [V_x,T_a] :
% 11.05/11.09 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 11.05/11.09 & class_Int_Onumber__ring(T_a) )
% 11.05/11.09 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 11.05/11.09 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__le__eq__number__of1,axiom,
% 11.05/11.09 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divide__le__eq__number__of,axiom,
% 11.05/11.09 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_le__divide__eq__number__of,axiom,
% 11.05/11.09 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_le__divide__eq__number__of1,axiom,
% 11.05/11.09 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 11.05/11.09 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 11.05/11.09 & class_Int_Onumber(T_b) )
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 11.05/11.09 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__of__aux__code,axiom,
% 11.05/11.09 ! [V_n,V_i] :
% 11.05/11.09 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.05/11.09 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 11.05/11.09 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.05/11.09 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Osize_I1_J,axiom,
% 11.05/11.09 c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Osize_I3_J,axiom,
% 11.05/11.09 hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 11.05/11.09 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 11.05/11.09
% 11.05/11.09 fof(fact_log_Osimps,axiom,
% 11.05/11.09 ! [V_i,V_b] :
% 11.05/11.09 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
% 11.05/11.09 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 11.05/11.09 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 11.05/11.09 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
% 11.05/11.09 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 11.05/11.09 => c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_field__le__epsilon,axiom,
% 11.05/11.09 ! [V_y,V_x,T_a] :
% 11.05/11.09 ( class_Fields_Olinordered__field(T_a)
% 11.05/11.09 => ( ! [B_e] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) )
% 11.05/11.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_minus__shift__def,axiom,
% 11.05/11.09 ! [V_r,V_l,V_k] :
% 11.05/11.09 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 11.05/11.09 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 11.05/11.09 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_inc__shift__def,axiom,
% 11.05/11.09 ! [V_k,V_v] :
% 11.05/11.09 ( ( V_v = V_k
% 11.05/11.09 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 11.05/11.09 & ( V_v != V_k
% 11.05/11.09 => c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Osize_I4_J,axiom,
% 11.05/11.09 ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Osize_I2_J,axiom,
% 11.05/11.09 ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_subtract__code__numeral__def,axiom,
% 11.05/11.09 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_minus__code__numeral__code,axiom,
% 11.05/11.09 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Oinject,axiom,
% 11.05/11.09 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 11.05/11.09 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 11.05/11.09 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 11.05/11.09 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 11.05/11.09 ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 11.05/11.09 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Suc__code__numeral__minus__one,axiom,
% 11.05/11.09 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n ).
% 11.05/11.09
% 11.05/11.09 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 11.05/11.09 ! [V_w] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
% 11.05/11.09 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
% 11.05/11.09 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__nat__number__of,axiom,
% 11.05/11.09 ! [V_v_2,V_v_H_2] :
% 11.05/11.09 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 11.05/11.09 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 11.05/11.09 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 11.05/11.09 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divmod__nat__step,axiom,
% 11.05/11.09 ! [V_m,V_n] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.05/11.09 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral__not__eq__zero,axiom,
% 11.05/11.09 ! [V_i_2] :
% 11.05/11.09 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divmod__nat__zero,axiom,
% 11.05/11.09 ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 11.05/11.09 ! [V_m_2,V_n_2] :
% 11.05/11.09 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 11.05/11.09 <=> V_n_2 = V_m_2 ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 11.05/11.09 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_fun__Compl__def,axiom,
% 11.05/11.09 ! [V_x_2,V_A_2,T_c,T_b] :
% 11.05/11.09 ( class_Groups_Ouminus(T_b)
% 11.05/11.09 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_fun__diff__def,axiom,
% 11.05/11.09 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 11.05/11.09 ( class_Groups_Ominus(T_b)
% 11.05/11.09 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divmod__nat__base,axiom,
% 11.05/11.09 ! [V_n,V_m] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.05/11.09 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__eq__Suc__le__raw,axiom,
% 11.05/11.09 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__number__of__Bit0,axiom,
% 11.05/11.09 ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_times__code__numeral__code,axiom,
% 11.05/11.09 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divmod__nat__div__mod,axiom,
% 11.05/11.09 ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__number__of__even,axiom,
% 11.05/11.09 ! [V_w_2,V_z_2,T_b] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_b)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zpower__number__of__even,axiom,
% 11.05/11.09 ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__number__of__even__number__of,axiom,
% 11.05/11.09 ! [V_w_2,V_v_2,T_b] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_b)
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__nat__eq__if,axiom,
% 11.05/11.09 ! [V_z_2,V_z_H_2] :
% 11.05/11.09 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 11.05/11.09 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 11.05/11.09 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_negDivAlg__div__mod,axiom,
% 11.05/11.09 ! [V_l,V_k] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 11.05/11.09 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_negDivAlg__minus1,axiom,
% 11.05/11.09 ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 11.05/11.09 ! [V_n_2,T_b] :
% 11.05/11.09 ( class_Rings_Osemiring__1(T_b)
% 11.05/11.09 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_adjust__eq,axiom,
% 11.05/11.09 ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zero__code__numeral__def,axiom,
% 11.05/11.09 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_one__code__numeral__def,axiom,
% 11.05/11.09 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__code__numeral__code,axiom,
% 11.05/11.09 ! [V_m_2,V_n_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_eq__number__of__Suc,axiom,
% 11.05/11.09 ! [V_n_2,V_v_2] :
% 11.05/11.09 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_Suc__eq__number__of,axiom,
% 11.05/11.09 ! [V_v_2,V_n_2] :
% 11.05/11.09 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_plus__code__numeral__code,axiom,
% 11.05/11.09 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__eq__code__numeral__code,axiom,
% 11.05/11.09 ! [V_m_2,V_n_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__number__of__Bit1,axiom,
% 11.05/11.09 ! [V_w_2] :
% 11.05/11.09 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 11.05/11.09 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 11.05/11.09 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__number__of__Suc,axiom,
% 11.05/11.09 ! [V_n_2,V_v_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__Suc__number__of,axiom,
% 11.05/11.09 ! [V_v_2,V_n_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_le__number__of__Suc,axiom,
% 11.05/11.09 ! [V_n_2,V_v_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_le__Suc__number__of,axiom,
% 11.05/11.09 ! [V_v_2,V_n_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 11.05/11.09 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_subtract__code__numeral__code,axiom,
% 11.05/11.09 ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__number__of__odd,axiom,
% 11.05/11.09 ! [V_z_2,V_w_2,T_b] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_b)
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_zpower__number__of__odd,axiom,
% 11.05/11.09 ! [V_z_2,V_w_2] :
% 11.05/11.09 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_negDivAlg_Osimps,axiom,
% 11.05/11.09 ! [V_b,V_a] :
% 11.05/11.09 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 11.05/11.09 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.05/11.09 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) )
% 11.05/11.09 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 11.05/11.09 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.05/11.09 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_power__number__of__odd__number__of,axiom,
% 11.05/11.09 ! [V_v_2,V_w_2,T_b] :
% 11.05/11.09 ( class_Int_Onumber__ring(T_b)
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 11.05/11.09 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 11.05/11.09 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 11.05/11.09
% 11.05/11.09 fof(fact_negDivAlg__eqn__number__of,axiom,
% 11.05/11.09 ! [V_w,V_v] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
% 11.05/11.09 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
% 11.05/11.09 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_negDivAlg__eqn,axiom,
% 11.05/11.09 ! [V_a,V_b] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 11.05/11.09 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 11.05/11.09 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_norm__frac_Osimps,axiom,
% 11.05/11.09 ! [V_a_2,V_b_2] :
% 11.05/11.09 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.09 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.09 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.09 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 11.05/11.09 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 11.05/11.09 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.09 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 11.05/11.09 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__case__add__eq__if,axiom,
% 11.05/11.09 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 11.05/11.09 ! [V_w] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 11.05/11.09 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 11.05/11.09 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_posDivAlg_Osimps,axiom,
% 11.05/11.09 ! [V_b,V_a] :
% 11.05/11.09 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 11.05/11.09 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.05/11.09 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) )
% 11.05/11.09 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 11.05/11.09 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.05/11.09 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_adjust__def,axiom,
% 11.05/11.09 ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__case__0,axiom,
% 11.05/11.09 ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__case__Suc,axiom,
% 11.05/11.09 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_posDivAlg__0,axiom,
% 11.05/11.09 ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 11.05/11.09 ! [V_n_2,V_m_2] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 11.05/11.09 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_diff__Suc,axiom,
% 11.05/11.09 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_posDivAlg__div__mod,axiom,
% 11.05/11.09 ! [V_l,V_k] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 11.05/11.09 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__case__number__of,axiom,
% 11.05/11.09 ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_posDivAlg__eqn,axiom,
% 11.05/11.09 ! [V_a,V_b] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 11.05/11.09 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 11.05/11.09 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_posDivAlg__eqn__number__of,axiom,
% 11.05/11.09 ! [V_w,V_v] :
% 11.05/11.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.09 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 11.05/11.09 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_of__int__num,axiom,
% 11.05/11.09 ! [V_k_2,T_b] :
% 11.05/11.09 ( class_Rings_Oring__1(T_b)
% 11.05/11.09 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.09 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 11.05/11.09 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.09 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) )
% 11.05/11.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.09 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_nat__rec__add__eq__if,axiom,
% 11.05/11.09 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 11.05/11.09 ! [V_c,V_r,V_q,V_b,V_a] :
% 11.05/11.09 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 11.05/11.09 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 11.05/11.09 ! [V_a,V_r,V_q,V_c,V_b] :
% 11.05/11.09 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 11.05/11.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 11.05/11.09 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ) ).
% 11.05/11.09
% 11.05/11.09 fof(fact_negDivAlg_Opsimps,axiom,
% 11.05/11.09 ! [V_b_2,V_a_2] :
% 11.05/11.09 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 11.05/11.10 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)))
% 11.05/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.05/11.10 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) )
% 11.05/11.10 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)))
% 11.05/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.05/11.10 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_accp_Osimps,axiom,
% 11.05/11.10 ! [V_a_2,V_r_2,T_b] :
% 11.05/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 11.05/11.10 <=> ! [B_x] :
% 11.05/11.10 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 11.05/11.10 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_accp_Oequations,axiom,
% 11.05/11.10 ! [V_a_2,V_r_2,T_b] :
% 11.05/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 11.05/11.10 <=> ! [B_x] :
% 11.05/11.10 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 11.05/11.10 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_accp__downward,axiom,
% 11.05/11.10 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 11.05/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 11.05/11.10 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 11.05/11.10 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_divmod__nat__rel__unique,axiom,
% 11.05/11.10 ! [V_qr_H,V_qr,V_n,V_m] :
% 11.05/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 11.05/11.10 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 11.05/11.10 => V_qr = V_qr_H ) ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_accp__subset,axiom,
% 11.05/11.10 ! [V_R2_2,V_R1_2,T_b] :
% 11.05/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2))
% 11.05/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_nat__rec__0,axiom,
% 11.05/11.10 ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 11.05/11.10
% 11.05/11.10 fof(fact_nat__rec__Suc,axiom,
% 11.05/11.10 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 11.05/11.10 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_divmod__nat__eq,axiom,
% 11.05/11.10 ! [V_qr,V_n,V_m] :
% 11.05/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 11.05/11.10 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_mod__eq,axiom,
% 11.05/11.10 ! [V_r,V_q,V_n,V_m] :
% 11.05/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 11.05/11.10 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_div__eq,axiom,
% 11.05/11.10 ! [V_r,V_q,V_n,V_m] :
% 11.05/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 11.05/11.10 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_divmod__nat__rel,axiom,
% 11.05/11.10 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_divmod__int__mod__div,axiom,
% 11.05/11.10 ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 11.05/11.10 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 11.05/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar)))
% 11.05/11.10 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br)))
% 11.05/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 11.05/11.10 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_nat__rec__number__of,axiom,
% 11.05/11.10 ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_posDivAlg_Opsimps,axiom,
% 11.05/11.10 ! [V_b_2,V_a_2] :
% 11.05/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 11.05/11.10 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 11.05/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.05/11.10 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) )
% 11.05/11.10 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 11.05/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.05/11.10 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_norm__frac_Opsimps,axiom,
% 11.05/11.10 ! [V_b_2,V_a_2] :
% 11.05/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 11.05/11.10 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.10 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 11.05/11.10 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.05/11.10 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.10 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 11.05/11.10 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 11.05/11.10 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.10 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 11.05/11.10 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_Nitpick_OFrac__def,axiom,
% 11.05/11.10 c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_divmod__int__def,axiom,
% 11.05/11.10 ! [V_b,V_a] :
% 11.05/11.10 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.10 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.10 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 11.05/11.10 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.10 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.10 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 11.05/11.10 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.05/11.10 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) )
% 11.05/11.10 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.05/11.10 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.10 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 11.05/11.10 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.05/11.10 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ).
% 11.05/11.10
% 11.05/11.10 fof(fact_negDivAlg_Opinduct,axiom,
% 11.05/11.10 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 11.05/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 11.05/11.10 => ( ! [B_a,B_b] :
% 11.05/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 11.05/11.10 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b)))
% 11.25/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_negateSnd__eq,axiom,
% 11.25/11.10 ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_prod__caseI,axiom,
% 11.25/11.10 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_splitI,axiom,
% 11.25/11.10 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_posDivAlg_Opinduct,axiom,
% 11.25/11.10 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 11.25/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 11.25/11.10 => ( ! [B_a,B_b] :
% 11.25/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 11.25/11.10 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 11.25/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_nat__gcd_Opsimps,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2] :
% 11.25/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)))
% 11.25/11.10 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.10 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 11.25/11.10 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.10 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__int__pdivmod,axiom,
% 11.25/11.10 ! [V_l_2,V_k_2] :
% 11.25/11.10 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 11.25/11.10 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) )
% 11.25/11.10 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_apsnd__conv,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Pair__inject,axiom,
% 11.25/11.10 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 11.25/11.10 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H)
% 11.25/11.10 => ~ ( V_a = V_a_H
% 11.25/11.10 => V_b != V_b_H ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Pair__eq,axiom,
% 11.25/11.10 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.10 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
% 11.25/11.10 <=> ( V_a_2 = V_a_H_2
% 11.25/11.10 & V_b_2 = V_b_H_2 ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_split__paired__All,axiom,
% 11.25/11.10 ! [T_c,T_b,V_Pa_2] :
% 11.25/11.10 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 11.25/11.10 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_negateSnd__def,axiom,
% 11.25/11.10 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_split__weak__cong,axiom,
% 11.25/11.10 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 11.25/11.10 ( V_p_2 = V_q_2
% 11.25/11.10 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_split__conv,axiom,
% 11.25/11.10 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_prod_Osimps_I2_J,axiom,
% 11.25/11.10 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_splitD,axiom,
% 11.25/11.10 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_split__eta,axiom,
% 11.25/11.10 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2 ).
% 11.25/11.10
% 11.25/11.10 fof(fact_split__twice,axiom,
% 11.25/11.10 ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_pdivmod__def,axiom,
% 11.25/11.10 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_pdivmod__posDivAlg,axiom,
% 11.25/11.10 ! [V_k,V_l] :
% 11.25/11.10 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)) )
% 11.25/11.10 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__int__code,axiom,
% 11.25/11.10 ! [V_l_2,V_k_2] :
% 11.25/11.10 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 11.25/11.10 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) )
% 11.25/11.10 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_div__mod__code__numeral__def,axiom,
% 11.25/11.10 ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_zmult2__lemma,axiom,
% 11.25/11.10 ! [V_c,V_r,V_q,V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 11.25/11.10 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_mod__pos__neg__1__number__of,axiom,
% 11.25/11.10 ! [V_w] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__int__rel__def,axiom,
% 11.25/11.10 ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_norm__frac_Opinduct,axiom,
% 11.25/11.10 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 11.25/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 11.25/11.10 => ( ! [B_a,B_b] :
% 11.25/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 11.25/11.10 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_splitD_H,axiom,
% 11.25/11.10 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_snd__eqD,axiom,
% 11.25/11.10 ! [V_a,V_y,V_x,T_a,T_b] :
% 11.25/11.10 ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a
% 11.25/11.10 => V_y = V_a ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_snd__conv,axiom,
% 11.25/11.10 ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b ).
% 11.25/11.10
% 11.25/11.10 fof(fact_snd__apsnd,axiom,
% 11.25/11.10 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_apsnd__eq__conv,axiom,
% 11.25/11.10 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 11.25/11.10 ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
% 11.25/11.10 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_snd__def,axiom,
% 11.25/11.10 ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_mod__int__def,axiom,
% 11.25/11.10 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__int__rel__0,axiom,
% 11.25/11.10 ! [V_b] :
% 11.25/11.10 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_self__remainder,axiom,
% 11.25/11.10 ! [V_r,V_q,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 11.25/11.10 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_unique__quotient,axiom,
% 11.25/11.10 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 11.25/11.10 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
% 11.25/11.10 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => V_q = V_q_H ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_unique__remainder,axiom,
% 11.25/11.10 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 11.25/11.10 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
% 11.25/11.10 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => V_r = V_r_H ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__int__rel__neg,axiom,
% 11.25/11.10 ! [V_qr,V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr))
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__int__correct,axiom,
% 11.25/11.10 ! [V_a,V_b] :
% 11.25/11.10 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_self__quotient,axiom,
% 11.25/11.10 ! [V_r,V_q,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 11.25/11.10 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__int__rel__mod,axiom,
% 11.25/11.10 ! [V_r,V_q,V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 11.25/11.10 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__int__rel__div,axiom,
% 11.25/11.10 ! [V_r,V_q,V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 11.25/11.10 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_negDivAlg__correct,axiom,
% 11.25/11.10 ! [V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_mod__neg__pos,axiom,
% 11.25/11.10 ! [V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.25/11.10 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__int__rel__div__mod,axiom,
% 11.25/11.10 ! [V_a,V_b] :
% 11.25/11.10 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_posDivAlg__correct,axiom,
% 11.25/11.10 ! [V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_mod__pos__pos,axiom,
% 11.25/11.10 ! [V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.25/11.10 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_mod__pos__pos__1__number__of,axiom,
% 11.25/11.10 ! [V_w] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 11.25/11.10 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_zadd1__lemma,axiom,
% 11.25/11.10 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar)))
% 11.25/11.10 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br)))
% 11.25/11.10 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_zminus1__lemma,axiom,
% 11.25/11.10 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)))
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_mod__pos__neg,axiom,
% 11.25/11.10 ! [V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__nat__if,axiom,
% 11.25/11.10 ! [V_m_2,V_n_2] :
% 11.25/11.10 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 11.25/11.10 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
% 11.25/11.10 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 11.25/11.10 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__int__relI,axiom,
% 11.25/11.10 ! [V_r,V_q,V_b,V_a] :
% 11.25/11.10 ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)
% 11.25/11.10 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 11.25/11.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 11.25/11.10 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 11.25/11.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_mod__neg__neg,axiom,
% 11.25/11.10 ! [V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_zmult1__lemma,axiom,
% 11.25/11.10 ! [V_a,V_r,V_q,V_c,V_b] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 11.25/11.10 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_equalityI,axiom,
% 11.25/11.10 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.10 => V_A_2 = V_B_2 ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_div__pos__neg__1__number__of,axiom,
% 11.25/11.10 ! [V_w] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_nat__gcd_Opinduct,axiom,
% 11.25/11.10 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 11.25/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2)))
% 11.25/11.10 => ( ! [B_x,B_y] :
% 11.25/11.10 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)))
% 11.25/11.10 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_div__neg__neg,axiom,
% 11.25/11.10 ! [V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__number__of__Suc,axiom,
% 11.25/11.10 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__Suc__Suc,axiom,
% 11.25/11.10 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__le__iff__disj,axiom,
% 11.25/11.10 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 11.25/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__infE,axiom,
% 11.25/11.10 ! [V_b,V_a,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
% 11.25/11.10 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 11.25/11.10 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__mono,axiom,
% 11.25/11.10 ! [V_d,V_b,V_c,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__greatest,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__infI,axiom,
% 11.25/11.10 ! [V_b,V_a,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__absorb2,axiom,
% 11.25/11.10 ! [V_x,V_y,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__absorb1,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__infI2,axiom,
% 11.25/11.10 ! [V_a,V_x,V_b,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__infI1,axiom,
% 11.25/11.10 ! [V_b,V_x,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__inf__iff,axiom,
% 11.25/11.10 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.25/11.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__iff__inf,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.25/11.10 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__le2,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__le1,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__0R,axiom,
% 11.25/11.10 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__0L,axiom,
% 11.25/11.10 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__add__distrib__left,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf_Oidem,axiom,
% 11.25/11.10 ! [V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf_Ocommute,axiom,
% 11.25/11.10 ! [V_b,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__commute,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 11.25/11.10 ! [V_b,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__left__idem,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 11.25/11.10 ! [V_c,V_a,V_b,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__left__commute,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf_Oassoc,axiom,
% 11.25/11.10 ! [V_c,V_b,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__assoc,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oless__infI2,axiom,
% 11.25/11.10 ! [V_a,V_x,V_b,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oless__infI1,axiom,
% 11.25/11.10 ! [V_b,V_x,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__less__iff__conj,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 11.25/11.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__less__iff__disj,axiom,
% 11.25/11.10 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 11.25/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__diff__distrib__left,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Groups_Oordered__ab__group__add(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__diff,axiom,
% 11.25/11.10 ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_fst__conv,axiom,
% 11.25/11.10 ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a ).
% 11.25/11.10
% 11.25/11.10 fof(fact_fst__eqD,axiom,
% 11.25/11.10 ! [V_a,V_y,V_x,T_b,T_a] :
% 11.25/11.10 ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a
% 11.25/11.10 => V_x = V_a ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Pair__fst__snd__eq,axiom,
% 11.25/11.10 ! [T_c,T_b,V_t_2,V_s_2] :
% 11.25/11.10 ( V_s_2 = V_t_2
% 11.25/11.10 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 11.25/11.10 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_prod__eqI,axiom,
% 11.25/11.10 ! [V_q,V_p,T_b,T_a] :
% 11.25/11.10 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 11.25/11.10 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 11.25/11.10 => V_p = V_q ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_fst__apsnd,axiom,
% 11.25/11.10 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_fst__def,axiom,
% 11.25/11.10 ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__number__of,axiom,
% 11.25/11.10 ! [V_v,V_u,T_b] :
% 11.25/11.10 ( ( class_Int_Onumber(T_b)
% 11.25/11.10 & class_Orderings_Oord(T_b) )
% 11.25/11.10 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) )
% 11.25/11.10 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_pair__collapse,axiom,
% 11.25/11.10 ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p ).
% 11.25/11.10
% 11.25/11.10 fof(fact_surjective__pairing,axiom,
% 11.25/11.10 ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_prod__case__beta,axiom,
% 11.25/11.10 ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_div__int__def,axiom,
% 11.25/11.10 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_mod__nat__def,axiom,
% 11.25/11.10 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_split__comp__eq,axiom,
% 11.25/11.10 ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_split__beta,axiom,
% 11.25/11.10 ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_split__def,axiom,
% 11.25/11.10 ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Diff__subset,axiom,
% 11.25/11.10 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Diff__mono,axiom,
% 11.25/11.10 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_double__diff,axiom,
% 11.25/11.10 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 11.25/11.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Compl__subset__Compl__iff,axiom,
% 11.25/11.10 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
% 11.25/11.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Compl__anti__mono,axiom,
% 11.25/11.10 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_subset__refl,axiom,
% 11.25/11.10 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_set__eq__subset,axiom,
% 11.25/11.10 ! [T_b,V_B_2,V_A_2] :
% 11.25/11.10 ( V_A_2 = V_B_2
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_equalityD1,axiom,
% 11.25/11.10 ! [T_b,V_B_2,V_A_2] :
% 11.25/11.10 ( V_A_2 = V_B_2
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_equalityD2,axiom,
% 11.25/11.10 ! [T_b,V_B_2,V_A_2] :
% 11.25/11.10 ( V_A_2 = V_B_2
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_subset__trans,axiom,
% 11.25/11.10 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_equalityE,axiom,
% 11.25/11.10 ! [T_b,V_B_2,V_A_2] :
% 11.25/11.10 ( V_A_2 = V_B_2
% 11.25/11.10 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_psubset__eq,axiom,
% 11.25/11.10 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 & V_A_2 != V_B_2 ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_subset__iff__psubset__eq,axiom,
% 11.25/11.10 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 | V_A_2 = V_B_2 ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_psubset__imp__subset,axiom,
% 11.25/11.10 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_psubset__subset__trans,axiom,
% 11.25/11.10 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_subset__psubset__trans,axiom,
% 11.25/11.10 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__Suc2,axiom,
% 11.25/11.10 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__Suc1,axiom,
% 11.25/11.10 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_div__neg__pos,axiom,
% 11.25/11.10 ! [V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.25/11.10 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_div__pos__pos,axiom,
% 11.25/11.10 ! [V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 11.25/11.10 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_div__pos__pos__1__number__of,axiom,
% 11.25/11.10 ! [V_w] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 11.25/11.10 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_div__pos__neg,axiom,
% 11.25/11.10 ! [V_b,V_a] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 11.25/11.10 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__Suc__number__of,axiom,
% 11.25/11.10 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_prod__size__simp,axiom,
% 11.25/11.10 ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_exI__realizer,axiom,
% 11.25/11.10 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_conjI__realizer,axiom,
% 11.25/11.10 ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
% 11.25/11.10 ( hBOOL(hAPP(V_Pa_2,V_p_2))
% 11.25/11.10 => ( hBOOL(hAPP(V_Qa_2,V_q_2))
% 11.25/11.10 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 11.25/11.10 & hBOOL(hAPP(V_Qa_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__ord__min,axiom,
% 11.25/11.10 ! [T_b] :
% 11.25/11.10 ( class_Orderings_Oord(T_b)
% 11.25/11.10 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_prod_Orecs,axiom,
% 11.25/11.10 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_double__complement,axiom,
% 11.25/11.10 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2 ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Compl__eq__Compl__iff,axiom,
% 11.25/11.10 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
% 11.25/11.10 <=> V_A_2 = V_B_2 ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Diff__idemp,axiom,
% 11.25/11.10 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_psubset__trans,axiom,
% 11.25/11.10 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_div__nat__def,axiom,
% 11.25/11.10 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__nat__rel__def,axiom,
% 11.25/11.10 ! [V_qr_2,V_n_2,V_m_2] :
% 11.25/11.10 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 11.25/11.10 <=> ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))
% 11.25/11.10 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.10 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.25/11.10 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.10 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 11.25/11.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)) ) )
% 11.25/11.10 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 11.25/11.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_range,axiom,
% 11.25/11.10 ! [V_s,V_k] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 11.25/11.10 ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__Suc__number__of,axiom,
% 11.25/11.10 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__number__of__Suc,axiom,
% 11.25/11.10 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_apfst__apsnd,axiom,
% 11.25/11.10 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__inf__absorb,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 11.25/11.10 ! [V_x,V_z,V_y,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 11.25/11.10 ! [V_x,V_z,V_y,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__less__iff__conj,axiom,
% 11.25/11.10 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 11.25/11.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_less__max__iff__disj,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 11.25/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oless__supI1,axiom,
% 11.25/11.10 ! [V_b,V_a,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Oless__supI2,axiom,
% 11.25/11.10 ! [V_a,V_b,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__diff__distrib__left,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Groups_Oordered__ab__group__add(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_le__max__iff__disj,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 11.25/11.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__supE,axiom,
% 11.25/11.10 ! [V_x,V_b,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
% 11.25/11.10 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 11.25/11.10 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__mono,axiom,
% 11.25/11.10 ! [V_d,V_b,V_c,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__least,axiom,
% 11.25/11.10 ! [V_z,V_x,V_y,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__supI,axiom,
% 11.25/11.10 ! [V_b,V_x,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__absorb1,axiom,
% 11.25/11.10 ! [V_x,V_y,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__absorb2,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__supI2,axiom,
% 11.25/11.10 ! [V_a,V_b,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__supI1,axiom,
% 11.25/11.10 ! [V_b,V_a,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__sup__iff,axiom,
% 11.25/11.10 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
% 11.25/11.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 11.25/11.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Ole__iff__sup,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.25/11.10 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_le__maxI2,axiom,
% 11.25/11.10 ! [V_x,V_y,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_le__maxI1,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__0R,axiom,
% 11.25/11.10 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__0L,axiom,
% 11.25/11.10 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__add__distrib__left,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup_Oidem,axiom,
% 11.25/11.10 ! [V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup_Ocommute,axiom,
% 11.25/11.10 ! [V_b,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__commute,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 11.25/11.10 ! [V_b,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__left__idem,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 11.25/11.10 ! [V_c,V_a,V_b,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__left__commute,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup_Oassoc,axiom,
% 11.25/11.10 ! [V_c,V_b,V_a,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Osup__assoc,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__Suc__Suc,axiom,
% 11.25/11.10 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_apfst__conv,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_fst__apfst,axiom,
% 11.25/11.10 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_apfst__eq__conv,axiom,
% 11.25/11.10 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 11.25/11.10 ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
% 11.25/11.10 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_snd__apfst,axiom,
% 11.25/11.10 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__number__of,axiom,
% 11.25/11.10 ! [V_v,V_u,T_b] :
% 11.25/11.10 ( ( class_Int_Onumber(T_b)
% 11.25/11.10 & class_Orderings_Oord(T_b) )
% 11.25/11.10 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) )
% 11.25/11.10 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Odistrib__sup__le,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_min__max_Odistrib__inf__le,axiom,
% 11.25/11.10 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_minus__min__eq__max,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Groups_Olinordered__ab__group__add(T_a)
% 11.25/11.10 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_minus__max__eq__min,axiom,
% 11.25/11.10 ! [V_y,V_x,T_a] :
% 11.25/11.10 ( class_Groups_Olinordered__ab__group__add(T_a)
% 11.25/11.10 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_nat__minus__add__max,axiom,
% 11.25/11.10 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_apsnd__apfst__commute,axiom,
% 11.25/11.10 ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__Suc2,axiom,
% 11.25/11.10 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__Suc1,axiom,
% 11.25/11.10 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_apsnd__apfst,axiom,
% 11.25/11.10 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_dual__min,axiom,
% 11.25/11.10 ! [T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_max__ord__max,axiom,
% 11.25/11.10 ! [T_b] :
% 11.25/11.10 ( class_Orderings_Oord(T_b)
% 11.25/11.10 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_code__numeral__decr,axiom,
% 11.25/11.10 ! [V_k] :
% 11.25/11.10 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 11.25/11.10 ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_pos__not__random__dseq__def,axiom,
% 11.25/11.10 ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_code__numeral_Onat__of__inject,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2] :
% 11.25/11.10 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 11.25/11.10 <=> V_x_2 = V_y_2 ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 11.25/11.10 ! [V_l_2,V_k_2] :
% 11.25/11.10 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 11.25/11.10 <=> V_k_2 = V_l_2 ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_nat__of__inverse,axiom,
% 11.25/11.10 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 11.25/11.10
% 11.25/11.10 fof(fact_of__nat__nat__of,axiom,
% 11.25/11.10 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 11.25/11.10
% 11.25/11.10 fof(fact_nat__of__of__nat,axiom,
% 11.25/11.10 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 11.25/11.10
% 11.25/11.10 fof(fact_less__code__numeral__def,axiom,
% 11.25/11.10 ! [V_m_2,V_n_2] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 11.25/11.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_nat__of__number,axiom,
% 11.25/11.10 ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_less__eq__code__numeral__def,axiom,
% 11.25/11.10 ! [V_m_2,V_n_2] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 11.25/11.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_nat__of__code,axiom,
% 11.25/11.10 ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_nat__of__aux__def,axiom,
% 11.25/11.10 ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Min_Oidem,axiom,
% 11.25/11.10 ! [V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Max_Oidem,axiom,
% 11.25/11.10 ! [V_x,T_a] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_a)
% 11.25/11.10 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_dual__max,axiom,
% 11.25/11.10 ! [T_b] :
% 11.25/11.10 ( class_Orderings_Olinorder(T_b)
% 11.25/11.10 => c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Suc__code__numeral__def,axiom,
% 11.25/11.10 ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_minus__code__numeral__def,axiom,
% 11.25/11.10 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_plus__code__numeral__def,axiom,
% 11.25/11.10 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_div__code__numeral__def,axiom,
% 11.25/11.10 ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_times__code__numeral__def,axiom,
% 11.25/11.10 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_mod__code__numeral__def,axiom,
% 11.25/11.10 ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Oone__frac__def,axiom,
% 11.25/11.10 ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 11.25/11.10 ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Ofrac__def,axiom,
% 11.25/11.10 ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_surjective__sum,axiom,
% 11.25/11.10 ! [V_f_2,T_c,T_d,T_b] : c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,hAPP(hAPP(c_COMBB(tc_sum(T_b,T_c),T_d,T_b),V_f_2),c_Sum__Type_OInl(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_sum(T_b,T_c),T_d,T_c),V_f_2),c_Sum__Type_OInr(T_c,T_b))) = V_f_2 ).
% 11.25/11.10
% 11.25/11.10 fof(fact_iterate_Osimps,axiom,
% 11.25/11.10 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 11.25/11.10 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.25/11.10 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) )
% 11.25/11.10 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.25/11.10 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_scomp__scomp,axiom,
% 11.25/11.10 ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_sum__case__KK,axiom,
% 11.25/11.10 ! [V_x_2,V_a_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_a_2),hAPP(c_COMBK(T_b,T_d),V_a_2)),V_x_2) = V_a_2 ).
% 11.25/11.10
% 11.25/11.10 fof(fact_sum__case__weak__cong,axiom,
% 11.25/11.10 ! [V_g_2,V_f_2,T_c,T_d,T_b,V_t_2,V_s_2] :
% 11.25/11.10 ( V_s_2 = V_t_2
% 11.25/11.10 => hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f_2,V_g_2),V_s_2) = hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f_2,V_g_2),V_t_2) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_sum__case__inject,axiom,
% 11.25/11.10 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_c,T_d,T_b] :
% 11.25/11.10 ( c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f1_2,V_f2_2) = c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_g1_2,V_g2_2)
% 11.25/11.10 => ~ ( V_f1_2 = V_g1_2
% 11.25/11.10 => V_f2_2 != V_g2_2 ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_scomp__Pair,axiom,
% 11.25/11.10 ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2 ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Pair__scomp,axiom,
% 11.25/11.10 ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_scomp__apply,axiom,
% 11.25/11.10 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_sum_Osimps_I6_J,axiom,
% 11.25/11.10 ! [V_b_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInr(T_d,T_c),V_b_2)) = hAPP(V_f2_2,V_b_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_sum_Osimps_I5_J,axiom,
% 11.25/11.10 ! [V_a_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInl(T_c,T_d),V_a_2)) = hAPP(V_f1_2,V_a_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_scomp__def,axiom,
% 11.25/11.10 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_scomp__unfold,axiom,
% 11.25/11.10 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 11.25/11.10 ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_internal__split__def,axiom,
% 11.25/11.10 ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_transfer__morphism__int__nat,axiom,
% 11.25/11.10 c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 11.25/11.10 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 11.25/11.10 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.25/11.10 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) )
% 11.25/11.10 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.25/11.10 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 11.25/11.10 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 11.25/11.10 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.25/11.10 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) )
% 11.25/11.10 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.25/11.10 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_internal__split__conv,axiom,
% 11.25/11.10 ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 11.25/11.10 ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Oof__frac__def,axiom,
% 11.25/11.10 ! [V_q,T_a,T_b] :
% 11.25/11.10 ( ( class_Rings_Oinverse(T_b)
% 11.25/11.10 & class_Rings_Oring__1(T_b) )
% 11.25/11.10 => c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 11.25/11.10 ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 11.25/11.10 ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 11.25/11.10 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Oless__frac__def,axiom,
% 11.25/11.10 ! [V_r_2,V_q_2,T_b] :
% 11.25/11.10 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 11.25/11.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 11.25/11.10 ! [V_r_2,V_q_2,T_b] :
% 11.25/11.10 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 11.25/11.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 11.25/11.10 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 11.25/11.10 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 11.25/11.10 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_pos__empty__def,axiom,
% 11.25/11.10 ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_neg__bind__def,axiom,
% 11.25/11.10 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 11.25/11.10 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_rev__predicate2D,axiom,
% 11.25/11.10 ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_predicate2D,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 11.25/11.10 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_rev__predicate1D,axiom,
% 11.25/11.10 ! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
% 11.25/11.10 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 11.25/11.10 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_predicate1D,axiom,
% 11.25/11.10 ! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 11.25/11.10 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 11.25/11.10 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_pos__bind__def,axiom,
% 11.25/11.10 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_The__split,axiom,
% 11.25/11.10 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Random_Osimps,axiom,
% 11.25/11.10 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 11.25/11.10 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 11.25/11.10 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) )
% 11.25/11.10 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 11.25/11.10 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_exE__realizer,axiom,
% 11.25/11.10 ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
% 11.25/11.10 => ( ! [B_x,B_y] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x))
% 11.25/11.10 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 11.25/11.10 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_beyond__def,axiom,
% 11.25/11.10 ! [V_l,V_k] :
% 11.25/11.10 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 11.25/11.10 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 11.25/11.10 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 11.25/11.10 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_beyond__zero,axiom,
% 11.25/11.10 ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_The__split__eq,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_split__paired__The,axiom,
% 11.25/11.10 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_divmod__nat__def,axiom,
% 11.25/11.10 ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Random__Sequence_Oempty__def,axiom,
% 11.25/11.10 ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_Random__Sequence_Osingle__def,axiom,
% 11.25/11.10 ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_the__sym__eq__trivial,axiom,
% 11.25/11.10 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 11.25/11.10
% 11.25/11.10 fof(fact_the__eq__trivial,axiom,
% 11.25/11.10 ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ).
% 11.25/11.10
% 11.25/11.10 fof(fact_curry__def,axiom,
% 11.25/11.10 ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_curryI,axiom,
% 11.25/11.10 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 11.25/11.10 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_curryD,axiom,
% 11.25/11.10 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 11.25/11.10 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_curryE,axiom,
% 11.25/11.10 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 11.25/11.10 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_curry__conv,axiom,
% 11.25/11.10 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_split__curry,axiom,
% 11.25/11.10 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2 ).
% 11.25/11.10
% 11.25/11.10 fof(fact_curry__split,axiom,
% 11.25/11.10 ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2 ).
% 11.25/11.10
% 11.25/11.10 fof(fact_power__dvd__imp__le,axiom,
% 11.25/11.10 ! [V_n,V_m,V_i] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_dvd__mult__cancel2,axiom,
% 11.25/11.10 ! [V_n_2,V_m_2] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2))
% 11.25/11.10 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_dvd__mult__cancel1,axiom,
% 11.25/11.10 ! [V_n_2,V_m_2] :
% 11.25/11.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2))
% 11.25/11.10 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_zdvd__mult__cancel1,axiom,
% 11.25/11.10 ! [V_n_2,V_m_2] :
% 11.25/11.10 ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.10 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)),V_m_2))
% 11.25/11.10 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_arith__series__int,axiom,
% 11.25/11.10 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_dvd_Oorder__refl,axiom,
% 11.25/11.10 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_dvd__0__right,axiom,
% 11.25/11.10 ! [V_a,T_a] :
% 11.25/11.10 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_dvd__1__left,axiom,
% 11.25/11.10 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_setsum__abs,axiom,
% 11.25/11.10 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.10 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 11.25/11.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 11.25/11.10
% 11.25/11.10 fof(fact_setsum__abs__ge__zero,axiom,
% 11.25/11.10 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.10 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_div__dvd__div,axiom,
% 11.25/11.11 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__0__left,axiom,
% 11.25/11.11 ! [V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 11.25/11.11 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__add,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_one__dvd,axiom,
% 11.25/11.11 ! [V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__asym,axiom,
% 11.25/11.11 ! [V_y,V_x] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 11.25/11.11 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__trans,axiom,
% 11.25/11.11 ! [V_z,V_y,V_x] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 11.25/11.11 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__asym_H,axiom,
% 11.25/11.11 ! [V_b,V_a] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 11.25/11.11 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__le__trans,axiom,
% 11.25/11.11 ! [V_z,V_y,V_x] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 11.25/11.11 => ( V_b = V_c
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 11.25/11.11 ! [V_y,V_x] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 11.25/11.11 => V_y != V_x ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 11.25/11.11 ! [V_y,V_x] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 11.25/11.11 => V_x != V_y ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__imp__not__less,axiom,
% 11.25/11.11 ! [V_y,V_x] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 11.25/11.11 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__imp__le,axiom,
% 11.25/11.11 ! [V_y,V_x] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__not__sym,axiom,
% 11.25/11.11 ! [V_y,V_x] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 11.25/11.11 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__imp__neq,axiom,
% 11.25/11.11 ! [V_y,V_x] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 11.25/11.11 => V_x != V_y ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Ole__less__trans,axiom,
% 11.25/11.11 ! [V_z,V_y,V_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a] :
% 11.25/11.11 ( V_a = V_b
% 11.25/11.11 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oorder__trans,axiom,
% 11.25/11.11 ! [V_z,V_y,V_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oantisym,axiom,
% 11.25/11.11 ! [V_y,V_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 11.25/11.11 => V_x = V_y ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__antisym,axiom,
% 11.25/11.11 ! [V_n,V_m] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 11.25/11.11 => V_m = V_n ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 11.25/11.11 => ( V_b = V_c
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a] :
% 11.25/11.11 ( V_a = V_b
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Ole__neq__trans,axiom,
% 11.25/11.11 ! [V_b,V_a] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 11.25/11.11 => ( V_a != V_b
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 11.25/11.11 ! [V_y,V_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 11.25/11.11 | V_x = V_y ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oantisym__conv,axiom,
% 11.25/11.11 ! [V_x_2,V_y_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.11 <=> V_x_2 = V_y_2 ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oeq__refl,axiom,
% 11.25/11.11 ! [V_y,V_x] :
% 11.25/11.11 ( V_x = V_y
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oneq__le__trans,axiom,
% 11.25/11.11 ! [V_b,V_a] :
% 11.25/11.11 ( V_a != V_b
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oless__le,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 11.25/11.11 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.11 & V_x_2 != V_y_2 ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Ole__less,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.11 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 11.25/11.11 | V_x_2 = V_y_2 ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Oeq__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2] :
% 11.25/11.11 ( V_x_2 = V_y_2
% 11.25/11.11 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_lessThan__eq__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 11.25/11.11 <=> V_x_2 = V_y_2 ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__trans,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__refl,axiom,
% 11.25/11.11 ! [V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__power__same,axiom,
% 11.25/11.11 ! [V_n,V_y,V_x,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mod__iff,axiom,
% 11.25/11.11 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_mod__mod__cancel,axiom,
% 11.25/11.11 ! [V_a,V_b,V_c,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 11.25/11.11 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mod,axiom,
% 11.25/11.11 ! [V_n,V_m,V_k,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mod__imp__dvd,axiom,
% 11.25/11.11 ! [V_n,V_m,V_k,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__int,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__int__nat__relations_I4_J,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mult__right,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mult__left,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvdI,axiom,
% 11.25/11.11 ! [V_k,V_b,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Odvd(T_a)
% 11.25/11.11 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_mult__dvd__mono,axiom,
% 11.25/11.11 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mult,axiom,
% 11.25/11.11 ! [V_b,V_c,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mult2,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__triv__right,axiom,
% 11.25/11.11 ! [V_b,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__triv__left,axiom,
% 11.25/11.11 ! [V_b,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__abs__iff,axiom,
% 11.25/11.11 ! [V_k_2,V_m_2,T_b] :
% 11.25/11.11 ( class_Rings_Olinordered__idom(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_abs__dvd__iff,axiom,
% 11.25/11.11 ! [V_k_2,V_m_2,T_b] :
% 11.25/11.11 ( class_Rings_Olinordered__idom(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__if__abs__eq,axiom,
% 11.25/11.11 ! [V_k,V_l,T_a] :
% 11.25/11.11 ( class_Rings_Olinordered__idom(T_a)
% 11.25/11.11 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__diff__nat,axiom,
% 11.25/11.11 ! [V_n,V_m,V_k] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__zmod,axiom,
% 11.25/11.11 ! [V_n,V_m,V_f] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__zmod__imp__zdvd,axiom,
% 11.25/11.11 ! [V_n,V_m,V_k] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_uminus__dvd__conv_I1_J,axiom,
% 11.25/11.11 ! [V_t_2,V_d_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_uminus__dvd__conv_I2_J,axiom,
% 11.25/11.11 ! [V_t_2,V_d_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__zdiffD,axiom,
% 11.25/11.11 ! [V_n,V_m,V_k] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),V_n)))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__reduce,axiom,
% 11.25/11.11 ! [V_n_2,V_k_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_of__nat__setsum,axiom,
% 11.25/11.11 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Rings_Osemiring__1(T_b)
% 11.25/11.11 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__diff,axiom,
% 11.25/11.11 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__ring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_minus__dvd__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Rings_Ocomm__ring__1(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__minus__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Rings_Ocomm__ring__1(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__lessThan__Suc,axiom,
% 11.25/11.11 ! [V_n_2,V_f_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_of__int__setsum,axiom,
% 11.25/11.11 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Rings_Oring__1(T_b)
% 11.25/11.11 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_nat__dvd__1__iff__1,axiom,
% 11.25/11.11 ! [V_m_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 11.25/11.11 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__commute,axiom,
% 11.25/11.11 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__antisym__abs,axiom,
% 11.25/11.11 ! [V_b,V_a] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a))
% 11.25/11.11 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__0,axiom,
% 11.25/11.11 ! [V_A_2,T_c,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__addf,axiom,
% 11.25/11.11 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__product,axiom,
% 11.25/11.11 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Rings_Osemiring__0(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__left__distrib,axiom,
% 11.25/11.11 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Rings_Osemiring__0(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__right__distrib,axiom,
% 11.25/11.11 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 11.25/11.11 ( class_Rings_Osemiring__0(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__subtractf,axiom,
% 11.25/11.11 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Groups_Oab__group__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__negf,axiom,
% 11.25/11.11 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Groups_Oab__group__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__divide__distrib,axiom,
% 11.25/11.11 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Fields_Ofield(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_abs__setsum__abs,axiom,
% 11.25/11.11 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 11.25/11.11 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__nat__int__relations_I4_J,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__int__iff,axiom,
% 11.25/11.11 ! [V_m_2,V_z_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))),V_m_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_int__dvd__iff,axiom,
% 11.25/11.11 ! [V_z_2,V_m_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_lessThan__subset__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mult__cancel__left,axiom,
% 11.25/11.11 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 11.25/11.11 ( class_Rings_Oidom(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 11.25/11.11 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.25/11.11 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mult__cancel__right,axiom,
% 11.25/11.11 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Rings_Oidom(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 11.25/11.11 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 11.25/11.11 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__imp__mod__0,axiom,
% 11.25/11.11 ! [V_b,V_a,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 11.25/11.11 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__eq__mod__eq__0,axiom,
% 11.25/11.11 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 11.25/11.11 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_lessThan__strict__subset__iff,axiom,
% 11.25/11.11 ! [V_n_2,V_m_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_div__add,axiom,
% 11.25/11.11 ! [V_y,V_x,V_z,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 11.25/11.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_div__mult__div__if__dvd,axiom,
% 11.25/11.11 ! [V_w,V_z,V_x,V_y,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__div__mult,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__div__mult__self,axiom,
% 11.25/11.11 ! [V_b,V_a,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_div__mult__swap,axiom,
% 11.25/11.11 ! [V_a,V_b,V_c,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mult__div__cancel,axiom,
% 11.25/11.11 ! [V_b,V_a,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__neg__div,axiom,
% 11.25/11.11 ! [V_x,V_y,T_a] :
% 11.25/11.11 ( class_Divides_Oring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 11.25/11.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__div__neg,axiom,
% 11.25/11.11 ! [V_x,V_y,T_a] :
% 11.25/11.11 ( class_Divides_Oring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 11.25/11.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_le__imp__power__dvd,axiom,
% 11.25/11.11 ! [V_a,V_n,V_m,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__power__le,axiom,
% 11.25/11.11 ! [V_m,V_n,V_y,V_x,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_power__le__dvd,axiom,
% 11.25/11.11 ! [V_m,V_b,V_n,V_a,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_div__power,axiom,
% 11.25/11.11 ! [V_n,V_x,V_y,T_a] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 11.25/11.11 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__antisym__nonneg,axiom,
% 11.25/11.11 ! [V_n,V_m] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 11.25/11.11 => V_m = V_n ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__not__zless,axiom,
% 11.25/11.11 ! [V_n,V_m] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n))
% 11.25/11.11 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__mono,axiom,
% 11.25/11.11 ! [V_t_2,V_m_2,V_k_2] :
% 11.25/11.11 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__mult__cancel,axiom,
% 11.25/11.11 ! [V_n,V_m,V_k] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)))
% 11.25/11.11 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__period,axiom,
% 11.25/11.11 ! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__reduce,axiom,
% 11.25/11.11 ! [V_m_2,V_n_2,V_k_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__1__iff__1,axiom,
% 11.25/11.11 ! [V_m_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 11.25/11.11 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_nat__dvd__not__less,axiom,
% 11.25/11.11 ! [V_n,V_m] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 11.25/11.11 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 11.25/11.11 ! [V_n_2,V_m_2,V_k_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 11.25/11.11 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.11 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__mult__div__cancel,axiom,
% 11.25/11.11 ! [V_m,V_n] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = V_m ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zmod__eq__dvd__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_n_2,V_x_2] :
% 11.25/11.11 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__diffD,axiom,
% 11.25/11.11 ! [V_n,V_m,V_k] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__diffD1,axiom,
% 11.25/11.11 ! [V_n,V_m,V_k] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd1__eq,axiom,
% 11.25/11.11 ! [V_x_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 11.25/11.11 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_abs__div,axiom,
% 11.25/11.11 ! [V_x,V_y] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x))
% 11.25/11.11 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_nat__dvd__iff,axiom,
% 11.25/11.11 ! [V_m_2,V_z_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2))
% 11.25/11.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) )
% 11.25/11.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 11.25/11.11 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_arith__series__general,axiom,
% 11.25/11.11 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_unity__coeff__ex,axiom,
% 11.25/11.11 ! [V_l_2,V_Pa_2,T_b] :
% 11.25/11.11 ( ( class_Rings_Odvd(T_b)
% 11.25/11.11 & class_Rings_Osemiring__0(T_b) )
% 11.25/11.11 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 11.25/11.11 <=> ? [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b))))
% 11.25/11.11 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_inf__period_I4_J,axiom,
% 11.25/11.11 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 11.25/11.11 ( ( class_Rings_Ocomm__ring(T_b)
% 11.25/11.11 & class_Rings_Odvd(T_b) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 11.25/11.11 => ! [B_x,B_k] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_inf__period_I3_J,axiom,
% 11.25/11.11 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 11.25/11.11 ( ( class_Rings_Ocomm__ring(T_b)
% 11.25/11.11 & class_Rings_Odvd(T_b) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 11.25/11.11 => ! [B_x,B_k] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( ( class_Divides_Osemiring__div(T_b)
% 11.25/11.11 & class_Int_Onumber(T_b) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 11.25/11.11 <=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__div__div__eq__mult,axiom,
% 11.25/11.11 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_b)
% 11.25/11.11 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.25/11.11 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
% 11.25/11.11 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
% 11.25/11.11 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__div__eq__mult,axiom,
% 11.25/11.11 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Divides_Osemiring__div(T_b)
% 11.25/11.11 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 11.25/11.11 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
% 11.25/11.11 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__imp__le,axiom,
% 11.25/11.11 ! [V_n,V_z] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2)))
% 11.25/11.11 <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__imp__le,axiom,
% 11.25/11.11 ! [V_n,V_k] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__mult__cancel,axiom,
% 11.25/11.11 ! [V_n,V_m,V_k] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_nat__mult__dvd__cancel1,axiom,
% 11.25/11.11 ! [V_n_2,V_m_2,V_k_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__imp__le__int,axiom,
% 11.25/11.11 ! [V_d,V_i] :
% 11.25/11.11 ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_d)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd__power,axiom,
% 11.25/11.11 ! [V_x,V_n,T_a] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.25/11.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 11.25/11.11 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Ostrict__monoD,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 11.25/11.11 ( class_Orderings_Oorder(T_b)
% 11.25/11.11 => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
% 11.25/11.11 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_arith__series__nat,axiom,
% 11.25/11.11 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_OmonoD,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 11.25/11.11 ( class_Orderings_Oorder(T_b)
% 11.25/11.11 => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__natinterval__difff,axiom,
% 11.25/11.11 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 11.25/11.11 ( class_Groups_Oab__group__add(T_b)
% 11.25/11.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 11.25/11.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_gauss__sum,axiom,
% 11.25/11.11 ! [V_n_2,T_b] :
% 11.25/11.11 ( class_Rings_Ocomm__semiring__1(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 11.25/11.11 ! [V_k_2,V_f_2] :
% 11.25/11.11 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Ostrict__mono__mono,axiom,
% 11.25/11.11 ! [V_f_2,T_b] :
% 11.25/11.11 ( class_Orderings_Oorder(T_b)
% 11.25/11.11 => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
% 11.25/11.11 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastatMost__subset__iff,axiom,
% 11.25/11.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Orderings_Oorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
% 11.25/11.11 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 11.25/11.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 11.25/11.11 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 11.25/11.11 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_int__setsum,axiom,
% 11.25/11.11 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 11.25/11.11 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastatMost__psubset__iff,axiom,
% 11.25/11.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Orderings_Oorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
% 11.25/11.11 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 11.25/11.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 11.25/11.11 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 11.25/11.11 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__head__Suc,axiom,
% 11.25/11.11 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__cl__ivl__Suc,axiom,
% 11.25/11.11 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 11.25/11.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__ub__add__nat,axiom,
% 11.25/11.11 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ex__nat__less,axiom,
% 11.25/11.11 ! [V_Pa_2,V_n_2] :
% 11.25/11.11 ( ? [B_m] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 11.25/11.11 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 11.25/11.11 <=> ? [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)))
% 11.25/11.11 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_all__nat__less,axiom,
% 11.25/11.11 ! [V_Pa_2,V_n_2] :
% 11.25/11.11 ( ! [B_m] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 11.25/11.11 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 11.25/11.11 <=> ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)))
% 11.25/11.11 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sum__diff__distrib,axiom,
% 11.25/11.11 ! [V_n_2,V_Pa_2,V_Qa_2] :
% 11.25/11.11 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_Pa_2,B_x)))
% 11.25/11.11 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Pa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Qa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_Pa_2)),V_Qa_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_geometric__sum,axiom,
% 11.25/11.11 ! [V_n_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Fields_Ofield(T_b)
% 11.25/11.11 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ex__nat__less__eq,axiom,
% 11.25/11.11 ! [V_Pa_2,V_n_2] :
% 11.25/11.11 ( ? [B_m] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 11.25/11.11 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 11.25/11.11 <=> ? [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
% 11.25/11.11 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_all__nat__less__eq,axiom,
% 11.25/11.11 ! [V_Pa_2,V_n_2] :
% 11.25/11.11 ( ! [B_m] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 11.25/11.11 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 11.25/11.11 <=> ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
% 11.25/11.11 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastLessThan__eq__iff,axiom,
% 11.25/11.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 11.25/11.11 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 11.25/11.11 <=> ( V_a_2 = V_c_2
% 11.25/11.11 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 11.25/11.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 11.25/11.11 => V_a_2 = V_c_2 ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 11.25/11.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 11.25/11.11 => V_b_2 = V_d_2 ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeast0LessThan,axiom,
% 11.25/11.11 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastLessThan__subset__iff,axiom,
% 11.25/11.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 11.25/11.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 11.25/11.11 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 11.25/11.11 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__diff,axiom,
% 11.25/11.11 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 11.25/11.11 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__add__nat__ivl,axiom,
% 11.25/11.11 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 11.25/11.11 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__diff__nat__ivl,axiom,
% 11.25/11.11 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 11.25/11.11 ( class_Groups_Oab__group__add(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 11.25/11.11 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 11.25/11.11 ! [V_k_2,V_f_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__head__upt__Suc,axiom,
% 11.25/11.11 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__op__ivl__Suc,axiom,
% 11.25/11.11 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 11.25/11.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_aset_I8_J,axiom,
% 11.25/11.11 ! [V_t_2,V_A_2,V_D_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.11 => ! [B_x] :
% 11.25/11.11 ( ! [B_xa] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.11 => ! [B_xb] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 11.25/11.11 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_bset_I6_J,axiom,
% 11.25/11.11 ! [V_t_2,V_B_2,V_D_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.11 => ! [B_x] :
% 11.25/11.11 ( ! [B_xa] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.11 => ! [B_xb] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 11.25/11.11 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_periodic__finite__ex,axiom,
% 11.25/11.11 ! [V_Pa_2,V_d_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 11.25/11.11 => ( ! [B_x,B_k] :
% 11.25/11.11 ( hBOOL(hAPP(V_Pa_2,B_x))
% 11.25/11.11 <=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
% 11.25/11.11 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 11.25/11.11 <=> ? [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2)))
% 11.25/11.11 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_bset_I5_J,axiom,
% 11.25/11.11 ! [V_t_2,V_B_2,V_D_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.11 => ! [B_x] :
% 11.25/11.11 ( ! [B_xa] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.11 => ! [B_xb] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 11.25/11.11 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_aset_I7_J,axiom,
% 11.25/11.11 ! [V_t_2,V_A_2,V_D_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.11 => ! [B_x] :
% 11.25/11.11 ( ! [B_xa] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.11 => ! [B_xb] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 11.25/11.11 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_bset_I9_J,axiom,
% 11.25/11.11 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 11.25/11.11 => ! [B_x] :
% 11.25/11.11 ( ! [B_xa] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.11 => ! [B_xb] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 11.25/11.11 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_aset_I9_J,axiom,
% 11.25/11.11 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 11.25/11.11 => ! [B_x] :
% 11.25/11.11 ( ! [B_xa] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.11 => ! [B_xb] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 11.25/11.11 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_bset_I10_J,axiom,
% 11.25/11.11 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 11.25/11.11 => ! [B_x] :
% 11.25/11.11 ( ! [B_xa] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.11 => ! [B_xb] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 11.25/11.11 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.11 => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 11.25/11.11 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_aset_I10_J,axiom,
% 11.25/11.11 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 11.25/11.11 => ! [B_x] :
% 11.25/11.11 ( ! [B_xa] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.11 => ! [B_xb] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 11.25/11.11 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.11 => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 11.25/11.11 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 11.25/11.11 ! [V_u_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 11.25/11.11 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__head,axiom,
% 11.25/11.11 ! [V_Pa_2,V_n_2,V_m_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_Ostrict__monoI,axiom,
% 11.25/11.11 ! [V_f_2,T_b] :
% 11.25/11.11 ( class_Orderings_Oorder(T_b)
% 11.25/11.11 => ( ! [B_x,B_y] :
% 11.25/11.11 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x)) )
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 11.25/11.11 => c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.25/11.11 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__uminus__atLeastLessThan,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.25/11.11 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__image,axiom,
% 11.25/11.11 ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2] :
% 11.25/11.11 ( V_A_2 = V_B_2
% 11.25/11.11 <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_subset__image__iff,axiom,
% 11.25/11.11 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 11.25/11.11 <=> ? [B_AA] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 11.25/11.11 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__mono,axiom,
% 11.25/11.11 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__diff__subset,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__uminus__atLeastAtMost,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.25/11.11 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 11.25/11.11 ! [V_A_2,V_f_2,T_b] :
% 11.25/11.11 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 & class_Groups_Ocomm__monoid__mult(T_b) )
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 11.25/11.11 ! [V_n_2,V_m_2] :
% 11.25/11.11 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 11.25/11.11 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 11.25/11.11 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__SucD,axiom,
% 11.25/11.11 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 11.25/11.11 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
% 11.25/11.11 => ? [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__ivl__cong,axiom,
% 11.25/11.11 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 11.25/11.11 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.11 & class_Orderings_Oord(T_b) )
% 11.25/11.11 => ( V_a_2 = V_c_2
% 11.25/11.11 => ( V_b_2 = V_d_2
% 11.25/11.11 => ( ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 11.25/11.11 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__atLeastAtMost__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__uminus__greaterThan,axiom,
% 11.25/11.11 ! [V_x_2,T_b] :
% 11.25/11.11 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.25/11.11 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__greaterThanAtMost__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_greaterThan__eq__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 11.25/11.11 <=> V_x_2 = V_y_2 ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__Suc__atLeastLessThan,axiom,
% 11.25/11.11 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__Suc__atLeastAtMost,axiom,
% 11.25/11.11 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__add__atLeastLessThan,axiom,
% 11.25/11.11 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__add__atLeastAtMost,axiom,
% 11.25/11.11 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__eq__setsum,axiom,
% 11.25/11.11 ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 11.25/11.11 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ).
% 11.25/11.11
% 11.25/11.11 fof(fact_greaterThan__subset__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__constant,axiom,
% 11.25/11.11 ! [V_A_2,V_y_2,T_c,T_b] :
% 11.25/11.11 ( class_Rings_Osemiring__1(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 11.25/11.11 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__atLeastLessThan__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 11.25/11.11 ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__add__int__atLeastLessThan,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__uminus__lessThan,axiom,
% 11.25/11.11 ! [V_x_2,T_b] :
% 11.25/11.11 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.25/11.11 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__greaterThanLessThan__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 11.25/11.11 ! [V_f_2,V_A_2,T_b] :
% 11.25/11.11 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 & class_Groups_Ocomm__monoid__mult(T_b) )
% 11.25/11.11 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2] :
% 11.25/11.11 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.11 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2] :
% 11.25/11.11 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.11 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 11.25/11.11 ! [V_A_2] :
% 11.25/11.11 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.11 => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__lessThan,axiom,
% 11.25/11.11 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2 ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2] :
% 11.25/11.11 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.11 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 11.25/11.11 => ( V_A_2 = V_B_2
% 11.25/11.11 <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__atLeastLessThan,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__greaterThanAtMost,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_nat__set__def,axiom,
% 11.25/11.11 ! [V_S_2] :
% 11.25/11.11 ( c_Nat__Transfer_Onat__set(V_S_2)
% 11.25/11.11 <=> ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.25/11.11 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 11.25/11.11 ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2] :
% 11.25/11.11 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 11.25/11.11 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__atLeastAtMost,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 11.25/11.11 ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_subset__card__intvl__is__intvl,axiom,
% 11.25/11.11 ! [V_k_2,V_A_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2)))))
% 11.25/11.11 => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 11.25/11.11 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 11.25/11.11 ! [V_A_2] :
% 11.25/11.11 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.11 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 11.25/11.11 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 11.25/11.11 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 11.25/11.11 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 & class_Groups_Ocomm__monoid__mult(T_b) )
% 11.25/11.11 => ( V_A_2 = V_B_2
% 11.25/11.11 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 11.25/11.11 => ( ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 11.25/11.11 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I19_J,axiom,
% 11.25/11.11 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I18_J,axiom,
% 11.25/11.11 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup1CI,axiom,
% 11.25/11.11 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 11.25/11.11 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 11.25/11.11 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 11.25/11.11 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup1E,axiom,
% 11.25/11.11 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 11.25/11.11 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 11.25/11.11 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I9_J,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__Un,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2] :
% 11.25/11.11 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.11 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 11.25/11.11 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup1I2,axiom,
% 11.25/11.11 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 11.25/11.11 ( hBOOL(hAPP(V_B_2,V_x_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup1I1,axiom,
% 11.25/11.11 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 11.25/11.11 ( hBOOL(hAPP(V_A_2,V_x_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ball__Un,axiom,
% 11.25/11.11 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 11.25/11.11 ( ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.11 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 11.25/11.11 <=> ( ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.11 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 11.25/11.11 & ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 11.25/11.11 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_bex__Un,axiom,
% 11.25/11.11 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 11.25/11.11 ( ? [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.11 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 11.25/11.11 <=> ( ? [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.11 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 11.25/11.11 | ? [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 11.25/11.11 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__assoc,axiom,
% 11.25/11.11 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__left__commute,axiom,
% 11.25/11.11 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__left__absorb,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__commute,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__absorb,axiom,
% 11.25/11.11 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__apply,axiom,
% 11.25/11.11 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Lattices_Olattice(T_b)
% 11.25/11.11 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__assoc,axiom,
% 11.25/11.11 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_inf__sup__aci_I6_J,axiom,
% 11.25/11.11 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Olattice(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup_Oassoc,axiom,
% 11.25/11.11 ! [V_c,V_b,V_a,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__left__commute,axiom,
% 11.25/11.11 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_inf__sup__aci_I7_J,axiom,
% 11.25/11.11 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Olattice(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup_Oleft__commute,axiom,
% 11.25/11.11 ! [V_c,V_a,V_b,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__left__idem,axiom,
% 11.25/11.11 ! [V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_inf__sup__aci_I8_J,axiom,
% 11.25/11.11 ! [V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Olattice(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup_Oleft__idem,axiom,
% 11.25/11.11 ! [V_b,V_a,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__commute,axiom,
% 11.25/11.11 ! [V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_inf__sup__aci_I5_J,axiom,
% 11.25/11.11 ! [V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Olattice(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup_Ocommute,axiom,
% 11.25/11.11 ! [V_b,V_a,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__idem,axiom,
% 11.25/11.11 ! [V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup_Oidem,axiom,
% 11.25/11.11 ! [V_a,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__fun__def,axiom,
% 11.25/11.11 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 11.25/11.11 ( class_Lattices_Olattice(T_b)
% 11.25/11.11 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__Diff,axiom,
% 11.25/11.11 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__Diff__cancel2,axiom,
% 11.25/11.11 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__Diff__cancel,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Sup__fin_Oidem,axiom,
% 11.25/11.11 ! [V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Olattice(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__max,axiom,
% 11.25/11.11 ! [T_b] :
% 11.25/11.11 ( ( class_Lattices_Osemilattice__sup(T_b)
% 11.25/11.11 & class_Orderings_Olinorder(T_b) )
% 11.25/11.11 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atMost__eq__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 11.25/11.11 <=> V_x_2 = V_y_2 ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_less__supI1,axiom,
% 11.25/11.11 ! [V_b,V_a,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_less__supI2,axiom,
% 11.25/11.11 ! [V_a,V_b,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__upper1,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__upper2,axiom,
% 11.25/11.11 ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_subset__Un__eq,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.11 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__absorb1,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__absorb2,axiom,
% 11.25/11.11 ! [V_A_2,V_B_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__least,axiom,
% 11.25/11.11 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__mono,axiom,
% 11.25/11.11 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_le__supE,axiom,
% 11.25/11.11 ! [V_x,V_b,V_a,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
% 11.25/11.11 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 11.25/11.11 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__mono,axiom,
% 11.25/11.11 ! [V_d,V_b,V_c,V_a,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__least,axiom,
% 11.25/11.11 ! [V_z,V_x,V_y,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_le__supI,axiom,
% 11.25/11.11 ! [V_b,V_x,V_a,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__absorb1,axiom,
% 11.25/11.11 ! [V_x,V_y,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__absorb2,axiom,
% 11.25/11.11 ! [V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_le__supI2,axiom,
% 11.25/11.11 ! [V_a,V_b,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_le__supI1,axiom,
% 11.25/11.11 ! [V_b,V_a,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_le__sup__iff,axiom,
% 11.25/11.11 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
% 11.25/11.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_le__iff__sup,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.25/11.11 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__ge2,axiom,
% 11.25/11.11 ! [V_x,V_y,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_inf__sup__ord_I4_J,axiom,
% 11.25/11.11 ! [V_x,V_y,T_a] :
% 11.25/11.11 ( class_Lattices_Olattice(T_a)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__ge1,axiom,
% 11.25/11.11 ! [V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Osemilattice__sup(T_a)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_inf__sup__ord_I3_J,axiom,
% 11.25/11.11 ! [V_y,V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Olattice(T_a)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__atMost,axiom,
% 11.25/11.11 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I10_J,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I7_J,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I17_J,axiom,
% 11.25/11.11 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Diff__subset__conv,axiom,
% 11.25/11.11 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Diff__partition,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I20_J,axiom,
% 11.25/11.11 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Compl__Diff__eq,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2] :
% 11.25/11.11 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.11 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeast0AtMost,axiom,
% 11.25/11.11 ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__greaterThanLessThan,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_lessThan__Suc__atMost,axiom,
% 11.25/11.11 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atMost__subset__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Orderings_Oorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I21_J,axiom,
% 11.25/11.11 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastLessThan__add__Un,axiom,
% 11.25/11.11 ! [V_k_2,V_j_2,V_i_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 11.25/11.11 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I8_J,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I22_J,axiom,
% 11.25/11.11 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I11_J,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Compl__greaterThan,axiom,
% 11.25/11.11 ! [V_k_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Compl__atMost,axiom,
% 11.25/11.11 ! [V_k_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I15_J,axiom,
% 11.25/11.11 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I16_J,axiom,
% 11.25/11.11 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__atMost__Suc,axiom,
% 11.25/11.11 ! [V_n_2,V_f_2,T_b] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I12_J,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I13_J,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__le__eq__Un0,axiom,
% 11.25/11.11 ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
% 11.25/11.11 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 11.25/11.11 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 11.25/11.11 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 11.25/11.11 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2)) )
% 11.25/11.11 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 11.25/11.11 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)) ) ) ) )
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__nat__def,axiom,
% 11.25/11.11 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeast__eq__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 11.25/11.11 <=> V_x_2 = V_y_2 ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_SUP1__iff,axiom,
% 11.25/11.11 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 11.25/11.11 <=> ? [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.11 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeast__Suc__greaterThan,axiom,
% 11.25/11.11 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeast__subset__iff,axiom,
% 11.25/11.11 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.11 ( class_Orderings_Oorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
% 11.25/11.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Compl__lessThan,axiom,
% 11.25/11.11 ! [V_k_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Compl__atLeast,axiom,
% 11.25/11.11 ! [V_k_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__le__add__shift,axiom,
% 11.25/11.11 ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ivl__disj__un_I14_J,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.11 ( class_Orderings_Olinorder(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
% 11.25/11.11 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 11.25/11.11 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 11.25/11.11 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__uminus__atMost,axiom,
% 11.25/11.11 ! [V_x_2,T_b] :
% 11.25/11.11 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.25/11.11 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__uminus__atLeast,axiom,
% 11.25/11.11 ! [V_x_2,T_b] :
% 11.25/11.11 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.25/11.11 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_SUP__subset,axiom,
% 11.25/11.11 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.11 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__simps_I6_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__extend__simps_I6_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_SUPR__apply,axiom,
% 11.25/11.11 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 11.25/11.11 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.25/11.11 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_ball__UN,axiom,
% 11.25/11.11 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.11 ( ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.11 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 11.25/11.11 <=> ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.25/11.11 => ! [B_xa] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 11.25/11.11 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_SUP__commute,axiom,
% 11.25/11.11 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 11.25/11.11 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.25/11.11 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__extend__simps_I9_J,axiom,
% 11.25/11.11 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__simps_I9_J,axiom,
% 11.25/11.11 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__UN__flatten,axiom,
% 11.25/11.11 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_SUP__le__iff,axiom,
% 11.25/11.11 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 11.25/11.11 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
% 11.25/11.11 <=> ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_less__SUP__iff,axiom,
% 11.25/11.11 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 11.25/11.11 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.25/11.11 & class_Orderings_Olinorder(T_b) )
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
% 11.25/11.11 <=> ? [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.25/11.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__subset__iff,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
% 11.25/11.11 <=> ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__simps_I10_J,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__UN,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__extend__simps_I10_J,axiom,
% 11.25/11.11 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__Un,axiom,
% 11.25/11.11 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__Un__distrib,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_greaterThan__0,axiom,
% 11.25/11.11 hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_dvd_OmonoI,axiom,
% 11.25/11.11 ! [V_f_2,T_b] :
% 11.25/11.11 ( class_Orderings_Oorder(T_b)
% 11.25/11.11 => ( ! [B_x,B_y] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 11.25/11.11 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_upto_Opinduct,axiom,
% 11.25/11.11 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 11.25/11.11 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 11.25/11.11 => ( ! [B_i,B_j] :
% 11.25/11.11 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j)))
% 11.25/11.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 11.25/11.11 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 11.25/11.11 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) )
% 11.25/11.11 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__ident,axiom,
% 11.25/11.11 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 11.25/11.11
% 11.25/11.11 fof(fact_top1I,axiom,
% 11.25/11.11 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__UNIV__right,axiom,
% 11.25/11.11 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__UNIV__left,axiom,
% 11.25/11.11 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_subset__UNIV,axiom,
% 11.25/11.11 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_top__apply,axiom,
% 11.25/11.11 ! [V_x_2,T_c,T_b] :
% 11.25/11.11 ( class_Orderings_Otop(T_b)
% 11.25/11.11 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_range__composition,axiom,
% 11.25/11.11 ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_top__greatest,axiom,
% 11.25/11.11 ! [V_x,T_a] :
% 11.25/11.11 ( class_Orderings_Otop(T_a)
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__top__left,axiom,
% 11.25/11.11 ! [V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Obounded__lattice__top(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__top__right,axiom,
% 11.25/11.11 ! [V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Obounded__lattice__top(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__lessThan__UNIV,axiom,
% 11.25/11.11 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__atMost__UNIV,axiom,
% 11.25/11.11 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__atLeast__UNIV,axiom,
% 11.25/11.11 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_surj__Compl__image__subset,axiom,
% 11.25/11.11 ! [V_A_2,V_f_2,T_b,T_c] :
% 11.25/11.11 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Compl__partition,axiom,
% 11.25/11.11 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Compl__partition2,axiom,
% 11.25/11.11 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 11.25/11.11 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeast__0,axiom,
% 11.25/11.11 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_sup__compl__top,axiom,
% 11.25/11.11 ! [V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Oboolean__algebra(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_compl__sup__top,axiom,
% 11.25/11.11 ! [V_x,T_a] :
% 11.25/11.11 ( class_Lattices_Oboolean__algebra(T_a)
% 11.25/11.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__UN__finite__eq,axiom,
% 11.25/11.11 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__finite2__subset,axiom,
% 11.25/11.11 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 11.25/11.11 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__finite2__eq,axiom,
% 11.25/11.11 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 11.25/11.11 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)
% 11.25/11.11 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__finite__subset,axiom,
% 11.25/11.11 ! [V_C_2,V_A_2,T_b] :
% 11.25/11.11 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_type__definition__code__numeral,axiom,
% 11.25/11.11 c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_card__UNIV__bool,axiom,
% 11.25/11.11 hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_type__definition_OAbs__image,axiom,
% 11.25/11.11 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 11.25/11.11 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 11.25/11.11 => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_type__definition_ORep__range,axiom,
% 11.25/11.11 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 11.25/11.11 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 11.25/11.11 => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 11.25/11.11 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__diff__nat,axiom,
% 11.25/11.11 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__atLeastLessThan,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__atLeastAtMost__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__atLeastAtMost,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__lessThan,axiom,
% 11.25/11.11 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__atMost,axiom,
% 11.25/11.11 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__atLeastLessThan__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__greaterThanAtMost,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__greaterThanAtMost__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__greaterThanLessThan__int,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__greaterThanLessThan,axiom,
% 11.25/11.11 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__insert__left,axiom,
% 11.25/11.11 ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_Un__insert__right,axiom,
% 11.25/11.11 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 11.25/11.11 ! [V_N_2] :
% 11.25/11.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 11.25/11.11 <=> ? [B_m] :
% 11.25/11.11 ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_insert__mono,axiom,
% 11.25/11.11 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_subset__insertI2,axiom,
% 11.25/11.11 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_subset__insertI,axiom,
% 11.25/11.11 ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__nat__set__iff__bounded,axiom,
% 11.25/11.11 ! [V_N_2] :
% 11.25/11.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 11.25/11.11 <=> ? [B_m] :
% 11.25/11.11 ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 11.25/11.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_insert__absorb2,axiom,
% 11.25/11.11 ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_insert__commute,axiom,
% 11.25/11.11 ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_insert__code,axiom,
% 11.25/11.11 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 11.25/11.11 <=> ( V_y_2 = V_x_2
% 11.25/11.11 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_image__insert,axiom,
% 11.25/11.11 ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 11.25/11.11 ! [V_A_2] :
% 11.25/11.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 11.25/11.11 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 11.25/11.11 ! [V_A_2] :
% 11.25/11.11 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 11.25/11.11 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum_Oinfinite,axiom,
% 11.25/11.11 ! [V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.11 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__infinite,axiom,
% 11.25/11.11 ! [V_f_2,V_A_2,T_b,T_c] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.11 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_lessThan__Suc,axiom,
% 11.25/11.11 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atMost__Suc,axiom,
% 11.25/11.11 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum__eq__0__iff,axiom,
% 11.25/11.11 ! [V_f_2,V_F_2,T_b] :
% 11.25/11.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 11.25/11.11 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.11 <=> ! [B_x] :
% 11.25/11.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 11.25/11.11 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_UN__insert,axiom,
% 11.25/11.11 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_setsum_Odistrib,axiom,
% 11.25/11.11 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.11 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 11.25/11.11 ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))) ).
% 11.25/11.11
% 11.25/11.11 fof(fact_atLeastAtMostSuc__conv,axiom,
% 11.25/11.12 ! [V_n_2,V_m_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 11.25/11.12 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__eq__Suc0__iff,axiom,
% 11.25/11.12 ! [V_f_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 11.25/11.12 <=> ? [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.12 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 11.25/11.12 & ! [B_xa] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 11.25/11.12 => ( B_x != B_xa
% 11.25/11.12 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__eq__1__iff,axiom,
% 11.25/11.12 ! [V_f_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 11.25/11.12 <=> ? [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.12 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 11.25/11.12 & ! [B_xa] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 11.25/11.12 => ( B_x != B_xa
% 11.25/11.12 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_type__definition_ORep__inject,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 11.25/11.12 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 11.25/11.12 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 11.25/11.12 <=> V_x_2 = V_y_2 ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_type__definition_ORep__inverse,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 11.25/11.12 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 11.25/11.12 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__diff,axiom,
% 11.25/11.12 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Oab__group__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__psubset,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_diff__card__le__card__Diff,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Diff__subset,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__Diff,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite_OinsertI,axiom,
% 11.25/11.12 ! [V_a_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__imageI,axiom,
% 11.25/11.12 ! [V_h_2,T_c,V_F_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_infinite__UNIV__int,axiom,
% 11.25/11.12 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UNIV__option__conv,axiom,
% 11.25/11.12 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( class_Finite__Set_Ofinite(T_b)
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__code,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( class_Finite__Set_Ofinite(T_b)
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__UNIV__unit,axiom,
% 11.25/11.12 hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_infinite__UNIV__nat,axiom,
% 11.25/11.12 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__insert,axiom,
% 11.25/11.12 ! [V_A_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 11.25/11.12 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__subset,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_rev__finite__subset,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__UNIV,axiom,
% 11.25/11.12 ! [T_b] :
% 11.25/11.12 ( class_Finite__Set_Ofinite(T_b)
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__option__UNIV,axiom,
% 11.25/11.12 ! [T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
% 11.25/11.12 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__Plus__UNIV__iff,axiom,
% 11.25/11.12 ! [T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
% 11.25/11.12 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.12 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__fun__UNIVD2,axiom,
% 11.25/11.12 ! [T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__Prod__UNIV,axiom,
% 11.25/11.12 ! [T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__UnI,axiom,
% 11.25/11.12 ! [V_G_2,V_F_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__Un,axiom,
% 11.25/11.12 ! [V_G_2,V_F_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 11.25/11.12 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__Diff2,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.12 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__UN,axiom,
% 11.25/11.12 ! [V_B_2,T_c,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.12 <=> ! [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__surj,axiom,
% 11.25/11.12 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__Diff__insert,axiom,
% 11.25/11.12 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
% 11.25/11.12 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__infinite,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.12 => ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.12 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__compl,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 11.25/11.12 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__range__imageI,axiom,
% 11.25/11.12 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__ge__0__finite,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__insert__le,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__mono,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__seteq,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 11.25/11.12 => V_A_2 = V_B_2 ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__image__le,axiom,
% 11.25/11.12 ! [V_f_2,T_c,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_psubset__card__mono,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__UNIV__card__ge__0,axiom,
% 11.25/11.12 ! [T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__fun__UNIVD1,axiom,
% 11.25/11.12 ! [T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 11.25/11.12 => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 11.25/11.12 ! [V_x_2,V_y_2,V_c_2] :
% 11.25/11.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 11.25/11.12 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 11.25/11.12 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.12 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 11.25/11.12 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__mono3,axiom,
% 11.25/11.12 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 11.25/11.12 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.12 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => ( ! [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Plus__conv__if,axiom,
% 11.25/11.12 ! [V_B_2,T_c,V_A_2,T_b] :
% 11.25/11.12 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) )
% 11.25/11.12 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite_OemptyI,axiom,
% 11.25/11.12 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_empty__subsetI,axiom,
% 11.25/11.12 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite_Oequations_I1_J,axiom,
% 11.25/11.12 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_empty__not__insert,axiom,
% 11.25/11.12 ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__not__empty,axiom,
% 11.25/11.12 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_doubleton__eq__iff,axiom,
% 11.25/11.12 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.12 <=> ( ( V_a_2 = V_c_2
% 11.25/11.12 & V_b_2 = V_d_2 )
% 11.25/11.12 | ( V_a_2 = V_d_2
% 11.25/11.12 & V_b_2 = V_c_2 ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_singleton__inject,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.12 => V_a_2 = V_b_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Un__empty,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Un__empty__right,axiom,
% 11.25/11.12 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Un__empty__left,axiom,
% 11.25/11.12 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 11.25/11.12
% 11.25/11.12 fof(fact_subset__empty,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.12 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bot__fun__def,axiom,
% 11.25/11.12 ! [V_x_2,T_c,T_b] :
% 11.25/11.12 ( class_Orderings_Obot(T_b)
% 11.25/11.12 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bot__apply,axiom,
% 11.25/11.12 ! [V_x_2,T_c,T_b] :
% 11.25/11.12 ( class_Orderings_Obot(T_b)
% 11.25/11.12 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Plus__eq__empty__conv,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.12 ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
% 11.25/11.12 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_empty__Diff,axiom,
% 11.25/11.12 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Diff__empty,axiom,
% 11.25/11.12 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Diff__cancel,axiom,
% 11.25/11.12 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_image__is__empty,axiom,
% 11.25/11.12 ! [V_A_2,V_f_2,T_b,T_c] :
% 11.25/11.12 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_image__empty,axiom,
% 11.25/11.12 ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_empty__is__image,axiom,
% 11.25/11.12 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.12 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
% 11.25/11.12 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_not__psubset__empty,axiom,
% 11.25/11.12 ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UNIV__not__empty,axiom,
% 11.25/11.12 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bot__least,axiom,
% 11.25/11.12 ! [V_x,T_a] :
% 11.25/11.12 ( class_Orderings_Obot(T_a)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_SUP__const,axiom,
% 11.25/11.12 ! [V_M_2,T_b,V_A_2,T_c] :
% 11.25/11.12 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UNION__empty__conv_I1_J,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.12 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
% 11.25/11.12 <=> ! [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.25/11.12 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__empty2,axiom,
% 11.25/11.12 ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__constant,axiom,
% 11.25/11.12 ! [V_c_2,T_c,T_b,V_A_2] :
% 11.25/11.12 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 11.25/11.12 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UNION__empty__conv_I2_J,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 <=> ! [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.25/11.12 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_sup__bot__left,axiom,
% 11.25/11.12 ! [V_x,T_a] :
% 11.25/11.12 ( class_Lattices_Obounded__lattice__bot(T_a)
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_sup__bot__right,axiom,
% 11.25/11.12 ! [V_x,T_a] :
% 11.25/11.12 ( class_Lattices_Obounded__lattice__bot(T_a)
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_sup__eq__bot__iff,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.12 ( class_Lattices_Obounded__lattice__bot(T_b)
% 11.25/11.12 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 11.25/11.12 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 11.25/11.12 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__Plus__iff,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__Plus,axiom,
% 11.25/11.12 ! [V_B_2,T_c,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__PlusD_I1_J,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_finite__PlusD_I2_J,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 11.25/11.12 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UNIV__Plus__UNIV,axiom,
% 11.25/11.12 ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum_Oempty,axiom,
% 11.25/11.12 ! [V_g_2,T_c,T_b] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__empty,axiom,
% 11.25/11.12 ! [V_f_2,T_c,T_b] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_subset__singletonD,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 11.25/11.12 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__is__Un,axiom,
% 11.25/11.12 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastatMost__empty__iff2,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
% 11.25/11.12 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastatMost__empty__iff,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastatMost__empty,axiom,
% 11.25/11.12 ! [V_a_2,V_b_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 11.25/11.12 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Diff__insert,axiom,
% 11.25/11.12 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Diff__insert2,axiom,
% 11.25/11.12 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__Diff__single,axiom,
% 11.25/11.12 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastLessThan__empty,axiom,
% 11.25/11.12 ! [V_a_2,V_b_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 11.25/11.12 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card_Oempty,axiom,
% 11.25/11.12 ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
% 11.25/11.12 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastLessThan__empty__iff,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Diff__UNIV,axiom,
% 11.25/11.12 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastAtMost__singleton_H,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( V_a_2 = V_b_2
% 11.25/11.12 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 11.25/11.12 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.12 <=> ( V_a_2 = V_b_2
% 11.25/11.12 & V_b_2 = V_c_2 ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastAtMost__singleton,axiom,
% 11.25/11.12 ! [V_a_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_subset__Compl__self__eq,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 11.25/11.12 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Compl__empty__eq,axiom,
% 11.25/11.12 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Compl__UNIV__eq,axiom,
% 11.25/11.12 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastLessThan0,axiom,
% 11.25/11.12 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_greaterThanAtMost__empty,axiom,
% 11.25/11.12 ! [V_k_2,V_l_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 11.25/11.12 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 11.25/11.12 ! [V_l_2,V_k_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
% 11.25/11.12 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 11.25/11.12 ! [V_l_2,V_k_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_greaterThanLessThan__empty,axiom,
% 11.25/11.12 ! [V_k_2,V_l_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 11.25/11.12 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_lessThan__0,axiom,
% 11.25/11.12 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_image__constant__conv,axiom,
% 11.25/11.12 ! [V_c_2,T_c,T_b,V_A_2] :
% 11.25/11.12 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 11.25/11.12 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__simps_I1_J,axiom,
% 11.25/11.12 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 11.25/11.12 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 11.25/11.12 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__singleton,axiom,
% 11.25/11.12 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__extend__simps_I1_J,axiom,
% 11.25/11.12 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 11.25/11.12 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
% 11.25/11.12 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 11.25/11.12 ! [V_a_2,V_b_2] :
% 11.25/11.12 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 11.25/11.12 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
% 11.25/11.12 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2] :
% 11.25/11.12 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 11.25/11.12 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2] :
% 11.25/11.12 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
% 11.25/11.12 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__simps_I3_J,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.25/11.12 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 11.25/11.12 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__simps_I2_J,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.25/11.12 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 11.25/11.12 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__extend__simps_I3_J,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.25/11.12 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 11.25/11.12 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__extend__simps_I2_J,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.25/11.12 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 11.25/11.12 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_compl__top__eq,axiom,
% 11.25/11.12 ! [T_a] :
% 11.25/11.12 ( class_Lattices_Oboolean__algebra(T_a)
% 11.25/11.12 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_compl__bot__eq,axiom,
% 11.25/11.12 ! [T_a] :
% 11.25/11.12 ( class_Lattices_Oboolean__algebra(T_a)
% 11.25/11.12 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__eq__0__iff,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.12 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_single__Diff__lessThan,axiom,
% 11.25/11.12 ! [V_k_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oorder(T_b)
% 11.25/11.12 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_image__eq__UN,axiom,
% 11.25/11.12 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastLessThan__singleton,axiom,
% 11.25/11.12 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atMost__0,axiom,
% 11.25/11.12 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 11.25/11.12 ! [V_c_2,V_b_2,V_a_2] :
% 11.25/11.12 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
% 11.25/11.12 <=> ( V_a_2 = V_b_2
% 11.25/11.12 & V_b_2 = V_c_2 ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 11.25/11.12 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2] :
% 11.25/11.12 ( V_a_2 = V_b_2
% 11.25/11.12 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Plus__def,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_sum(T_b,T_c),c_Sum__Type_OInl(T_b,T_c)),V_A_2)),hAPP(c_Set_Oimage(T_c,tc_sum(T_b,T_c),c_Sum__Type_OInr(T_c,T_b)),V_B_2)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeast__Suc,axiom,
% 11.25/11.12 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_greaterThan__Suc,axiom,
% 11.25/11.12 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__gt__0__iff,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 11.25/11.12 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ivl__disj__un_I2_J,axiom,
% 11.25/11.12 ! [V_u_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeastLessThanSuc,axiom,
% 11.25/11.12 ! [V_n_2,V_m_2] :
% 11.25/11.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.25/11.12 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.25/11.12 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ivl__disj__un_I1_J,axiom,
% 11.25/11.12 ! [V_l_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Plus,axiom,
% 11.25/11.12 ! [V_B_2,T_c,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum_Oinsert__remove,axiom,
% 11.25/11.12 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__insert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Diff1__le,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ivl__disj__un_I6_J,axiom,
% 11.25/11.12 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ivl__disj__un_I5_J,axiom,
% 11.25/11.12 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ivl__disj__un_I3_J,axiom,
% 11.25/11.12 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ivl__disj__un_I4_J,axiom,
% 11.25/11.12 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card_Oinsert__remove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_the__elem__def,axiom,
% 11.25/11.12 ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 11.25/11.12 ! [V_k_2,V_l_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 11.25/11.12 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_the__elem__eq,axiom,
% 11.25/11.12 ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 11.25/11.12 ! [V_x_2,T_b] : c_Option_Oset(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 11.25/11.12 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bot__nat__def,axiom,
% 11.25/11.12 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 11.25/11.12 c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 11.25/11.12 c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_simp__from__to,axiom,
% 11.25/11.12 ! [V_i_2,V_j_2] :
% 11.25/11.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 11.25/11.12 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 11.25/11.12 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_set__empty__eq,axiom,
% 11.25/11.12 ! [V_xo_2,T_b] :
% 11.25/11.12 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 11.25/11.12 ! [T_b] : c_Option_Oset(T_b,c_Option_Ooption_ONone(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_nat__def,axiom,
% 11.25/11.12 ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Diff__singleton__if,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Diff__singleton,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.12 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.12 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_equalityCE,axiom,
% 11.25/11.12 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 11.25/11.12 ( V_A_2 = V_B_2
% 11.25/11.12 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 11.25/11.12 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_SUP2__I,axiom,
% 11.25/11.12 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_emptyE,axiom,
% 11.25/11.12 ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insertCI,axiom,
% 11.25/11.12 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 11.25/11.12 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 11.25/11.12 => V_a_2 = V_b_2 )
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insertE,axiom,
% 11.25/11.12 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 11.25/11.12 => ( V_a_2 != V_b_2
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_subsetD,axiom,
% 11.25/11.12 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UNIV__I,axiom,
% 11.25/11.12 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_image__eqI,axiom,
% 11.25/11.12 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 11.25/11.12 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UnE,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UnCI,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 11.25/11.12 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_DiffE,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.12 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_DiffI,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ComplI,axiom,
% 11.25/11.12 ! [V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_SUP1__I,axiom,
% 11.25/11.12 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__I,axiom,
% 11.25/11.12 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_mem__splitI,axiom,
% 11.25/11.12 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_pair__imageI,axiom,
% 11.25/11.12 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_InrI,axiom,
% 11.25/11.12 ! [V_A_2,T_c,V_B_2,V_b_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(tc_sum(T_c,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_c),V_b_2)),c_Sum__Type_OPlus(T_c,T_b,V_A_2,V_B_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_InlI,axiom,
% 11.25/11.12 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(tc_sum(T_b,T_c)),hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bot__empty__eq2,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_all__not__in__conv,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.12 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ex__in__conv,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.12 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_empty__iff,axiom,
% 11.25/11.12 ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_equals0D,axiom,
% 11.25/11.12 ! [V_a_2,T_b,V_A_2] :
% 11.25/11.12 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_rev__image__eqI,axiom,
% 11.25/11.12 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_imageI,axiom,
% 11.25/11.12 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_image__iff,axiom,
% 11.25/11.12 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 11.25/11.12 <=> ? [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.25/11.12 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 11.25/11.12 ! [V_A_2,V_x_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_DiffD2,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.12 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_DiffD1,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Diff__iff,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Un__iff,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UnI1,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UnI2,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bot__empty__eq,axiom,
% 11.25/11.12 ! [V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 11.25/11.12 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 11.25/11.12 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_pred__equals__eq2,axiom,
% 11.25/11.12 ! [V_S_2,V_R_2,T_c,T_b] :
% 11.25/11.12 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)
% 11.25/11.12 <=> V_R_2 = V_S_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_sup__Un__eq2,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_pred__subset__eq,axiom,
% 11.25/11.12 ! [V_S_2,V_R_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_sup__Un__eq,axiom,
% 11.25/11.12 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_set__mp,axiom,
% 11.25/11.12 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_set__rev__mp,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_in__mono,axiom,
% 11.25/11.12 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Rep__Integ__inject,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2] :
% 11.25/11.12 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 11.25/11.12 <=> V_x_2 = V_y_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_mem__def,axiom,
% 11.25/11.12 ! [V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_eqset__imp__iff,axiom,
% 11.25/11.12 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 11.25/11.12 ( V_A_2 = V_B_2
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_eqelem__imp__iff,axiom,
% 11.25/11.12 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 11.25/11.12 ( V_x_2 = V_y_2
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_eq__mem__trans,axiom,
% 11.25/11.12 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 11.25/11.12 ( V_a_2 = V_b_2
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_eq__mem,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 11.25/11.12 <=> V_x_2 = V_y_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_pred__equals__eq,axiom,
% 11.25/11.12 ! [V_S_2,V_R_2,T_b] :
% 11.25/11.12 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
% 11.25/11.12 <=> V_R_2 = V_S_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Compl__iff,axiom,
% 11.25/11.12 ! [V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 11.25/11.12 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ComplD,axiom,
% 11.25/11.12 ! [V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 11.25/11.12 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ComplE,axiom,
% 11.25/11.12 ! [V_A_2,V_c_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 11.25/11.12 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_psubsetD,axiom,
% 11.25/11.12 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_type__definition_OAbs__inject,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 11.25/11.12 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 11.25/11.12 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 11.25/11.12 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_type__definition_OAbs__inverse,axiom,
% 11.25/11.12 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 11.25/11.12 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 11.25/11.12 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_type__definition_ORep,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 11.25/11.12 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__absorb,axiom,
% 11.25/11.12 ! [V_A_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insertI2,axiom,
% 11.25/11.12 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__ident,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 11.25/11.12 => ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
% 11.25/11.12 <=> V_A_2 = V_B_2 ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__iff,axiom,
% 11.25/11.12 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 11.25/11.12 <=> ( V_a_2 = V_b_2
% 11.25/11.12 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insertI1,axiom,
% 11.25/11.12 ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_folding__image__simple_Oinsert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.12 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__iff,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.12 <=> ? [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.25/11.12 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_folding__image__simple_Oempty,axiom,
% 11.25/11.12 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.12 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.25/11.12 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_singleton__iff,axiom,
% 11.25/11.12 ! [V_a_2,V_b_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 11.25/11.12 <=> V_b_2 = V_a_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_singletonE,axiom,
% 11.25/11.12 ! [V_a_2,V_b_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 11.25/11.12 => V_b_2 = V_a_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_subset__insert,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__subset,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 11.25/11.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__image,axiom,
% 11.25/11.12 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_range__eqI,axiom,
% 11.25/11.12 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 11.25/11.12 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_rangeI,axiom,
% 11.25/11.12 ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__Diff__if,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 11.25/11.12 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 11.25/11.12 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 11.25/11.12 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__Diff1,axiom,
% 11.25/11.12 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 11.25/11.12 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_lessThan__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_i_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oord(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 11.25/11.12 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 11.25/11.12 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 11.25/11.12 ! [V_A_2,V_x_2] :
% 11.25/11.12 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 11.25/11.12 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atMost__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_i_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oord(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_atLeast__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_i_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oord(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_greaterThan__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_i_2,T_b] :
% 11.25/11.12 ( class_Orderings_Oord(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 11.25/11.12 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 11.25/11.12 <=> V_x_2 = V_y_2 ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_le__SUPI,axiom,
% 11.25/11.12 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 11.25/11.12 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_nat__of,axiom,
% 11.25/11.12 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2] :
% 11.25/11.12 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 11.25/11.12 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_SUP__UN__eq2,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_folding__image__simple_Oremove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.12 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__insert__distrib,axiom,
% 11.25/11.12 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__upper,axiom,
% 11.25/11.12 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_SUP__UN__eq,axiom,
% 11.25/11.12 ! [V_x_2,V_r_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_UN__absorb,axiom,
% 11.25/11.12 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_elem__set,axiom,
% 11.25/11.12 ! [V_xo_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
% 11.25/11.12 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_pred__subset__eq2,axiom,
% 11.25/11.12 ! [V_S_2,V_R_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Diff__insert__absorb,axiom,
% 11.25/11.12 ! [V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_insert__Diff,axiom,
% 11.25/11.12 ! [V_A_2,V_a_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2] :
% 11.25/11.12 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__delta_H,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.12 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__delta,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.12 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_image__constant,axiom,
% 11.25/11.12 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_of__nat__inverse,axiom,
% 11.25/11.12 ! [V_y_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 11.25/11.12 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__insert,axiom,
% 11.25/11.12 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum_Oinsert,axiom,
% 11.25/11.12 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_subset__insert__iff,axiom,
% 11.25/11.12 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 11.25/11.12 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_diff__single__insert,axiom,
% 11.25/11.12 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__insert__disjoint,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__insert__if,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card_Oinsert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_psubset__insert__iff,axiom,
% 11.25/11.12 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 11.25/11.12 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 11.25/11.12 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__diff1__nat,axiom,
% 11.25/11.12 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 11.25/11.12 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__diff1_H,axiom,
% 11.25/11.12 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum_Oremove,axiom,
% 11.25/11.12 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__diff1__ring,axiom,
% 11.25/11.12 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( class_Rings_Oring(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__diff1,axiom,
% 11.25/11.12 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Oab__group__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Suc__Diff1,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Diff1__less,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Diff2__less,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Diff__insert,axiom,
% 11.25/11.12 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card_Oremove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_in__rel__def,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 11.25/11.12 ! [V_f_2,V_A_2,T_b] :
% 11.25/11.12 ( ! [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.12 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_aset_I6_J,axiom,
% 11.25/11.12 ! [V_A_2,V_t_2,V_D_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
% 11.25/11.12 => ! [B_x] :
% 11.25/11.12 ( ! [B_xa] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.12 => ! [B_xb] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 11.25/11.12 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bset_I8_J,axiom,
% 11.25/11.12 ! [V_B_2,V_t_2,V_D_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
% 11.25/11.12 => ! [B_x] :
% 11.25/11.12 ( ! [B_xa] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.12 => ! [B_xb] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 11.25/11.12 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_sup2CI,axiom,
% 11.25/11.12 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 11.25/11.12 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 11.25/11.12 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_sup2E,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bot2E,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_less__by__empty,axiom,
% 11.25/11.12 ! [V_B_2,T_b,V_A_2] :
% 11.25/11.12 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_SUP2__iff,axiom,
% 11.25/11.12 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 11.25/11.12 <=> ? [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.12 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_sup2I2,axiom,
% 11.25/11.12 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_sup2I1,axiom,
% 11.25/11.12 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nitpick_Orefl_H__def,axiom,
% 11.25/11.12 ! [V_r_2,T_b] :
% 11.25/11.12 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 11.25/11.12 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OlessThan__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_i_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
% 11.25/11.12 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OgreaterThan__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_i_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
% 11.25/11.12 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ord_OlessThan__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ord_OgreaterThan__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bset_I3_J,axiom,
% 11.25/11.12 ! [V_B_2,V_t_2,V_D_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
% 11.25/11.12 => ( ! [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.12 => ! [B_xa] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 11.25/11.12 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 11.25/11.12 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_aset_I3_J,axiom,
% 11.25/11.12 ! [V_A_2,V_t_2,V_D_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
% 11.25/11.12 => ( ! [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.12 => ! [B_xa] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 11.25/11.12 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 11.25/11.12 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_aset_I5_J,axiom,
% 11.25/11.12 ! [V_A_2,V_t_2,V_D_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 11.25/11.12 => ! [B_x] :
% 11.25/11.12 ( ! [B_xa] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.12 => ! [B_xb] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 11.25/11.12 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_aset_I4_J,axiom,
% 11.25/11.12 ! [V_A_2,V_t_2,V_D_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 11.25/11.12 => ! [B_x] :
% 11.25/11.12 ( ! [B_xa] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.12 => ! [B_xb] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 11.25/11.12 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.12 => ( B_x != V_t_2
% 11.25/11.12 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bset_I4_J,axiom,
% 11.25/11.12 ! [V_B_2,V_t_2,V_D_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 11.25/11.12 => ! [B_x] :
% 11.25/11.12 ( ! [B_xa] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.12 => ! [B_xb] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 11.25/11.12 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.12 => ( B_x != V_t_2
% 11.25/11.12 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_bset_I7_J,axiom,
% 11.25/11.12 ! [V_B_2,V_t_2,V_D_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 11.25/11.12 => ! [B_x] :
% 11.25/11.12 ( ! [B_xa] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 11.25/11.12 => ! [B_xb] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 11.25/11.12 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_in__measure,axiom,
% 11.25/11.12 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatLeast__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_i_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatMost__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_i_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ord_OatLeast__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ord_OatMost__iff,axiom,
% 11.25/11.12 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_folding__one_Oremove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.12 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 11.25/11.12 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
% 11.25/11.12 => c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__mono2,axiom,
% 11.25/11.12 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 => ( ! [B_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 11.25/11.12 ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 11.25/11.12 ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_folding__one_Osingleton,axiom,
% 11.25/11.12 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 11.25/11.12 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 11.25/11.12 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_folding__one_Oinsert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.12 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_folding__one_Oinsert__remove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.12 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_flat__lub__def,axiom,
% 11.25/11.12 ! [V_b_2,V_A_2,T_b] :
% 11.25/11.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 11.25/11.12 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 11.25/11.12 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_mlex__leq,axiom,
% 11.25/11.12 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_mlex__less,axiom,
% 11.25/11.12 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__bounded,axiom,
% 11.25/11.12 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 11.25/11.12 & class_Rings_Osemiring__1(T_c) )
% 11.25/11.12 => ( ! [B_i] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_card__Suc__eq,axiom,
% 11.25/11.12 ! [V_k_2,V_A_2,T_b] :
% 11.25/11.12 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 11.25/11.12 <=> ? [B_b,B_B] :
% 11.25/11.12 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 11.25/11.12 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 11.25/11.12 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 11.25/11.12 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.25/11.12 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 11.25/11.12 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 11.25/11.12 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 11.25/11.12 ! [V_k_2,V_l_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 11.25/11.12 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 11.25/11.12 ! [V_l_2,V_k_2] :
% 11.25/11.12 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 11.25/11.12 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 11.25/11.12 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 11.25/11.12 ! [V_l_2,V_k_2] :
% 11.25/11.12 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
% 11.25/11.12 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 11.25/11.12 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 11.25/11.12 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 11.25/11.12 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nats__number__of,axiom,
% 11.25/11.12 ! [V_w_2,T_b] :
% 11.25/11.12 ( class_Int_Onumber__ring(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 11.25/11.12 ! [V_a_2,V_b_2] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 11.25/11.12 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nats__0,axiom,
% 11.25/11.12 ! [T_b] :
% 11.25/11.12 ( class_Rings_Osemiring__1(T_b)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nats__add,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Rings_Osemiring__1(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nats__mult,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Rings_Osemiring__1(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Nats__1,axiom,
% 11.25/11.12 ! [T_b] :
% 11.25/11.12 ( class_Rings_Osemiring__1(T_b)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_of__nat__in__Nats,axiom,
% 11.25/11.12 ! [V_n_2,T_b] :
% 11.25/11.12 ( class_Rings_Osemiring__1(T_b)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2] :
% 11.25/11.12 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
% 11.25/11.12 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 11.25/11.12 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2] :
% 11.25/11.12 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 11.25/11.12 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 11.25/11.12 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_hoare__derivs_OCall,axiom,
% 11.25/11.12 ! [V_a_2,V_X_2,V_s_H_2,V_Qa_2,V_pna_2,V_Pa_2,V_G_2,T_b] :
% 11.25/11.12 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pna_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Qa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,V_s_H_2)))),V_X_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 11.25/11.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),V_a_2)))),c_Com_Ocom_OCall(V_X_2,V_pna_2,V_a_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__odd__less__0,axiom,
% 11.25/11.12 ! [V_a_2,T_b] :
% 11.25/11.12 ( class_Rings_Olinordered__idom(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 11.25/11.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Sup__fin_Oremove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Lattices_Olattice(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_hoare__derivs_Oinsert,axiom,
% 11.25/11.12 ! [V_ts_2,V_t_2,V_G_2,T_b] :
% 11.25/11.12 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 11.25/11.12 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_2)
% 11.25/11.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_hoare__derivs_OSkip,axiom,
% 11.25/11.12 ! [V_Pa_2,V_G_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 11.25/11.12 ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Comp,axiom,
% 11.25/11.12 ! [V_R_2,V_d_2,V_Qa_2,V_c_2,V_Pa_2,V_G_2,T_b] :
% 11.25/11.12 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 11.25/11.12 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Qa_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 11.25/11.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 11.25/11.12 ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_empty,axiom,
% 11.25/11.12 ! [V_G_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_weaken,axiom,
% 11.25/11.12 ! [V_ts_2,V_ts_H_2,V_G_2,T_b] :
% 11.25/11.12 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
% 11.25/11.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_asm,axiom,
% 11.25/11.12 ! [V_G_2,V_ts_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_G_2))
% 11.25/11.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 11.25/11.12 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_a2_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_a3_2)),V_a4_2))),c_Com_Ocom_OAss(V_a3_2,V_a4_2)),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ass,axiom,
% 11.25/11.12 ! [V_a_2,V_X_2,V_Pa_2,V_G_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_cut,axiom,
% 11.25/11.12 ! [V_G_2,V_ts_2,V_G_H_2,T_b] :
% 11.25/11.12 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 11.25/11.12 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_H_2)
% 11.25/11.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_triple_Oinject,axiom,
% 11.25/11.12 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 11.25/11.12 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_H_2),V_com_H_2),V_fun2_H_2)
% 11.25/11.12 <=> ( V_fun1_2 = V_fun1_H_2
% 11.25/11.12 & V_com_2 = V_com_H_2
% 11.25/11.12 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Sup__fin_Osingleton,axiom,
% 11.25/11.12 ! [V_x_2,T_b] :
% 11.25/11.12 ( class_Lattices_Olattice(T_b)
% 11.25/11.12 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_hoare__derivs_OBody,axiom,
% 11.25/11.12 ! [V_Procs_2,V_Qa_2,V_Pa_2,V_G_2,T_b] :
% 11.25/11.12 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Qa_2)),V_Procs_2))
% 11.25/11.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procs_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__0,axiom,
% 11.25/11.12 ! [T_b] :
% 11.25/11.12 ( class_Rings_Oring__1(T_b)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__add,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Rings_Oring__1(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__mult,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Rings_Oring__1(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__diff,axiom,
% 11.25/11.12 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Rings_Oring__1(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__number__of,axiom,
% 11.25/11.12 ! [V_w_2,T_b] :
% 11.25/11.12 ( class_Int_Onumber__ring(T_b)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__1,axiom,
% 11.25/11.12 ! [T_b] :
% 11.25/11.12 ( class_Rings_Oring__1(T_b)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__minus,axiom,
% 11.25/11.12 ! [V_a_2,T_b] :
% 11.25/11.12 ( class_Rings_Oring__1(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_hoare__derivs_OLocal,axiom,
% 11.25/11.12 ! [V_a_2,V_s_H_2,V_X_2,V_Qa_2,V_c_2,V_Pa_2,V_G_2,T_b] :
% 11.25/11.12 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Qa_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),hAPP(hAPP(c_Natural_Ogetlocs,V_s_H_2),V_X_2))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 11.25/11.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),V_a_2)))),c_Com_Ocom_OLocal(V_X_2,V_a_2,V_c_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__of__nat,axiom,
% 11.25/11.12 ! [V_n_2,T_b] :
% 11.25/11.12 ( class_Rings_Oring__1(T_b)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__power,axiom,
% 11.25/11.12 ! [V_n_2,V_a_2,T_b] :
% 11.25/11.12 ( class_Rings_Oring__1(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__of__int,axiom,
% 11.25/11.12 ! [V_z_2,T_b] :
% 11.25/11.12 ( class_Rings_Oring__1(T_b)
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Sup__fin_Oin__idem,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Lattices_Olattice(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__double__eq__0__iff,axiom,
% 11.25/11.12 ! [V_a_2,T_b] :
% 11.25/11.12 ( class_Int_Oring__char__0(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 11.25/11.12 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Lattices_Olattice(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Sup__fin_Osubset__idem,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Lattices_Olattice(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Sup__fin_Ounion__idem,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Lattices_Olattice(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Ints__odd__nonzero,axiom,
% 11.25/11.12 ! [V_a_2,T_b] :
% 11.25/11.12 ( class_Int_Oring__char__0(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 11.25/11.12 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Sup__fin_Oinsert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Lattices_Olattice(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Lattices_Olattice(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_triple_Osize_I1_J,axiom,
% 11.25/11.12 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_MGT__def,axiom,
% 11.25/11.12 ! [V_c_2] : c_Hoare__Mirabelle_OMGT(V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),c_Natural_Oevalc(V_c_2)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_triple_Osize_I2_J,axiom,
% 11.25/11.12 ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_triple_Orecs,axiom,
% 11.25/11.12 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_triple_Osimps_I2_J,axiom,
% 11.25/11.12 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Sup__fin_Oclosed,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( class_Lattices_Olattice(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max_Oremove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min_Oremove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_iso__tuple__UNIV__I,axiom,
% 11.25/11.12 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_minus__Max__eq__Min,axiom,
% 11.25/11.12 ! [V_S_2,T_b] :
% 11.25/11.12 ( class_Groups_Olinordered__ab__group__add(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.12 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_minus__Min__eq__Max,axiom,
% 11.25/11.12 ! [V_S_2,T_b] :
% 11.25/11.12 ( class_Groups_Olinordered__ab__group__add(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.12 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min_Osingleton,axiom,
% 11.25/11.12 ! [V_x_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max_Osingleton,axiom,
% 11.25/11.12 ! [V_x_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min__le,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max__ge,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min__in,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max__in,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min_Oin__idem,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max_Oin__idem,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max__mono,axiom,
% 11.25/11.12 ! [V_N_2,V_M_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 11.25/11.12 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min__antimono,axiom,
% 11.25/11.12 ! [V_N_2,V_M_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 11.25/11.12 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min__insert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max__insert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min_Osubset__idem,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max_Osubset__idem,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min__Un,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max__Un,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min_Oinsert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max_Oinsert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min_Oinsert__remove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max_Oinsert__remove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Max_Oclosed,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_Min_Oclosed,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 11.25/11.12 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 11.25/11.12 ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
% 11.25/11.12 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 11.25/11.12 | ? [B_x,B_y] :
% 11.25/11.12 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 11.25/11.12 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 11.25/11.12 & c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_in__lex__prod,axiom,
% 11.25/11.12 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2))
% 11.25/11.12 | ( V_a_2 = V_a_H_2
% 11.25/11.12 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_in__finite__psubset,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
% 11.25/11.12 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.12 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_triple__valid__def2,axiom,
% 11.25/11.12 ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2,T_b] :
% 11.25/11.12 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
% 11.25/11.12 <=> ! [B_Z,B_s] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 11.25/11.12 => ! [B_s_H] :
% 11.25/11.12 ( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
% 11.25/11.12 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_same__fstI,axiom,
% 11.25/11.12 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
% 11.25/11.12 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OInf__le__Sup,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 11.25/11.12 ! [V_x_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 11.25/11.12 ! [V_x_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 11.25/11.12 ! [V_a_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 11.25/11.12 ! [V_a_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.12 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 11.25/11.12 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 11.25/11.12 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 11.25/11.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 11.25/11.12 ! [V_A_2,T_b] :
% 11.25/11.12 ( class_Orderings_Olinorder(T_b)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_folding__one_Oclosed,axiom,
% 11.25/11.12 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.12 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.12 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fun__upd__image,axiom,
% 11.25/11.12 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 11.25/11.12 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.12 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setprod__gen__delta,axiom,
% 11.25/11.12 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.12 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 11.25/11.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setsum__nonneg__leq__bound,axiom,
% 11.25/11.12 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 11.25/11.12 ( class_Groups_Oordered__ab__group__add(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 11.25/11.12 => ( ! [B_i] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 11.25/11.12 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 11.25/11.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 11.25/11.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fun__upd__triv,axiom,
% 11.25/11.12 ! [V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 11.25/11.12
% 11.25/11.12 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 11.25/11.12 ! [V_A_2,V_f_2,T_b] :
% 11.25/11.12 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.12 & class_Groups_Ocomm__monoid__mult(T_b) )
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_abs__setprod,axiom,
% 11.25/11.12 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.12 ( class_Fields_Olinordered__field(T_b)
% 11.25/11.12 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_of__int__setprod,axiom,
% 11.25/11.12 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.12 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 11.25/11.12 & class_Rings_Oring__1(T_b) )
% 11.25/11.12 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 11.25/11.12 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_int__setprod,axiom,
% 11.25/11.12 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_of__nat__setprod,axiom,
% 11.25/11.12 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.12 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 11.25/11.12 & class_Rings_Osemiring__1(T_b) )
% 11.25/11.12 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setprod__1,axiom,
% 11.25/11.12 ! [V_A_2,T_c,T_b] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__mult(T_b)
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setprod__timesf,axiom,
% 11.25/11.12 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 11.25/11.12 ( class_Groups_Ocomm__monoid__mult(T_b)
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fun__upd__idem__iff,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 11.25/11.12 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
% 11.25/11.12 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fun__upd__upd,axiom,
% 11.25/11.12 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_z_2) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fun__upd__same,axiom,
% 11.25/11.12 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fun__upd__apply,axiom,
% 11.25/11.12 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 11.25/11.12 ( ( V_z_2 = V_x_2
% 11.25/11.12 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 )
% 11.25/11.12 & ( V_z_2 != V_x_2
% 11.25/11.12 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fun__upd__twist,axiom,
% 11.25/11.12 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 11.25/11.12 ( V_a_2 != V_c_2
% 11.25/11.12 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fun__upd__other,axiom,
% 11.25/11.12 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 11.25/11.12 ( V_z_2 != V_x_2
% 11.25/11.12 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fun__upd__idem,axiom,
% 11.25/11.12 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 11.25/11.12 ( hAPP(V_f_2,V_x_2) = V_y_2
% 11.25/11.12 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_fun__upd__def,axiom,
% 11.25/11.12 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 11.25/11.12 ( ( V_x_2 = V_a_2
% 11.25/11.12 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 )
% 11.25/11.12 & ( V_x_2 != V_a_2
% 11.25/11.12 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setprod__zero,axiom,
% 11.25/11.12 ! [V_f_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( class_Rings_Ocomm__semiring__1(T_c)
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( ? [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.12 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 11.25/11.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setprod__zero__iff,axiom,
% 11.25/11.12 ! [V_f_2,V_A_2,T_b,T_c] :
% 11.25/11.12 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 11.25/11.12 & class_Rings_Ono__zero__divisors(T_c) )
% 11.25/11.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.12 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
% 11.25/11.12 <=> ? [B_x] :
% 11.25/11.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.12 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 11.25/11.12
% 11.25/11.12 fof(fact_setprod_Oempty,axiom,
% 11.25/11.13 ! [V_g_2,T_c,T_b] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__empty,axiom,
% 11.25/11.13 ! [V_f_2,T_c,T_b] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod_Oinfinite,axiom,
% 11.25/11.13 ! [V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__infinite,axiom,
% 11.25/11.13 ! [V_f_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__eq__1__iff,axiom,
% 11.25/11.13 ! [V_f_2,V_F_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 11.25/11.13 <=> ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 11.25/11.13 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 11.25/11.13 ! [V_f_2,V_A_2,T_b] :
% 11.25/11.13 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.13 & class_Groups_Ocomm__monoid__mult(T_b) )
% 11.25/11.13 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod_Odistrib,axiom,
% 11.25/11.13 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__dividef,axiom,
% 11.25/11.13 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Fields_Ofield__inverse__zero(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_dvd__setprod,axiom,
% 11.25/11.13 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Rings_Ocomm__semiring__1(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__pos__nat__iff,axiom,
% 11.25/11.13 ! [V_f_2,V_S_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
% 11.25/11.13 <=> ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__dvd__setprod__subset,axiom,
% 11.25/11.13 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 11.25/11.13 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 & class_Rings_Odvd(T_c) )
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__delta_H,axiom,
% 11.25/11.13 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.13 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 11.25/11.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__delta,axiom,
% 11.25/11.13 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.13 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 11.25/11.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__constant,axiom,
% 11.25/11.13 ! [V_y_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__insert,axiom,
% 11.25/11.13 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod_Oinsert,axiom,
% 11.25/11.13 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod_Oinsert__remove,axiom,
% 11.25/11.13 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod_Oremove,axiom,
% 11.25/11.13 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__diff1,axiom,
% 11.25/11.13 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Fields_Ofield(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 11.25/11.13 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 11.25/11.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_finite__range__updI,axiom,
% 11.25/11.13 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 11.25/11.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_image__map__upd,axiom,
% 11.25/11.13 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 11.25/11.13 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),V_m_2),V_A_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_map__upd__nonempty,axiom,
% 11.25/11.13 ! [V_x_2,V_k_2,V_t_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_map__upd__eqD1,axiom,
% 11.25/11.13 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
% 11.25/11.13 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))
% 11.25/11.13 => V_x_2 = V_y_2 ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_map__upd__triv,axiom,
% 11.25/11.13 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
% 11.25/11.13 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 11.25/11.13 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = V_t_2 ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_map__upd__Some__unfold,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
% 11.25/11.13 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 11.25/11.13 <=> ( ( V_x_2 = V_a_2
% 11.25/11.13 & V_b_2 = V_y_2 )
% 11.25/11.13 | ( V_x_2 != V_a_2
% 11.25/11.13 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_empty__upd__none,axiom,
% 11.25/11.13 ! [V_xa_2,V_x_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2),c_Option_Ooption_ONone(T_b)),V_xa_2) = c_Option_Ooption_ONone(T_b) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 11.25/11.13 ! [V_f_2,V_A_2,T_b] :
% 11.25/11.13 ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.13 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ran__map__upd,axiom,
% 11.25/11.13 ! [V_b_2,T_c,T_b,V_a_2,V_m_2] :
% 11.25/11.13 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b)
% 11.25/11.13 => c_Map_Oran(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_fun__upd__None__restrict,axiom,
% 11.25/11.13 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 11.25/11.13 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 11.25/11.13 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) )
% 11.25/11.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 11.25/11.13 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_restrict__in,axiom,
% 11.25/11.13 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_restrict__map__empty,axiom,
% 11.25/11.13 ! [V_x_2,V_D_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_restrict__out,axiom,
% 11.25/11.13 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 11.25/11.13 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_restrict__map__insert,axiom,
% 11.25/11.13 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_restrict__map__def,axiom,
% 11.25/11.13 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 11.25/11.13 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) )
% 11.25/11.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_restrict__map__to__empty,axiom,
% 11.25/11.13 ! [V_x_2,V_m_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ranI,axiom,
% 11.25/11.13 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 11.25/11.13 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_fun__upd__restrict,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ran__empty,axiom,
% 11.25/11.13 ! [T_b,T_c] : c_Map_Oran(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_restrict__fun__upd,axiom,
% 11.25/11.13 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 11.25/11.13 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 11.25/11.13 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) )
% 11.25/11.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 11.25/11.13 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_fun__upd__restrict__conv,axiom,
% 11.25/11.13 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 11.25/11.13 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_restrict__complement__singleton__eq,axiom,
% 11.25/11.13 ! [V_x_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_c)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_restrict__upd__same,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__nonneg__0,axiom,
% 11.25/11.13 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Oordered__ab__group__add(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 11.25/11.13 => ( ! [B_i] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 11.25/11.13 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 11.25/11.13 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_pair__lessI2,axiom,
% 11.25/11.13 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 11.25/11.13 ! [V_N_2,V_h_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.13 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_pair__lessI1,axiom,
% 11.25/11.13 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_pair__leqI2,axiom,
% 11.25/11.13 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_smin__insertI,axiom,
% 11.25/11.13 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_smax__insertI,axiom,
% 11.25/11.13 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_smin__emptyI,axiom,
% 11.25/11.13 ! [V_X_2] :
% 11.25/11.13 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_smax__emptyI,axiom,
% 11.25/11.13 ! [V_Y_2] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 11.25/11.13 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_pair__leqI1,axiom,
% 11.25/11.13 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_wmax__insertI,axiom,
% 11.25/11.13 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_wmin__insertI,axiom,
% 11.25/11.13 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_wmin__emptyI,axiom,
% 11.25/11.13 ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_wmax__emptyI,axiom,
% 11.25/11.13 ! [V_X_2] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_min__weak__def,axiom,
% 11.25/11.13 c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_max__weak__def,axiom,
% 11.25/11.13 c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_min__rpair__set,axiom,
% 11.25/11.13 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_max__strict__def,axiom,
% 11.25/11.13 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_max__ext__additive,axiom,
% 11.25/11.13 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_min__strict__def,axiom,
% 11.25/11.13 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_max__rpair__set,axiom,
% 11.25/11.13 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_max__extp__max__ext__eq,axiom,
% 11.25/11.13 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 11.25/11.13 ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_less__than__iff,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_intrel__iff,axiom,
% 11.25/11.13 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
% 11.25/11.13 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_pair__less__def,axiom,
% 11.25/11.13 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_mlex__prod__def,axiom,
% 11.25/11.13 ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_rp__inv__image__rp,axiom,
% 11.25/11.13 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 11.25/11.13 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 11.25/11.13 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 11.25/11.13 ! [V_N_2,V_h_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.13 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_rp__inv__image__def,axiom,
% 11.25/11.13 ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_in__inv__image,axiom,
% 11.25/11.13 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Max_Ohom__commute,axiom,
% 11.25/11.13 ! [V_N_2,V_h_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.13 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Min_Ohom__commute,axiom,
% 11.25/11.13 ! [V_N_2,V_h_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.13 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_measure__def,axiom,
% 11.25/11.13 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_irrefl__def,axiom,
% 11.25/11.13 ! [V_r_2,T_b] :
% 11.25/11.13 ( c_Relation_Oirrefl(T_b,V_r_2)
% 11.25/11.13 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Field__insert,axiom,
% 11.25/11.13 ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Id__on__def,axiom,
% 11.25/11.13 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Id__on__def_H,axiom,
% 11.25/11.13 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Id__on__empty,axiom,
% 11.25/11.13 ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Field__empty,axiom,
% 11.25/11.13 ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_mono__Field,axiom,
% 11.25/11.13 ! [V_s_2,V_r_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Field__Un,axiom,
% 11.25/11.13 ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_finite__Field,axiom,
% 11.25/11.13 ! [V_r_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 11.25/11.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Id__on__eqI,axiom,
% 11.25/11.13 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 11.25/11.13 ( V_a_2 = V_b_2
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Id__on__iff,axiom,
% 11.25/11.13 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
% 11.25/11.13 <=> ( V_x_2 = V_y_2
% 11.25/11.13 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Id__onE,axiom,
% 11.25/11.13 ! [V_A_2,V_c_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 11.25/11.13 => ~ ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.13 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Sup__fin_Ohom__commute,axiom,
% 11.25/11.13 ! [V_N_2,V_h_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.13 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__mono__one__left,axiom,
% 11.25/11.13 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 11.25/11.13 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__mono__one__right,axiom,
% 11.25/11.13 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 11.25/11.13 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__mono__zero__right,axiom,
% 11.25/11.13 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 11.25/11.13 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__mono__zero__left,axiom,
% 11.25/11.13 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 11.25/11.13 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_card__Pow,axiom,
% 11.25/11.13 ! [V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_finite__empty__induct,axiom,
% 11.25/11.13 ! [V_Pa_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(V_Pa_2,V_A_2))
% 11.25/11.13 => ( ! [B_a,B_A] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 11.25/11.13 => ( hBOOL(hAPP(V_Pa_2,B_A))
% 11.25/11.13 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 11.25/11.13 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_PowI,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Pow__insert,axiom,
% 11.25/11.13 ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Pow__empty,axiom,
% 11.25/11.13 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Pow__bottom,axiom,
% 11.25/11.13 ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Pow__not__empty,axiom,
% 11.25/11.13 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Un__Pow__subset,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Pow__iff,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_PowD,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Pow__top,axiom,
% 11.25/11.13 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Pow__UNIV,axiom,
% 11.25/11.13 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__one__idem_Oidem,axiom,
% 11.25/11.13 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 11.25/11.13 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Pow__mono,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Cantors__paradox,axiom,
% 11.25/11.13 ! [V_A_2,T_b] :
% 11.25/11.13 ~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_image__Pow__surj,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 11.25/11.13 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 11.25/11.13 => hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_finite__Pow__iff,axiom,
% 11.25/11.13 ! [V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 11.25/11.13 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__Pow__subset,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_image__Pow__mono,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__one__idem_Oin__idem,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Powp__Pow__eq,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_finite__subset__induct,axiom,
% 11.25/11.13 ! [V_Pa_2,V_A_2,V_F_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.13 => ( ! [B_a,B_F] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 11.25/11.13 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 11.25/11.13 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 11.25/11.13 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 11.25/11.13 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__strict__mono,axiom,
% 11.25/11.13 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.13 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Powp__mono,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equiv__intrel__iff,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2] :
% 11.25/11.13 ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__Plus,axiom,
% 11.25/11.13 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__add(T_d)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(T_b,T_c),T_d),V_f_2),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(tc_sum(T_b,T_c),T_d,T_b,V_f_2),c_Sum__Type_OInl(T_b,T_c))),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(c_Fun_Ocomp(tc_sum(T_b,T_c),T_d,T_c,V_f_2),c_Sum__Type_OInr(T_c,T_b))),V_B_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 11.25/11.13 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.13 & class_Groups_Ocomm__monoid__mult(T_b) )
% 11.25/11.13 => ( V_A_2 = V_B_2
% 11.25/11.13 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 11.25/11.13 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Image__empty,axiom,
% 11.25/11.13 ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Image__Un,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Image__UN,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_image__compose,axiom,
% 11.25/11.13 ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_o__def,axiom,
% 11.25/11.13 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_o__eq__elim,axiom,
% 11.25/11.13 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 11.25/11.13 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
% 11.25/11.13 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_o__eq__dest,axiom,
% 11.25/11.13 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 11.25/11.13 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
% 11.25/11.13 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_o__apply,axiom,
% 11.25/11.13 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_o__assoc,axiom,
% 11.25/11.13 ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_apfst__compose,axiom,
% 11.25/11.13 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_apsnd__compose,axiom,
% 11.25/11.13 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_comp__cong,axiom,
% 11.25/11.13 ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
% 11.25/11.13 ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))
% 11.25/11.13 => hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_K__record__comp,axiom,
% 11.25/11.13 ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2 ).
% 11.25/11.13
% 11.25/11.13 fof(fact_o__eq__dest__lhs,axiom,
% 11.25/11.13 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 11.25/11.13 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 11.25/11.13 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_fun__upd__comp,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_d),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_comp__surj,axiom,
% 11.25/11.13 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 11.25/11.13 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
% 11.25/11.13 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Image__mono,axiom,
% 11.25/11.13 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Un__Image,axiom,
% 11.25/11.13 ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_rev__ImageI,axiom,
% 11.25/11.13 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Image__iff,axiom,
% 11.25/11.13 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 11.25/11.13 <=> ? [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.25/11.13 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Image__eq__UN,axiom,
% 11.25/11.13 ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Image__singleton__iff,axiom,
% 11.25/11.13 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_of__int,axiom,
% 11.25/11.13 ! [V_j_2,V_i_2,T_b] :
% 11.25/11.13 ( class_Rings_Oring__1(T_b)
% 11.25/11.13 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_One__int__def,axiom,
% 11.25/11.13 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_mult,axiom,
% 11.25/11.13 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__o,axiom,
% 11.25/11.13 ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Rep__Integ__inverse,axiom,
% 11.25/11.13 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 11.25/11.13
% 11.25/11.13 fof(fact_split__comp,axiom,
% 11.25/11.13 ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_number__of__code__numeral__def,axiom,
% 11.25/11.13 c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_int__of__def,axiom,
% 11.25/11.13 c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_minus,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Zero__int__def,axiom,
% 11.25/11.13 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_int__def,axiom,
% 11.25/11.13 ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_add,axiom,
% 11.25/11.13 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_nat,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_minus__int__def,axiom,
% 11.25/11.13 ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_less,axiom,
% 11.25/11.13 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_le,axiom,
% 11.25/11.13 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_hoare__derivs_OIf,axiom,
% 11.25/11.13 ! [V_d_2,V_Qa_2,V_c_2,V_b_2,V_Pa_2,V_G_2,T_b] :
% 11.25/11.13 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 11.25/11.13 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 11.25/11.13 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Loop,axiom,
% 11.25/11.13 ! [V_c_2,V_b_2,V_Pa_2,V_G_2,T_b] :
% 11.25/11.13 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_c_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 11.25/11.13 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Nitpick_Odenom__def,axiom,
% 11.25/11.13 ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_peek__and__def,axiom,
% 11.25/11.13 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
% 11.25/11.13 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2))
% 11.25/11.13 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Nitpick_Onum__def,axiom,
% 11.25/11.13 ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Oremove,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_eq__Abs__Integ,axiom,
% 11.25/11.13 ! [V_z_2] :
% 11.25/11.13 ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Oinsert__remove,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Ocommute__left__comp,axiom,
% 11.25/11.13 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Ocommute__comp,axiom,
% 11.25/11.13 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 11.25/11.13 ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Ocommute__comp_H,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 11.25/11.13 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 11.25/11.13 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Oinsert,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__reindex__nonzero,axiom,
% 11.25/11.13 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__add(T_d)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 11.25/11.13 => ! [B_y] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 11.25/11.13 => ( B_x != B_y
% 11.25/11.13 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 11.25/11.13 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Random__Sequence_Omap__def,axiom,
% 11.25/11.13 ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_quotient__def,axiom,
% 11.25/11.13 ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_quotient__empty,axiom,
% 11.25/11.13 ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_quotient__is__empty2,axiom,
% 11.25/11.13 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
% 11.25/11.13 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_quotient__is__empty,axiom,
% 11.25/11.13 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 11.25/11.13 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_quotientI,axiom,
% 11.25/11.13 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_singleton__quotient,axiom,
% 11.25/11.13 ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_subset__equiv__class,axiom,
% 11.25/11.13 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_quotientE,axiom,
% 11.25/11.13 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => ~ ! [B_x] :
% 11.25/11.13 ( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.13 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_eq__equiv__class__iff2,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equiv__intrel,axiom,
% 11.25/11.13 c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equiv__class__self,axiom,
% 11.25/11.13 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equiv__class__eq,axiom,
% 11.25/11.13 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 11.25/11.13 => hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_quotient__eq__iff,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 11.25/11.13 => ( V_X_2 = V_Y_2
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_quotient__eqI,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 11.25/11.13 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_eq__equiv__class,axiom,
% 11.25/11.13 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 11.25/11.13 ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.13 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_eq__equiv__class__iff,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 11.25/11.13 => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equiv__class__eq__iff,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 11.25/11.13 <=> ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.13 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equiv__class__subset,axiom,
% 11.25/11.13 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__equiv__class,axiom,
% 11.25/11.13 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__equiv__class2,axiom,
% 11.25/11.13 ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 11.25/11.13 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 11.25/11.13 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 11.25/11.13 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equiv__class__nondisjoint,axiom,
% 11.25/11.13 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf1E,axiom,
% 11.25/11.13 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 11.25/11.13 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 11.25/11.13 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf1I,axiom,
% 11.25/11.13 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 11.25/11.13 ( hBOOL(hAPP(V_A_2,V_x_2))
% 11.25/11.13 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_IntE,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.13 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.13 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_IntI,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_finite__Int,axiom,
% 11.25/11.13 ! [V_G_2,V_F_2,T_b] :
% 11.25/11.13 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 11.25/11.13 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) )
% 11.25/11.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__sup__ord_I1_J,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__le1,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__sup__ord_I2_J,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__le2,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_le__iff__inf,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.25/11.13 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_le__inf__iff,axiom,
% 11.25/11.13 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
% 11.25/11.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.25/11.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_le__infI1,axiom,
% 11.25/11.13 ! [V_b,V_x,V_a,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_le__infI2,axiom,
% 11.25/11.13 ! [V_a,V_x,V_b,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__absorb1,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__absorb2,axiom,
% 11.25/11.13 ! [V_x,V_y,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_le__infI,axiom,
% 11.25/11.13 ! [V_b,V_a,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__greatest,axiom,
% 11.25/11.13 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__mono,axiom,
% 11.25/11.13 ! [V_d,V_b,V_c,V_a,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_le__infE,axiom,
% 11.25/11.13 ! [V_b,V_a,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
% 11.25/11.13 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 11.25/11.13 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__mono,axiom,
% 11.25/11.13 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__greatest,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__absorb1,axiom,
% 11.25/11.13 ! [V_A_2,V_B_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__absorb2,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__lower2,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__lower1,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__top__left,axiom,
% 11.25/11.13 ! [V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Obounded__lattice__top(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__top__right,axiom,
% 11.25/11.13 ! [V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Obounded__lattice__top(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__eq__top__iff,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,T_b] :
% 11.25/11.13 ( class_Lattices_Obounded__lattice__top(T_b)
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 11.25/11.13 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 11.25/11.13 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__UNIV__left,axiom,
% 11.25/11.13 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__UNIV__right,axiom,
% 11.25/11.13 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__Int__eq,axiom,
% 11.25/11.13 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_IntD2,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_IntD1,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__iff,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.13 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.13 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Un__Int__crazy,axiom,
% 11.25/11.13 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Un__Int__distrib2,axiom,
% 11.25/11.13 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__Un__distrib2,axiom,
% 11.25/11.13 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Un__Int__distrib,axiom,
% 11.25/11.13 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__Un__distrib,axiom,
% 11.25/11.13 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_sup__inf__distrib2,axiom,
% 11.25/11.13 ! [V_x,V_z,V_y,T_a] :
% 11.25/11.13 ( class_Lattices_Odistrib__lattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__sup__distrib2,axiom,
% 11.25/11.13 ! [V_x,V_z,V_y,T_a] :
% 11.25/11.13 ( class_Lattices_Odistrib__lattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_sup__inf__distrib1,axiom,
% 11.25/11.13 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Odistrib__lattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__sup__distrib1,axiom,
% 11.25/11.13 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Odistrib__lattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_sup__inf__absorb,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__sup__absorb,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_disjoint__iff__not__equal,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 <=> ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.13 => ! [B_xa] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 11.25/11.13 => B_x != B_xa ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__empty__right,axiom,
% 11.25/11.13 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__empty__left,axiom,
% 11.25/11.13 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__bot__right,axiom,
% 11.25/11.13 ! [V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Obounded__lattice__bot(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__bot__left,axiom,
% 11.25/11.13 ! [V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Obounded__lattice__bot(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_insert__inter__insert,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_restrict__restrict,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2] :
% 11.25/11.13 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.13 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 11.25/11.13 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf1D2,axiom,
% 11.25/11.13 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 11.25/11.13 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf1D1,axiom,
% 11.25/11.13 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 11.25/11.13 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__assoc,axiom,
% 11.25/11.13 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__left__commute,axiom,
% 11.25/11.13 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__left__absorb,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__commute,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__absorb,axiom,
% 11.25/11.13 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__apply,axiom,
% 11.25/11.13 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__assoc,axiom,
% 11.25/11.13 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__sup__aci_I2_J,axiom,
% 11.25/11.13 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf_Oassoc,axiom,
% 11.25/11.13 ! [V_c,V_b,V_a,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__left__commute,axiom,
% 11.25/11.13 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__sup__aci_I3_J,axiom,
% 11.25/11.13 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf_Oleft__commute,axiom,
% 11.25/11.13 ! [V_c,V_a,V_b,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__left__idem,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__sup__aci_I4_J,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf_Oleft__idem,axiom,
% 11.25/11.13 ! [V_b,V_a,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__commute,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__sup__aci_I1_J,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf_Ocommute,axiom,
% 11.25/11.13 ! [V_b,V_a,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__idem,axiom,
% 11.25/11.13 ! [V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf_Oidem,axiom,
% 11.25/11.13 ! [V_a,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__fun__def,axiom,
% 11.25/11.13 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__min,axiom,
% 11.25/11.13 ! [T_b] :
% 11.25/11.13 ( ( class_Lattices_Osemilattice__inf(T_b)
% 11.25/11.13 & class_Orderings_Olinorder(T_b) )
% 11.25/11.13 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Oidem,axiom,
% 11.25/11.13 ! [V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_less__infI1,axiom,
% 11.25/11.13 ! [V_b,V_x,V_a,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_less__infI2,axiom,
% 11.25/11.13 ! [V_a,V_x,V_b,T_a] :
% 11.25/11.13 ( class_Lattices_Osemilattice__inf(T_a)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Diff__Int__distrib,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__Diff,axiom,
% 11.25/11.13 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Diff__Int__distrib2,axiom,
% 11.25/11.13 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Diff__Int2,axiom,
% 11.25/11.13 ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Pow__Int__eq,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__simps_I5_J,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__simps_I4_J,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__extend__simps_I5_J,axiom,
% 11.25/11.13 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__UN__distrib,axiom,
% 11.25/11.13 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__extend__simps_I4_J,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__UN__distrib2,axiom,
% 11.25/11.13 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_distrib__sup__le,axiom,
% 11.25/11.13 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_distrib__inf__le,axiom,
% 11.25/11.13 ! [V_z,V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Olattice(T_a)
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_compl__inf__bot,axiom,
% 11.25/11.13 ! [V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Oboolean__algebra(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__compl__bot,axiom,
% 11.25/11.13 ! [V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Oboolean__algebra(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_diff__eq,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Oboolean__algebra(T_a)
% 11.25/11.13 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_compl__sup,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Oboolean__algebra(T_a)
% 11.25/11.13 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_compl__inf,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Oboolean__algebra(T_a)
% 11.25/11.13 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__insert__right,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 11.25/11.13 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 11.25/11.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__insert__left,axiom,
% 11.25/11.13 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 11.25/11.13 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) )
% 11.25/11.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__insert__right__if0,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 11.25/11.13 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__insert__left__if0,axiom,
% 11.25/11.13 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 11.25/11.13 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__insert__right__if1,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__insert__left__if1,axiom,
% 11.25/11.13 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_image__Int__subset,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Diff__triv,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Diff__disjoint,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Un__Int__assoc__eq,axiom,
% 11.25/11.13 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Un__Diff__Int,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Diff__Un,axiom,
% 11.25/11.13 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Diff__Int,axiom,
% 11.25/11.13 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I11_J,axiom,
% 11.25/11.13 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Compl__disjoint2,axiom,
% 11.25/11.13 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Compl__disjoint,axiom,
% 11.25/11.13 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Image__Int__subset,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Compl__Un,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Compl__Int,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Diff__Compl,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Diff__eq,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I14_J,axiom,
% 11.25/11.13 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Image__Id__on,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2] :
% 11.25/11.13 ( c_Nat__Transfer_Onat__set(V_A_2)
% 11.25/11.13 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_congruent2__implies__congruent,axiom,
% 11.25/11.13 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 11.25/11.13 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__Sup__absorb,axiom,
% 11.25/11.13 ! [V_a_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_disjoint__eq__subset__Compl,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I15_J,axiom,
% 11.25/11.13 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__atLeastAtMost,axiom,
% 11.25/11.13 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__atLeastLessThan,axiom,
% 11.25/11.13 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I4_J,axiom,
% 11.25/11.13 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I2_J,axiom,
% 11.25/11.13 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I16_J,axiom,
% 11.25/11.13 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I13_J,axiom,
% 11.25/11.13 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I12_J,axiom,
% 11.25/11.13 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__greaterThanAtMost,axiom,
% 11.25/11.13 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I9_J,axiom,
% 11.25/11.13 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__greaterThanLessThan,axiom,
% 11.25/11.13 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__atLeastAtMostR1,axiom,
% 11.25/11.13 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__atLeastAtMostL1,axiom,
% 11.25/11.13 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I8_J,axiom,
% 11.25/11.13 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I7_J,axiom,
% 11.25/11.13 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__atLeastAtMostR2,axiom,
% 11.25/11.13 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Int__atLeastAtMostL2,axiom,
% 11.25/11.13 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I3_J,axiom,
% 11.25/11.13 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I10_J,axiom,
% 11.25/11.13 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I1_J,axiom,
% 11.25/11.13 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I6_J,axiom,
% 11.25/11.13 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_ivl__disj__int_I5_J,axiom,
% 11.25/11.13 ! [V_u_2,V_l_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.25/11.13 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_compl__unique,axiom,
% 11.25/11.13 ! [V_y,V_x,T_a] :
% 11.25/11.13 ( class_Lattices_Oboolean__algebra(T_a)
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 11.25/11.13 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__Un__Int,axiom,
% 11.25/11.13 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod_Ounion__inter,axiom,
% 11.25/11.13 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__Un__Int,axiom,
% 11.25/11.13 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_card_Ounion__inter,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_card__Un__Int,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_card__Diff__subset__Int,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.13 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__restrict__set,axiom,
% 11.25/11.13 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Ounion__inter,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_quotient__disj,axiom,
% 11.25/11.13 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => ( V_X_2 = V_Y_2
% 11.25/11.13 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_atMost__Int__atLeast,axiom,
% 11.25/11.13 ! [V_n_2,T_b] :
% 11.25/11.13 ( class_Orderings_Oorder(T_b)
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__one_Ounion__disjoint,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__one_Ounion__inter,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__Un__disjoint,axiom,
% 11.25/11.13 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__Un,axiom,
% 11.25/11.13 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Oab__group__add(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod_Ounion__disjoint,axiom,
% 11.25/11.13 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__Un__disjoint,axiom,
% 11.25/11.13 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_card__Un__disjoint,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Sup__fin_Ounion__inter,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Min_Ounion__inter,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Min_Ounion__disjoint,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Max_Ounion__disjoint,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Max_Ounion__inter,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Orderings_Olinorder(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_congruent2D,axiom,
% 11.25/11.13 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
% 11.25/11.13 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__Un__nat,axiom,
% 11.25/11.13 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding_Ounion,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_congruentD,axiom,
% 11.25/11.13 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
% 11.25/11.13 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_congruent2__implies__congruent__UN,axiom,
% 11.25/11.13 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 11.25/11.13 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 11.25/11.13 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 11.25/11.13 => c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__equiv__class__inject,axiom,
% 11.25/11.13 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 11.25/11.13 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.13 => ! [B_y] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 11.25/11.13 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) )
% 11.25/11.13 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__equiv__class__type2,axiom,
% 11.25/11.13 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 11.25/11.13 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 11.25/11.13 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
% 11.25/11.13 => ( ! [B_x1] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 11.25/11.13 => ! [B_x2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_UN__equiv__class__type,axiom,
% 11.25/11.13 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__nat__def,axiom,
% 11.25/11.13 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf__Int__eq2,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_card_Ounion__inter__neutral,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.13 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.25/11.13 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__Un,axiom,
% 11.25/11.13 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Fields_Ofield(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.13 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Integ__def,axiom,
% 11.25/11.13 c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf2E,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 11.25/11.13 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 11.25/11.13 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf2I,axiom,
% 11.25/11.13 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf2D2,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inf2D1,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Rep__Integ,axiom,
% 11.25/11.13 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_type__definition__Integ,axiom,
% 11.25/11.13 c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 11.25/11.13 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.13 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setprod__Un__one,axiom,
% 11.25/11.13 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 11.25/11.13 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum__Un__zero,axiom,
% 11.25/11.13 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 11.25/11.13 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 11.25/11.13 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.13 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 11.25/11.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Oremove,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 11.25/11.13 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equiv__imp__dvd__card,axiom,
% 11.25/11.13 ! [V_k_2,V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.13 => ( ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) )
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Osingleton,axiom,
% 11.25/11.13 ! [V_x_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_sup__Inf__absorb,axiom,
% 11.25/11.13 ! [V_a_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Oin__idem,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Osubset__idem,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Ounion__idem,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__le__Sup,axiom,
% 11.25/11.13 ! [V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Oinsert,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 11.25/11.13 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Ounion__inter,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Oclosed,axiom,
% 11.25/11.13 ! [V_A_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__idem_Ounion__idem,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equivp__equiv,axiom,
% 11.25/11.13 ! [V_A_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 11.25/11.13 <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_identity__equivp,axiom,
% 11.25/11.13 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equivp__def,axiom,
% 11.25/11.13 ! [V_R_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 11.25/11.13 <=> ! [B_x,B_y] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 11.25/11.13 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equivp__reflp,axiom,
% 11.25/11.13 ! [V_x_2,V_R_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 11.25/11.13 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equivp__symp,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_equivp__transp,axiom,
% 11.25/11.13 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 11.25/11.13 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__idem_Oidem__comp,axiom,
% 11.25/11.13 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 11.25/11.13 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__idem_Oinsert__idem,axiom,
% 11.25/11.13 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.25/11.13 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_card__quotient__disjoint,axiom,
% 11.25/11.13 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
% 11.25/11.13 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_fold__Un__disjoint,axiom,
% 11.25/11.13 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.13 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.13 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_Inf__fin_Ohom__commute,axiom,
% 11.25/11.13 ! [V_N_2,V_h_2,T_b] :
% 11.25/11.13 ( class_Lattices_Olattice(T_b)
% 11.25/11.13 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.13 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__empty,axiom,
% 11.25/11.13 ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__uminus,axiom,
% 11.25/11.13 ! [V_A_2,T_b] :
% 11.25/11.13 ( class_Groups_Oordered__ab__group__add(T_b)
% 11.25/11.13 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__contraD,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.13 => ( V_x_2 != V_y_2
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 11.25/11.13 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__iff,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 11.25/11.13 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 11.25/11.13 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__onD,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.13 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 11.25/11.13 => V_x_2 = V_y_2 ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_card__image,axiom,
% 11.25/11.13 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.13 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.13 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
% 11.25/11.13 <=> V_A_2 = V_B_2 ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_comp__inj__on__iff,axiom,
% 11.25/11.13 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.13 => ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
% 11.25/11.13 <=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_comp__inj__on,axiom,
% 11.25/11.13 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.13 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
% 11.25/11.13 => c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__imageI,axiom,
% 11.25/11.13 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2)
% 11.25/11.13 => c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_finite__imageD,axiom,
% 11.25/11.13 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 11.25/11.13 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 11.25/11.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_subset__inj__on,axiom,
% 11.25/11.13 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.13 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_fold__image__empty,axiom,
% 11.25/11.13 ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__id2,axiom,
% 11.25/11.13 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__def,axiom,
% 11.25/11.13 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.13 <=> ! [B_x] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.13 => ! [B_xa] :
% 11.25/11.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 11.25/11.13 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 11.25/11.13 => B_x = B_xa ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__diff,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.13 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__imageI2,axiom,
% 11.25/11.13 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2)
% 11.25/11.13 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_fold__image__reindex,axiom,
% 11.25/11.13 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 11.25/11.13 ( class_Groups_Oab__semigroup__mult(T_d)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 11.25/11.13 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__image__eq__iff,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.13 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
% 11.25/11.13 <=> V_A_2 = V_B_2 ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__eq,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.13 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 11.25/11.13 <=> V_x_2 = V_y_2 ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_injD,axiom,
% 11.25/11.13 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.13 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 11.25/11.13 => V_x_2 = V_y_2 ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__fun,axiom,
% 11.25/11.13 ! [T_d,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.13 => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__comp,axiom,
% 11.25/11.13 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.13 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 11.25/11.13 => c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__strict__subset,axiom,
% 11.25/11.13 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__Int,axiom,
% 11.25/11.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.13 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 11.25/11.13 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_range__ex1__eq,axiom,
% 11.25/11.13 ! [V_b_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 11.25/11.13 <=> ? [B_x] :
% 11.25/11.13 ( V_b_2 = hAPP(V_f_2,B_x)
% 11.25/11.13 & ! [B_y] :
% 11.25/11.13 ( V_b_2 = hAPP(V_f_2,B_y)
% 11.25/11.13 => B_y = B_x ) ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__image__mem__iff,axiom,
% 11.25/11.13 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 11.25/11.13 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 11.25/11.13 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.13 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.25/11.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.13 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_inj__on__iff__surj,axiom,
% 11.25/11.13 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 11.25/11.13 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => ( ? [B_f] :
% 11.25/11.13 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 11.25/11.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2)) )
% 11.25/11.13 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_endo__inj__surj,axiom,
% 11.25/11.13 ! [V_f_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
% 11.25/11.13 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 11.25/11.13 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_finite__surj__inj,axiom,
% 11.25/11.13 ! [V_f_2,V_A_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
% 11.25/11.13 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_finite__UNIV__surj__inj,axiom,
% 11.25/11.13 ! [V_f_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.13 => ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.13 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 11.25/11.13
% 11.25/11.13 fof(fact_finite__UNIV__inj__surj,axiom,
% 11.25/11.13 ! [V_f_2,T_b] :
% 11.25/11.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.13 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__image__subset__iff,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
% 11.25/11.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__image__Int,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 11.25/11.14 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_image__Int,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__iff__eq__card,axiom,
% 11.25/11.14 ! [V_f_2,T_c,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_eq__card__imp__inj__on,axiom,
% 11.25/11.14 ! [V_f_2,T_c,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
% 11.25/11.14 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__image__set__diff,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 11.25/11.14 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_image__set__diff,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__reindex,axiom,
% 11.25/11.14 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_d)
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_pigeonhole,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
% 11.25/11.14 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__fun__updI,axiom,
% 11.25/11.14 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 11.25/11.14 => c_Fun_Oinj__on(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setprod__reindex__cong,axiom,
% 11.25/11.14 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_d)
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 11.25/11.14 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setprod__reindex,axiom,
% 11.25/11.14 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_d)
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__singleton,axiom,
% 11.25/11.14 ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum_Oreindex,axiom,
% 11.25/11.14 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card__bij__eq,axiom,
% 11.25/11.14 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 11.25/11.14 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.25/11.14 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setprod_Oreindex,axiom,
% 11.25/11.14 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__image__distrib,axiom,
% 11.25/11.14 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__image__Compl__subset,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__image__insert,axiom,
% 11.25/11.14 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Oab__semigroup__mult(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum_Oeq__fold,axiom,
% 11.25/11.14 ! [V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum_OF__eq,axiom,
% 11.25/11.14 ! [V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.14 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setprod_OF__eq,axiom,
% 11.25/11.14 ! [V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.14 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setprod_Oeq__fold,axiom,
% 11.25/11.14 ! [V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__insert,axiom,
% 11.25/11.14 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 11.25/11.14 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 & ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__Un,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.14 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 11.25/11.14 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card__inj__on__le,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__iff__card__le,axiom,
% 11.25/11.14 ! [V_B_2,T_c,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.25/11.14 => ( ? [B_f] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 11.25/11.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2)) )
% 11.25/11.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_quotient__diff1,axiom,
% 11.25/11.14 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__image__Un__Int,axiom,
% 11.25/11.14 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_image__eq__fold__image,axiom,
% 11.25/11.14 ! [V_f_2,T_c,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card__def,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card_Oeq__fold__g,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_comm__monoid__big_OF__eq,axiom,
% 11.25/11.14 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 11.25/11.14 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.14 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.14 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_folding__image_Oreindex,axiom,
% 11.25/11.14 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.14 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 11.25/11.14 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__image__Un__one,axiom,
% 11.25/11.14 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 11.25/11.14 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 11.25/11.14 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__of__nat,axiom,
% 11.25/11.14 ! [T_b] :
% 11.25/11.14 ( class_Nat_Osemiring__char__0(T_b)
% 11.25/11.14 => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__add__nat,axiom,
% 11.25/11.14 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__Suc,axiom,
% 11.25/11.14 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__Some,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b),V_A_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__Inr,axiom,
% 11.25/11.14 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(T_b,tc_sum(T_c,T_b),c_Sum__Type_OInr(T_b,T_c),V_A_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__Inl,axiom,
% 11.25/11.14 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(T_b,tc_sum(T_b,T_c),c_Sum__Type_OInl(T_b,T_c),V_A_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__int,axiom,
% 11.25/11.14 c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_swap__inj__on,axiom,
% 11.25/11.14 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_folding__image_Odistrib,axiom,
% 11.25/11.14 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.14 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_folding__image_Oeq__fold,axiom,
% 11.25/11.14 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.14 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 11.25/11.14 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 11.25/11.14 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.14 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_the__inv__into__comp,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
% 11.25/11.14 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
% 11.25/11.14 => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_the__inv__into__into,axiom,
% 11.25/11.14 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__vimage__singleton,axiom,
% 11.25/11.14 ! [V_a_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimageI,axiom,
% 11.25/11.14 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 11.25/11.14 ( hAPP(V_f_2,V_a_2) = V_b_2
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__Diff,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_image__vimage__subset,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_surj__image__vimage__eq,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_b,T_c] :
% 11.25/11.14 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__eq,axiom,
% 11.25/11.14 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 11.25/11.14 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimageD,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimageI2,axiom,
% 11.25/11.14 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__mono,axiom,
% 11.25/11.14 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__Un,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__empty,axiom,
% 11.25/11.14 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__ident,axiom,
% 11.25/11.14 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__Compl,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__code,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 11.25/11.14 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__UN,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__compose,axiom,
% 11.25/11.14 ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__UNIV,axiom,
% 11.25/11.14 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__Int,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__singleton__eq,axiom,
% 11.25/11.14 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 11.25/11.14 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__insert,axiom,
% 11.25/11.14 ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__vimageD,axiom,
% 11.25/11.14 ! [V_F_2,V_h_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 11.25/11.14 => ( hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__subsetD,axiom,
% 11.25/11.14 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 11.25/11.14 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_image__vimage__eq,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__vimageI,axiom,
% 11.25/11.14 ! [V_h_2,T_c,V_F_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 11.25/11.14 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__vimage__image__eq,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__const,axiom,
% 11.25/11.14 ! [T_c,V_A_2,V_c_2,T_b] :
% 11.25/11.14 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.14 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.14 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__eq__UN,axiom,
% 11.25/11.14 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_the__inv__into__f__f,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.14 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_the__inv__into__f__eq,axiom,
% 11.25/11.14 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.14 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_the__inv__f__f,axiom,
% 11.25/11.14 ! [V_x_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_the__inv__into__onto,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__the__inv__into,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__subsetI,axiom,
% 11.25/11.14 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_the__inv__into__def,axiom,
% 11.25/11.14 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__if,axiom,
% 11.25/11.14 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 11.25/11.14 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.14 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 11.25/11.14 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 11.25/11.14 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 11.25/11.14 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 11.25/11.14 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 11.25/11.14 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_f__the__inv__into__f,axiom,
% 11.25/11.14 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 11.25/11.14 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_ImageE,axiom,
% 11.25/11.14 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 11.25/11.14 => ~ ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
% 11.25/11.14 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_strong__setprod__reindex__cong,axiom,
% 11.25/11.14 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_d)
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) )
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_dom__eq__singleton__conv,axiom,
% 11.25/11.14 ! [V_x_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Map_Odom(T_b,T_c,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),B_v)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__dom__body,axiom,
% 11.25/11.14 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_domIff,axiom,
% 11.25/11.14 ! [V_m_2,T_c,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
% 11.25/11.14 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_domI,axiom,
% 11.25/11.14 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 11.25/11.14 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_insert__dom,axiom,
% 11.25/11.14 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
% 11.25/11.14 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 11.25/11.14 => hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) = c_Map_Odom(T_c,T_b,V_f_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_dom__restrict,axiom,
% 11.25/11.14 ! [V_A_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m_2)),V_A_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_dom__empty,axiom,
% 11.25/11.14 ! [T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_dom__eq__empty__conv,axiom,
% 11.25/11.14 ! [V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_dom__const,axiom,
% 11.25/11.14 ! [V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_dom__minus,axiom,
% 11.25/11.14 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
% 11.25/11.14 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b)
% 11.25/11.14 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),V_A_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_dom__fun__upd,axiom,
% 11.25/11.14 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
% 11.25/11.14 ( ( V_y_2 = c_Option_Ooption_ONone(T_b)
% 11.25/11.14 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) )
% 11.25/11.14 & ( V_y_2 != c_Option_Ooption_ONone(T_b)
% 11.25/11.14 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__graph__permute__diff,axiom,
% 11.25/11.14 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 11.25/11.14 ( class_Groups_Oab__semigroup__mult(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_ran__restrictD,axiom,
% 11.25/11.14 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Map_Oran(T_c,T_b,c_Map_Orestrict__map(T_c,T_b,V_m_2,V_A_2))))
% 11.25/11.14 => ? [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.25/11.14 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_accp__acc__eq,axiom,
% 11.25/11.14 ! [V_x_2,V_r_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
% 11.25/11.14 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__graph__imp__finite,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_empty__fold__graphE,axiom,
% 11.25/11.14 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))
% 11.25/11.14 => V_x_2 = V_z_2 ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__graph_OemptyI,axiom,
% 11.25/11.14 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 11.25/11.14 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__graph_OinsertI,axiom,
% 11.25/11.14 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 11.25/11.14 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_acc__subset,axiom,
% 11.25/11.14 ! [V_R2_2,V_R1_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__graph__insert__swap,axiom,
% 11.25/11.14 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 11.25/11.14 ( class_Groups_Oab__semigroup__mult(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
% 11.25/11.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_acc__downward,axiom,
% 11.25/11.14 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_acc_Osimps,axiom,
% 11.25/11.14 ! [V_r_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 11.25/11.14 <=> ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Diff1__fold__graph,axiom,
% 11.25/11.14 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1Set_Ointros,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 11.25/11.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_max__extp_Oequations,axiom,
% 11.25/11.14 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 11.25/11.14 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 11.25/11.14 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 11.25/11.14 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 & ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 11.25/11.14 => ? [B_xa] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 11.25/11.14 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_max__ext_Ointros,axiom,
% 11.25/11.14 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 11.25/11.14 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 11.25/11.14 => ? [B_xa] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 11.25/11.14 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) )
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1Set__nonempty,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 11.25/11.14 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_empty__fold1SetE,axiom,
% 11.25/11.14 ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1Set__sing,axiom,
% 11.25/11.14 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
% 11.25/11.14 <=> V_a_2 = V_b_2 ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1Set_Oequations,axiom,
% 11.25/11.14 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
% 11.25/11.14 <=> ? [B_a,B_A] :
% 11.25/11.14 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 11.25/11.14 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 11.25/11.14 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_insert__fold1SetE,axiom,
% 11.25/11.14 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2))
% 11.25/11.14 => ~ ! [B_a,B_A] :
% 11.25/11.14 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_image__split__eq__Sigma,axiom,
% 11.25/11.14 ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_SigmaI,axiom,
% 11.25/11.14 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sigma__Diff__distrib2,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Times__Diff__distrib1,axiom,
% 11.25/11.14 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sigma__Diff__distrib1,axiom,
% 11.25/11.14 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Times__eq__cancel2,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 11.25/11.14 => ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
% 11.25/11.14 <=> V_A_2 = V_B_2 ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sigma__empty1,axiom,
% 11.25/11.14 ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_UNIV__char,axiom,
% 11.25/11.14 c_Orderings_Otop__class_Otop(tc_fun(tc_String_Ochar,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_prod(tc_String_Onibble,tc_String_Onibble),tc_String_Ochar,hAPP(c_Product__Type_Oprod_Oprod__case(tc_String_Onibble,tc_String_Onibble,tc_String_Ochar),c_String_Ochar_OChar)),hAPP(hAPP(c_Product__Type_OSigma(tc_String_Onibble,tc_String_Onibble),c_Orderings_Otop__class_Otop(tc_fun(tc_String_Onibble,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(tc_String_Onibble,tc_HOL_Obool),tc_String_Onibble),c_Orderings_Otop__class_Otop(tc_fun(tc_String_Onibble,tc_HOL_Obool))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card__cartesian__product,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__cartesian__product,axiom,
% 11.25/11.14 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sigma__empty2,axiom,
% 11.25/11.14 ! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Times__empty,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.14 ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
% 11.25/11.14 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Compl__Times__UNIV1,axiom,
% 11.25/11.14 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Compl__Times__UNIV2,axiom,
% 11.25/11.14 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setprod__cartesian__product,axiom,
% 11.25/11.14 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_b)
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sigma__Un__distrib1,axiom,
% 11.25/11.14 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Times__Un__distrib1,axiom,
% 11.25/11.14 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sigma__Un__distrib2,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_swap__product,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__cartesian__product,axiom,
% 11.25/11.14 ! [V_B_2,T_c,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_equiv__type,axiom,
% 11.25/11.14 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.14 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sigma__Int__distrib1,axiom,
% 11.25/11.14 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Times__Int__distrib1,axiom,
% 11.25/11.14 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sigma__Int__distrib2,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Id__on__subset__Times,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_UNIV__Times__UNIV,axiom,
% 11.25/11.14 ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_mem__Sigma__iff,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 11.25/11.14 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_SigmaD1,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_SigmaD2,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_SigmaE2,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 11.25/11.14 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card__cartesian__product__singleton,axiom,
% 11.25/11.14 ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Times__subset__cancel2,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
% 11.25/11.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Image__subset,axiom,
% 11.25/11.14 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__cartesian__productD2,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__cartesian__productD1,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 11.25/11.14 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fst__image__times,axiom,
% 11.25/11.14 ! [V_A_2,T_c,T_b,V_B_2] :
% 11.25/11.14 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 11.25/11.14 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_snd__image__times,axiom,
% 11.25/11.14 ! [V_B_2,T_c,T_b,V_A_2] :
% 11.25/11.14 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 11.25/11.14 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2 ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_insert__times__insert,axiom,
% 11.25/11.14 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__equiv__class,axiom,
% 11.25/11.14 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_UN__Times__distrib,axiom,
% 11.25/11.14 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sigma__def,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__quotient,axiom,
% 11.25/11.14 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__Times,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 11.25/11.14 ! [V_A_2,V_I_2,T_c,T_b] :
% 11.25/11.14 ? [B_f] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))
% 11.25/11.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__image__Sigma,axiom,
% 11.25/11.14 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_d)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 11.25/11.14 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__SigmaI,axiom,
% 11.25/11.14 ! [V_B_2,T_c,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ! [B_a] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setprod__Sigma,axiom,
% 11.25/11.14 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_d)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__Sigma,axiom,
% 11.25/11.14 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_d)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card__SigmaI,axiom,
% 11.25/11.14 ! [V_B_2,T_c,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 11.25/11.14 => hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_SigmaE,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 11.25/11.14 => ~ ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => ! [B_y] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 11.25/11.14 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair__surj,axiom,
% 11.25/11.14 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 11.25/11.14 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
% 11.25/11.14 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair__inj__on,axiom,
% 11.25/11.14 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 11.25/11.14 => c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair__imageI,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fst__comp__map__pair,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_snd__comp__map__pair,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair_Ocomp,axiom,
% 11.25/11.14 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair__compose,axiom,
% 11.25/11.14 ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair_Ocompositionality,axiom,
% 11.25/11.14 ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair__ident,axiom,
% 11.25/11.14 ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_snd__prod__fun,axiom,
% 11.25/11.14 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fst__map__pair,axiom,
% 11.25/11.14 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair__simp,axiom,
% 11.25/11.14 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair__def,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair__surj__on,axiom,
% 11.25/11.14 ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 11.25/11.14 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 11.25/11.14 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 11.25/11.14 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_prod__fun__imageE,axiom,
% 11.25/11.14 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
% 11.25/11.14 => ~ ! [B_x,B_y] :
% 11.25/11.14 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 11.25/11.14 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_refl__on__def,axiom,
% 11.25/11.14 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.14 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 11.25/11.14 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 11.25/11.14 & ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_refl__on__Id__on,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_refl__on__empty,axiom,
% 11.25/11.14 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_refl__on__Un,axiom,
% 11.25/11.14 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 11.25/11.14 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 11.25/11.14 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 11.25/11.14 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_refl__on__Int,axiom,
% 11.25/11.14 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 11.25/11.14 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 11.25/11.14 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 11.25/11.14 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_refl__onD,axiom,
% 11.25/11.14 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 11.25/11.14 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_refl__onD1,axiom,
% 11.25/11.14 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 11.25/11.14 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_refl__onD2,axiom,
% 11.25/11.14 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 11.25/11.14 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_refl__onI,axiom,
% 11.25/11.14 ! [V_A_2,V_r_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
% 11.25/11.14 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__Un,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Groups_Oab__semigroup__mult(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.14 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__singleton,axiom,
% 11.25/11.14 ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__singleton__def,axiom,
% 11.25/11.14 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 11.25/11.14 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 11.25/11.14 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_folding__one_Oeq__fold,axiom,
% 11.25/11.14 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.14 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__def,axiom,
% 11.25/11.14 ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sup__fin_OF__eq,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( class_Lattices_Olattice(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Inf__fin_OF__eq,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( class_Lattices_Olattice(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Min_OF__eq,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Max_OF__eq,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__belowI,axiom,
% 11.25/11.14 ! [V_a_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Lattices_Osemilattice__inf(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_below__fold1__iff,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Lattices_Osemilattice__inf(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
% 11.25/11.14 <=> ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__max_Ofold1__belowI,axiom,
% 11.25/11.14 ! [V_a_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__insert__idem,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
% 11.25/11.14 <=> ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__below__iff,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
% 11.25/11.14 <=> ? [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__Un2,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.14 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__strict__below__iff,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
% 11.25/11.14 <=> ? [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_strict__below__fold1__iff,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
% 11.25/11.14 <=> ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__insert,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Groups_Oab__semigroup__mult(T_b)
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.14 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__antimono,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_semilattice__big_OF__eq,axiom,
% 11.25/11.14 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 11.25/11.14 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold1__in,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( class_Groups_Oab__semigroup__mult(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_hom__fold1__commute,axiom,
% 11.25/11.14 ! [V_N_2,V_h_2,T_b] :
% 11.25/11.14 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 11.25/11.14 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.14 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setprod__pos__nat,axiom,
% 11.25/11.14 ! [V_f_2,V_S_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) )
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 11.25/11.14 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 11.25/11.14 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 11.25/11.14 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.14 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Rep__Integ__cases,axiom,
% 11.25/11.14 ! [V_y_2] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 11.25/11.14 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Rep__Integ__induct,axiom,
% 11.25/11.14 ! [V_Pa_2,V_y_2] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 11.25/11.14 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
% 11.25/11.14 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fun__left__comm__idem__remove,axiom,
% 11.25/11.14 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 11.25/11.14 ! [V_x_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 11.25/11.14 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 11.25/11.14 ! [T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fun__left__comm__idem,axiom,
% 11.25/11.14 ! [T_b] :
% 11.25/11.14 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 11.25/11.14 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fun__left__comm__idem__sup,axiom,
% 11.25/11.14 ! [T_b] :
% 11.25/11.14 ( class_Lattices_Osemilattice__sup(T_b)
% 11.25/11.14 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 11.25/11.14 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 11.25/11.14 => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 11.25/11.14 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 11.25/11.14 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fun__left__comm__idem__insert,axiom,
% 11.25/11.14 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fun__left__comm__idem__inf,axiom,
% 11.25/11.14 ! [T_b] :
% 11.25/11.14 ( class_Lattices_Osemilattice__inf(T_b)
% 11.25/11.14 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 11.25/11.14 ! [T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.25/11.14 => hAPP(V_g_2,B_x) = V_z_2 )
% 11.25/11.14 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card__less__Suc2,axiom,
% 11.25/11.14 ! [V_i_2,V_M_2] :
% 11.25/11.14 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 11.25/11.14 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_CollectI,axiom,
% 11.25/11.14 ! [T_b,V_a_2,V_Pa_2] :
% 11.25/11.14 ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__Collect__conjI,axiom,
% 11.25/11.14 ! [V_Qa_2,V_Pa_2,T_b] :
% 11.25/11.14 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 11.25/11.14 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) )
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__Collect__less__nat,axiom,
% 11.25/11.14 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__Collect__le__nat,axiom,
% 11.25/11.14 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Collect__conv__if,axiom,
% 11.25/11.14 ! [T_b,V_a_2,V_Pa_2] :
% 11.25/11.14 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 11.25/11.14 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 11.25/11.14 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Collect__conv__if2,axiom,
% 11.25/11.14 ! [T_b,V_a_2,V_Pa_2] :
% 11.25/11.14 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 11.25/11.14 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 11.25/11.14 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_singleton__conv,axiom,
% 11.25/11.14 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_singleton__conv2,axiom,
% 11.25/11.14 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_insert__compr,axiom,
% 11.25/11.14 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_insert__compr__raw,axiom,
% 11.25/11.14 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__Collect__disjI,axiom,
% 11.25/11.14 ! [V_Qa_2,V_Pa_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2))))
% 11.25/11.14 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 11.25/11.14 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Collect__conj__eq,axiom,
% 11.25/11.14 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Collect__def,axiom,
% 11.25/11.14 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_insert__Collect,axiom,
% 11.25/11.14 ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_empty__def,axiom,
% 11.25/11.14 ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_empty__Collect__eq,axiom,
% 11.25/11.14 ! [V_Pa_2,T_b] :
% 11.25/11.14 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
% 11.25/11.14 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Collect__empty__eq,axiom,
% 11.25/11.14 ! [V_Pa_2,T_b] :
% 11.25/11.14 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Collect__disj__eq,axiom,
% 11.25/11.14 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_CollectE,axiom,
% 11.25/11.14 ! [V_Pa_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 11.25/11.14 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_CollectD,axiom,
% 11.25/11.14 ! [V_Pa_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 11.25/11.14 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_mem__Collect__eq,axiom,
% 11.25/11.14 ! [V_Pa_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 11.25/11.14 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Collect__mem__eq,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Collect__neg__eq,axiom,
% 11.25/11.14 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_UNIV__def,axiom,
% 11.25/11.14 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__Collect__eq,axiom,
% 11.25/11.14 ! [V_Pa_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Collect__split,axiom,
% 11.25/11.14 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_SetCompr__Sigma__eq,axiom,
% 11.25/11.14 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Qa_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Int__Collect,axiom,
% 11.25/11.14 ! [V_Pa_2,V_A_2,V_x_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))))
% 11.25/11.14 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.14 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Int__def,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Un__def,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_set__diff__eq,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__Collect__not,axiom,
% 11.25/11.14 ! [V_Pa_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))))
% 11.25/11.14 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_insert__def,axiom,
% 11.25/11.14 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Compl__eq,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__def,axiom,
% 11.25/11.14 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Collect__imp__eq,axiom,
% 11.25/11.14 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_dom__def,axiom,
% 11.25/11.14 ! [V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_c)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__M__bounded__by__nat,axiom,
% 11.25/11.14 ! [V_i_2,V_Pa_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_Pa_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__setsum__restrict,axiom,
% 11.25/11.14 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_d)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_if__image__distrib,axiom,
% 11.25/11.14 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_dom__if,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,V_Pa_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),T_b),c_If(tc_Option_Ooption(T_c))),V_Pa_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_g_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_nat__seg__image__imp__finite,axiom,
% 11.25/11.14 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 11.25/11.14 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2)))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__restrict__set_H,axiom,
% 11.25/11.14 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__image__gen,axiom,
% 11.25/11.14 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Image__singleton,axiom,
% 11.25/11.14 ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__cases,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card__less__Suc,axiom,
% 11.25/11.14 ! [V_i_2,V_M_2] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 11.25/11.14 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card__less,axiom,
% 11.25/11.14 ! [V_i_2,V_M_2] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 11.25/11.14 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_dom__override__on,axiom,
% 11.25/11.14 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Fun_Ooverride__on(T_b,tc_Option_Ooption(T_c),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2)))))),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__multicount,axiom,
% 11.25/11.14 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 11.25/11.14 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__Collect__subsets,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Pow__def,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_override__on__apply__in,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_override__on__apply__notin,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 11.25/11.14 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_override__on__emptyset,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__graph,axiom,
% 11.25/11.14 ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 11.25/11.14 ! [V_Pa_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_override__on__def,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 11.25/11.14 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) )
% 11.25/11.14 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.25/11.14 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__psubset__def,axiom,
% 11.25/11.14 ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inv__image__def,axiom,
% 11.25/11.14 ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 11.25/11.14 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 11.25/11.14 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_Pa_2),c_Int_Onat)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Nitpick_Oprod__def,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_int__ge__less__than__def,axiom,
% 11.25/11.14 ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_int__ge__less__than2__def,axiom,
% 11.25/11.14 ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_reflp__def,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Predicate_Oreflp(T_b,V_r_2)
% 11.25/11.14 <=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_reflpE,axiom,
% 11.25/11.14 ! [V_x_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Predicate_Oreflp(T_b,V_r_2)
% 11.25/11.14 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.14 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.14 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__Collect__bounded__ex,axiom,
% 11.25/11.14 ! [V_Qa_2,T_c,V_Pa_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2)))))
% 11.25/11.14 <=> ! [B_y] :
% 11.25/11.14 ( hBOOL(hAPP(V_Pa_2,B_y))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Qa_2),B_y)))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__image__set,axiom,
% 11.25/11.14 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_Pa_2))))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_ran__def,axiom,
% 11.25/11.14 ! [V_m_2,T_b,T_c] : c_Map_Oran(T_c,T_b,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_b)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Pow__Compl,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_add__Min__commute,axiom,
% 11.25/11.14 ! [V_k_2,V_N_2,T_b] :
% 11.25/11.14 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.14 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_add__Max__commute,axiom,
% 11.25/11.14 ! [V_k_2,V_N_2,T_b] :
% 11.25/11.14 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 11.25/11.14 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_sup__Inf1__distrib,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Lattices_Odistrib__lattice(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_sup__Inf2__distrib,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Lattices_Odistrib__lattice(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.14 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inf__Sup2__distrib,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Lattices_Odistrib__lattice(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.14 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inf__Sup1__distrib,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Lattices_Odistrib__lattice(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 11.25/11.14 ( class_Rings_Osemiring__0(T_d)
% 11.25/11.14 => ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
% 11.25/11.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__multicount__gen,axiom,
% 11.25/11.14 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 11.25/11.14 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__id,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_o__id,axiom,
% 11.25/11.14 ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_id__o,axiom,
% 11.25/11.14 ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_o__eq__id__dest,axiom,
% 11.25/11.14 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 11.25/11.14 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2)
% 11.25/11.14 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_vimage__id,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_id__def,axiom,
% 11.25/11.14 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_id__apply,axiom,
% 11.25/11.14 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 11.25/11.14
% 11.25/11.14 fof(fact_apfst__id,axiom,
% 11.25/11.14 ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_apsnd__id,axiom,
% 11.25/11.14 ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_of__int__eq__id,axiom,
% 11.25/11.14 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair_Oidentity,axiom,
% 11.25/11.14 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_map__pair_Oid,axiom,
% 11.25/11.14 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_image__id,axiom,
% 11.25/11.14 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_surj__id,axiom,
% 11.25/11.14 ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_folding_Oempty,axiom,
% 11.25/11.14 ! [V_F_2,V_f_2,T_c,T_b] :
% 11.25/11.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.25/11.14 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_apfst__def,axiom,
% 11.25/11.14 ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_apsnd__def,axiom,
% 11.25/11.14 ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_split__Pair,axiom,
% 11.25/11.14 ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__reindex__id,axiom,
% 11.25/11.14 ! [V_B_2,V_f_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setprod__reindex__id,axiom,
% 11.25/11.14 ! [V_B_2,V_f_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__conv__nat__seg__image,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rel__comp__def,axiom,
% 11.25/11.14 ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rel__compI,axiom,
% 11.25/11.14 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_O__assoc,axiom,
% 11.25/11.14 ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rel__comp__mono,axiom,
% 11.25/11.14 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rel__comp__distrib,axiom,
% 11.25/11.14 ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rel__comp__distrib2,axiom,
% 11.25/11.14 ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rel__comp__empty1,axiom,
% 11.25/11.14 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rel__comp__empty2,axiom,
% 11.25/11.14 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rel__comp__UNION__distrib,axiom,
% 11.25/11.14 ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rel__comp__UNION__distrib2,axiom,
% 11.25/11.14 ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_union__comp__emptyR,axiom,
% 11.25/11.14 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 11.25/11.14 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 11.25/11.14 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_union__comp__emptyL,axiom,
% 11.25/11.14 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 11.25/11.14 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 11.25/11.14 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 11.25/11.14 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rel__comp__subset__Sigma,axiom,
% 11.25/11.14 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2)))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_max__ext__compat,axiom,
% 11.25/11.14 ! [V_S_2,V_R_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__ext__compat,axiom,
% 11.25/11.14 ! [V_S_2,V_R_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_pred__comp__rel__comp__eq,axiom,
% 11.25/11.14 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 11.25/11.14 ( c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2),V_x_2,V_y_2)
% 11.25/11.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_reduction__pairI,axiom,
% 11.25/11.14 ! [V_S_2,V_R_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_R_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 11.25/11.14 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__less__than,axiom,
% 11.25/11.14 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_pred__comp_Ointros,axiom,
% 11.25/11.14 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 11.25/11.14 => c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a_2,V_c_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__empty,axiom,
% 11.25/11.14 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__inv__image,axiom,
% 11.25/11.14 ! [V_f_2,T_c,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__lex__prod,axiom,
% 11.25/11.14 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 11.25/11.14 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 11.25/11.14 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__measure,axiom,
% 11.25/11.14 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__comp__self,axiom,
% 11.25/11.14 ! [V_R_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_R_2)
% 11.25/11.14 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__no__loop,axiom,
% 11.25/11.14 ! [V_R_2,T_b] :
% 11.25/11.14 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 11.25/11.14 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__union__merge,axiom,
% 11.25/11.14 ! [V_S_2,V_R_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 11.25/11.14 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__less,axiom,
% 11.25/11.14 c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__int__ge__less__than,axiom,
% 11.25/11.14 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_acc__wfD,axiom,
% 11.25/11.14 ! [V_x_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__acc__iff,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__irrefl,axiom,
% 11.25/11.14 ! [V_a_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__asym,axiom,
% 11.25/11.14 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 11.25/11.14 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__not__sym,axiom,
% 11.25/11.14 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 11.25/11.14 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__not__refl,axiom,
% 11.25/11.14 ! [V_a_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__subset,axiom,
% 11.25/11.14 ! [V_p_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
% 11.25/11.14 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_min__ext__wf,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__finite__psubset,axiom,
% 11.25/11.14 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_pred__comp_Oequations,axiom,
% 11.25/11.14 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 11.25/11.14 ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2)
% 11.25/11.14 <=> ? [B_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 11.25/11.14 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__pair__less,axiom,
% 11.25/11.14 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__mlex,axiom,
% 11.25/11.14 ! [V_f_2,V_R_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_R_2)
% 11.25/11.14 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_max__ext__wf,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__Int1,axiom,
% 11.25/11.14 ! [V_r_H_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__Int2,axiom,
% 11.25/11.14 ! [V_r_H_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__int__ge__less__than2,axiom,
% 11.25/11.14 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 <=> ~ ? [B_f] :
% 11.25/11.14 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wfE__pf,axiom,
% 11.25/11.14 ! [V_A_2,V_R_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_R_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
% 11.25/11.14 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__union__compatible,axiom,
% 11.25/11.14 ! [V_S_2,V_R_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_R_2)
% 11.25/11.14 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 11.25/11.14 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf,axiom,
% 11.25/11.14 ! [T_b] :
% 11.25/11.14 ( class_Orderings_Owellorder(T_b)
% 11.25/11.14 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_reduction__pair__def,axiom,
% 11.25/11.14 ! [V_Pa_2,T_b] :
% 11.25/11.14 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 11.25/11.14 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))
% 11.25/11.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_reduction__pair__lemma,axiom,
% 11.25/11.14 ! [V_S_2,V_R_2,V_Pa_2,T_b] :
% 11.25/11.14 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 11.25/11.14 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 11.25/11.14 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__map__pair__image,axiom,
% 11.25/11.14 ! [V_f_2,T_c,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.25/11.14 => c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__lenlex,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__if__measure,axiom,
% 11.25/11.14 ! [T_b,V_g_2,V_f_2,V_Pa_2] :
% 11.25/11.14 ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(V_Pa_2,B_x))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) )
% 11.25/11.14 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_pred__nat__def,axiom,
% 11.25/11.14 c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__lex,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__pred__nat,axiom,
% 11.25/11.14 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_lex__def,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__lexn,axiom,
% 11.25/11.14 ! [V_n_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_lexn_Osimps_I1_J,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__same__fst,axiom,
% 11.25/11.14 ! [T_b,V_R_2,T_c,V_Pa_2] :
% 11.25/11.14 ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(V_Pa_2,B_x))
% 11.25/11.14 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 11.25/11.14 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Range__Collect__split,axiom,
% 11.25/11.14 ! [V_Pa_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_RangeI,axiom,
% 11.25/11.14 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Range__Id__on,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Range__empty__iff,axiom,
% 11.25/11.14 ! [V_r_2,T_b,T_c] :
% 11.25/11.14 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Range__empty,axiom,
% 11.25/11.14 ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Range__Un__eq,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__Range,axiom,
% 11.25/11.14 ! [V_r_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_snd__eq__Range,axiom,
% 11.25/11.14 ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Range__iff,axiom,
% 11.25/11.14 ! [V_r_2,T_c,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 11.25/11.14 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Range__insert,axiom,
% 11.25/11.14 ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Range__Int__subset,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Range__Diff__subset,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_RangeP__Range__eq,axiom,
% 11.25/11.14 ! [V_x_2,V_r_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
% 11.25/11.14 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_RangeE,axiom,
% 11.25/11.14 ! [V_r_2,T_c,V_b_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 11.25/11.14 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_RangeP_Ointros,axiom,
% 11.25/11.14 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 11.25/11.14 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_RangeP_Oequations,axiom,
% 11.25/11.14 ! [V_a2_2,V_r_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 11.25/11.14 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__Un,axiom,
% 11.25/11.14 ! [V_s_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 11.25/11.14 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wfP__def,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 11.25/11.14 <=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wfP__empty,axiom,
% 11.25/11.14 ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_DomainI,axiom,
% 11.25/11.14 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wfP__accp__iff,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 11.25/11.14 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_accp__wfPD,axiom,
% 11.25/11.14 ! [V_x_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 11.25/11.14 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__Id__on,axiom,
% 11.25/11.14 ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wfP__subset,axiom,
% 11.25/11.14 ! [V_p_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
% 11.25/11.14 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__empty__iff,axiom,
% 11.25/11.14 ! [V_r_2,T_c,T_b] :
% 11.25/11.14 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__empty,axiom,
% 11.25/11.14 ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__mono,axiom,
% 11.25/11.14 ! [V_s_2,V_r_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__Un__eq,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__Domain,axiom,
% 11.25/11.14 ! [V_r_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fst__eq__Domain,axiom,
% 11.25/11.14 ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__iff,axiom,
% 11.25/11.14 ! [V_r_2,T_c,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 11.25/11.14 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__insert,axiom,
% 11.25/11.14 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__Int__subset,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__Diff__subset,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Field__def,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__in__rel,axiom,
% 11.25/11.14 ! [V_R_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_R_2)
% 11.25/11.14 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wfP__wf__eq,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
% 11.25/11.14 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__Collect__split,axiom,
% 11.25/11.14 ! [V_Pa_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_DomainP__Domain__eq,axiom,
% 11.25/11.14 ! [V_x_2,V_r_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
% 11.25/11.14 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_DomainE,axiom,
% 11.25/11.14 ! [V_r_2,T_c,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 11.25/11.14 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_DomainP_Ointros,axiom,
% 11.25/11.14 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 11.25/11.14 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_DomainP_Oequations,axiom,
% 11.25/11.14 ! [V_a1_2,V_r_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 11.25/11.14 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wfP__acyclicP,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_pos__map__def,axiom,
% 11.25/11.14 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__acyclic,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_acyclic__subset,axiom,
% 11.25/11.14 ! [V_r_2,V_s_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 11.25/11.14 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__acyclic__wf,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 11.25/11.14 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 11.25/11.14 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_pos__single__def,axiom,
% 11.25/11.14 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Nitpick_Owf_H__def,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 11.25/11.14 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 11.25/11.14 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 11.25/11.14 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_New__DSequence_Opos__single__def,axiom,
% 11.25/11.14 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Osingle(T_a,V_x) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_neg__map__def,axiom,
% 11.25/11.14 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_neg__single__def,axiom,
% 11.25/11.14 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_pigeonhole__infinite,axiom,
% 11.25/11.14 ! [V_f_2,T_c,V_A_2,T_b] :
% 11.25/11.14 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 11.25/11.14 => ? [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 11.25/11.14 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_refl__on__def_H,axiom,
% 11.25/11.14 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.14 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 11.25/11.14 <=> ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) )
% 11.25/11.14 & ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Powp__def,axiom,
% 11.25/11.14 ! [V_B_2,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 11.25/11.14 <=> ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 11.25/11.14 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_ball__empty,axiom,
% 11.25/11.14 ! [V_Pa_2,T_b,B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.14 => hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_congruent__def,axiom,
% 11.25/11.14 ! [V_f_2,V_r_2,T_c,T_b] :
% 11.25/11.14 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 11.25/11.14 <=> ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Abs__Integ__cases,axiom,
% 11.25/11.14 ! [V_x_2] :
% 11.25/11.14 ~ ! [B_y] :
% 11.25/11.14 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 11.25/11.14 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Abs__Integ__induct,axiom,
% 11.25/11.14 ! [V_x_2,V_Pa_2] :
% 11.25/11.14 ( ! [B_y] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 11.25/11.14 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 11.25/11.14 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_hoare__valids__def,axiom,
% 11.25/11.14 ! [V_ts_2,V_G_2,T_b] :
% 11.25/11.14 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_G_2,V_ts_2)
% 11.25/11.14 <=> ! [B_n] :
% 11.25/11.14 ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_G_2))
% 11.25/11.14 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
% 11.25/11.14 => ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2))
% 11.25/11.14 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__UN__I,axiom,
% 11.25/11.14 ! [V_B_2,T_c,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ! [B_a] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 11.25/11.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_inj__on__diff__nat,axiom,
% 11.25/11.14 ! [V_k_2,V_N_2] :
% 11.25/11.14 ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 11.25/11.14 => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wfP__SUP,axiom,
% 11.25/11.14 ! [T_b,V_r_2,T_c] :
% 11.25/11.14 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 11.25/11.14 => ( ! [B_i,B_j] :
% 11.25/11.14 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 11.25/11.14 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 11.25/11.14 => c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__map__freshness,axiom,
% 11.25/11.14 ! [V_f_2,T_c,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2)))
% 11.25/11.14 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 11.25/11.14 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_mem__splitI2,axiom,
% 11.25/11.14 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 11.25/11.14 ( ! [B_a,B_b] :
% 11.25/11.14 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_mem__splitE,axiom,
% 11.25/11.14 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2)))
% 11.25/11.14 => ~ ! [B_x,B_y] :
% 11.25/11.14 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 11.25/11.14 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Eps__split,axiom,
% 11.25/11.14 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_exE__some,axiom,
% 11.25/11.14 ! [T_b,V_c_2,V_Pa_2] :
% 11.25/11.14 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 11.25/11.14 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
% 11.25/11.14 => hBOOL(hAPP(V_Pa_2,V_c_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_tfl__some,axiom,
% 11.25/11.14 ! [T_b,B_P] :
% 11.25/11.14 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 11.25/11.14 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_someI,axiom,
% 11.25/11.14 ! [T_b,V_x_2,V_Pa_2] :
% 11.25/11.14 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 11.25/11.14 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_some__sym__eq__trivial,axiom,
% 11.25/11.14 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_some__eq__trivial,axiom,
% 11.25/11.14 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ).
% 11.25/11.14
% 11.25/11.14 fof(fact_some__eq__ex,axiom,
% 11.25/11.14 ! [T_b,V_Pa_2] :
% 11.25/11.14 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
% 11.25/11.14 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_someI__ex,axiom,
% 11.25/11.14 ! [T_b,V_Pa_2] :
% 11.25/11.14 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 11.25/11.14 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_split__paired__Eps,axiom,
% 11.25/11.14 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Eps__split__eq,axiom,
% 11.25/11.14 ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wfI__pf,axiom,
% 11.25/11.14 ! [V_R_2,T_b] :
% 11.25/11.14 ( ! [B_A] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A)))
% 11.25/11.14 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 11.25/11.14 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Sigma__mono,axiom,
% 11.25/11.14 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) )
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_not__acc__down,axiom,
% 11.25/11.14 ! [V_R_2,V_x_2,T_b] :
% 11.25/11.14 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 11.25/11.14 => ~ ! [B_z] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_acc_OaccI,axiom,
% 11.25/11.14 ! [V_r_2,V_x_2,T_b] :
% 11.25/11.14 ( ! [B_y] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__image__1,axiom,
% 11.25/11.14 ! [V_f_2,V_S_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__mult(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 11.25/11.14 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 11.25/11.14 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_card_Oneutral,axiom,
% 11.25/11.14 ! [V_A_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.25/11.14 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_max__ext_Osimps,axiom,
% 11.25/11.14 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 11.25/11.14 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 11.25/11.14 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 11.25/11.14 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.25/11.14 & ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 11.25/11.14 => ? [B_xa] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 11.25/11.14 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_fold__image__cong,axiom,
% 11.25/11.14 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 11.25/11.14 ( class_Groups_Oab__semigroup__mult(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 11.25/11.14 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setprod__dvd__setprod__subset2,axiom,
% 11.25/11.14 ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 11.25/11.14 ( class_Rings_Ocomm__semiring__1(T_c)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.25/11.14 => ( ! [B_x] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Min__eqI,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ! [B_y] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.14 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Max__eqI,axiom,
% 11.25/11.14 ! [V_x_2,V_A_2,T_b] :
% 11.25/11.14 ( class_Orderings_Olinorder(T_b)
% 11.25/11.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.25/11.14 => ( ! [B_y] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.25/11.14 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__no__infinite__down__chainE,axiom,
% 11.25/11.14 ! [V_f_2,V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_setsum__reindex__cong,axiom,
% 11.25/11.14 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 11.25/11.14 ( class_Groups_Ocomm__monoid__add(T_d)
% 11.25/11.14 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 11.25/11.14 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 11.25/11.14 => ( ! [B_a] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 11.25/11.14 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 11.25/11.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_less__eq,axiom,
% 11.25/11.14 ! [V_n_2,V_m_2] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
% 11.25/11.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_wf__trancl,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.14 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_less__than__def,axiom,
% 11.25/11.14 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_acyclic__def,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 11.25/11.14 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl_Or__into__trancl,axiom,
% 11.25/11.14 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__subset__Field2,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_r__into__trancl_H,axiom,
% 11.25/11.14 ! [V_r_2,V_p_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__empty,axiom,
% 11.25/11.14 ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__domain,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__range,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_finite__trancl,axiom,
% 11.25/11.14 ! [V_r_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 11.25/11.14 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__trans,axiom,
% 11.25/11.14 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 11.25/11.14 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__into__trancl2,axiom,
% 11.25/11.14 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_r__r__into__trancl,axiom,
% 11.25/11.14 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__mono,axiom,
% 11.25/11.14 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__unfold,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__subset__Sigma,axiom,
% 11.25/11.14 ! [V_A_2,V_r_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__Int__subset,axiom,
% 11.25/11.14 ! [V_s_2,V_r_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 11.25/11.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__insert,axiom,
% 11.25/11.14 ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_reflcl__set__eq,axiom,
% 11.25/11.14 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
% 11.25/11.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_r__into__rtrancl,axiom,
% 11.25/11.14 ! [V_r_2,V_p_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 11.25/11.14 ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_IdI,axiom,
% 11.25/11.14 ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__into__rtrancl,axiom,
% 11.25/11.14 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 11.25/11.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rtrancl__trancl__absorb,axiom,
% 11.25/11.14 ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__rtrancl__absorb,axiom,
% 11.25/11.14 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_reflcl__trancl,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__reflcl,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__unfold__left,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_trancl__unfold__right,axiom,
% 11.25/11.14 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Domain__rtrancl,axiom,
% 11.25/11.14 ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_Range__rtrancl,axiom,
% 11.25/11.14 ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rtrancl__empty,axiom,
% 11.25/11.14 ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b) ).
% 11.25/11.14
% 11.25/11.14 fof(fact_rtrancl__Int__subset,axiom,
% 11.25/11.14 ! [V_r_2,V_s_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__idemp__self__comp,axiom,
% 11.25/11.15 ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_r__comp__rtrancl__eq,axiom,
% 11.25/11.15 ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__unfold,axiom,
% 11.25/11.15 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_in__rtrancl__UnI,axiom,
% 11.25/11.15 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 11.25/11.15 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 11.25/11.15 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Image__closed__trancl,axiom,
% 11.25/11.15 ! [V_X_2,V_r_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2))
% 11.25/11.15 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__mono,axiom,
% 11.25/11.15 ! [V_s_2,V_r_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__subset,axiom,
% 11.25/11.15 ! [V_S_2,V_R_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 11.25/11.15 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__subset__rtrancl,axiom,
% 11.25/11.15 ! [V_s_2,V_r_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__reflcl,axiom,
% 11.25/11.15 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__Un__rtrancl,axiom,
% 11.25/11.15 ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__reflcl__absorb,axiom,
% 11.25/11.15 ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__Un__subset,axiom,
% 11.25/11.15 ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__idemp,axiom,
% 11.25/11.15 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__trans,axiom,
% 11.25/11.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 11.25/11.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 11.25/11.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__r__diff__Id,axiom,
% 11.25/11.15 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_refl__rtrancl,axiom,
% 11.25/11.15 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Image__Id,axiom,
% 11.25/11.15 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 11.25/11.15
% 11.25/11.15 fof(fact_R__O__Id,axiom,
% 11.25/11.15 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2 ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Id__O__R,axiom,
% 11.25/11.15 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2 ).
% 11.25/11.15
% 11.25/11.15 fof(fact_pair__in__Id__conv,axiom,
% 11.25/11.15 ! [V_b_2,V_a_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
% 11.25/11.15 <=> V_a_2 = V_b_2 ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__trancl__trancl,axiom,
% 11.25/11.15 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_trancl__rtrancl__trancl,axiom,
% 11.25/11.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__into__trancl1,axiom,
% 11.25/11.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtranclD,axiom,
% 11.25/11.15 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 11.25/11.15 => ( V_a_2 = V_b_2
% 11.25/11.15 | ( V_a_2 != V_b_2
% 11.25/11.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__into__trancl2,axiom,
% 11.25/11.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__eq__or__trancl,axiom,
% 11.25/11.15 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 11.25/11.15 <=> ( V_x_2 = V_y_2
% 11.25/11.15 | ( V_x_2 != V_y_2
% 11.25/11.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Domain__Id,axiom,
% 11.25/11.15 ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Range__Id,axiom,
% 11.25/11.15 ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_refl__Id,axiom,
% 11.25/11.15 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_pair__leq__def,axiom,
% 11.25/11.15 c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Not__Domain__rtrancl,axiom,
% 11.25/11.15 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 11.25/11.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 11.25/11.15 <=> V_x_2 = V_y_2 ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_acc__downwards__aux,axiom,
% 11.25/11.15 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_acc__downwards,axiom,
% 11.25/11.15 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_wf__insert,axiom,
% 11.25/11.15 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 11.25/11.15 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
% 11.25/11.15 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.25/11.15 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_acyclic__insert,axiom,
% 11.25/11.15 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 11.25/11.15 ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
% 11.25/11.15 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 11.25/11.15 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_refl__reflcl,axiom,
% 11.25/11.15 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Id__def,axiom,
% 11.25/11.15 ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_irrefl__diff__Id,axiom,
% 11.25/11.15 ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_pred__nat__trancl__eq__le,axiom,
% 11.25/11.15 ! [V_n_2,V_m_2] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
% 11.25/11.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_trancl__subset__Sigma__aux,axiom,
% 11.25/11.15 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 11.25/11.15 => ( V_a_2 = V_b_2
% 11.25/11.15 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_irrefl__tranclI,axiom,
% 11.25/11.15 ! [V_x_2,V_r_2,T_b] :
% 11.25/11.15 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 11.25/11.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_sequence__trans,axiom,
% 11.25/11.15 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 11.25/11.15 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__converse,axiom,
% 11.25/11.15 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__Id,axiom,
% 11.25/11.15 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_acyclic__converse,axiom,
% 11.25/11.15 ! [V_r_2,T_b] :
% 11.25/11.15 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 11.25/11.15 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__rel__comp,axiom,
% 11.25/11.15 ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__Un,axiom,
% 11.25/11.15 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_finite__converse,axiom,
% 11.25/11.15 ! [V_r_2,T_c,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 11.25/11.15 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__Int,axiom,
% 11.25/11.15 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__converse,axiom,
% 11.25/11.15 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2 ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__Id__on,axiom,
% 11.25/11.15 ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Field__converse,axiom,
% 11.25/11.15 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__inv__image,axiom,
% 11.25/11.15 ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converseD,axiom,
% 11.25/11.15 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converseI,axiom,
% 11.25/11.15 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__iff,axiom,
% 11.25/11.15 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 11.25/11.15 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_refl__on__converse,axiom,
% 11.25/11.15 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.15 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 11.25/11.15 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__UNION,axiom,
% 11.25/11.15 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_equiv__comp__eq,axiom,
% 11.25/11.15 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.15 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.25/11.15 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Range__converse,axiom,
% 11.25/11.15 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Domain__converse,axiom,
% 11.25/11.15 ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Range__def,axiom,
% 11.25/11.15 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_trancl__converse,axiom,
% 11.25/11.15 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_wf__converse__trancl,axiom,
% 11.25/11.15 ! [V_r_2,T_b] :
% 11.25/11.15 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 11.25/11.15 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__converseI,axiom,
% 11.25/11.15 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__converseD,axiom,
% 11.25/11.15 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_trancl__converseI,axiom,
% 11.25/11.15 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_trancl__converseD,axiom,
% 11.25/11.15 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_Image__subset__eq,axiom,
% 11.25/11.15 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
% 11.25/11.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_refl__on__comp__subset,axiom,
% 11.25/11.15 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.15 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_comp__equivI,axiom,
% 11.25/11.15 ! [V_A_2,V_r_2,T_b] :
% 11.25/11.15 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
% 11.25/11.15 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 11.25/11.15 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_finite__acyclic__wf__converse,axiom,
% 11.25/11.15 ! [V_r_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 11.25/11.15 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 11.25/11.15 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_converse__def,axiom,
% 11.25/11.15 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_total__on__diff__Id,axiom,
% 11.25/11.15 ! [V_r_2,V_A_2,T_b] :
% 11.25/11.15 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
% 11.25/11.15 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 11.25/11.15 ! [V_R_2,V_p_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_relpow_Osimps_I1_J,axiom,
% 11.25/11.15 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rtrancl__power,axiom,
% 11.25/11.15 ! [V_R_2,V_p_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 11.25/11.15 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rel__pow__imp__rtrancl,axiom,
% 11.25/11.15 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 11.25/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 11.25/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rel__pow__commute,axiom,
% 11.25/11.15 ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_relpow_Osimps_I2_J,axiom,
% 11.25/11.15 ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rel__pow__add,axiom,
% 11.25/11.15 ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_rel__pow__1,axiom,
% 11.25/11.15 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ).
% 11.25/11.15
% 11.25/11.15 fof(fact_wf__exp,axiom,
% 11.25/11.15 ! [V_R_2,V_n_2,T_b] :
% 11.25/11.15 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))
% 11.25/11.15 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_funpow__swap1,axiom,
% 11.25/11.15 ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ).
% 11.25/11.15
% 11.25/11.15 fof(fact_funpow__mult,axiom,
% 11.25/11.15 ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ).
% 11.25/11.15
% 11.41/11.15 fof(fact_comp__funpow,axiom,
% 11.41/11.15 ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_total__on__empty,axiom,
% 11.41/11.15 ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_total__on__converse,axiom,
% 11.41/11.15 ! [V_r_2,V_A_2,T_b] :
% 11.41/11.15 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 11.41/11.15 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rel__pow__0__E,axiom,
% 11.41/11.15 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
% 11.41/11.15 => V_x_2 = V_y_2 ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rel__pow__0__I,axiom,
% 11.41/11.15 ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rel__pow__Suc__I,axiom,
% 11.41/11.15 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rel__pow__Suc__I2,axiom,
% 11.41/11.15 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_funpow_Osimps_I2_J,axiom,
% 11.41/11.15 ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_funpow__add,axiom,
% 11.41/11.15 ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_funpow_Osimps_I1_J,axiom,
% 11.41/11.15 ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_trancl__power,axiom,
% 11.41/11.15 ! [V_R_2,V_p_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 11.41/11.15 <=> ? [B_n] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 11.41/11.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_total__on__def,axiom,
% 11.41/11.15 ! [V_r_2,V_A_2,T_b] :
% 11.41/11.15 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.41/11.15 => ! [B_xa] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 11.41/11.15 => ( B_x != B_xa
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
% 11.41/11.15 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2)) ) ) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 11.41/11.15 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_funpow__code__def,axiom,
% 11.41/11.15 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rel__pow__E,axiom,
% 11.41/11.15 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 11.41/11.15 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.15 => V_x_2 != V_z_2 )
% 11.41/11.15 => ~ ! [B_y,B_m] :
% 11.41/11.15 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rel__pow__E2,axiom,
% 11.41/11.15 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 11.41/11.15 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.15 => V_x_2 != V_z_2 )
% 11.41/11.15 => ~ ! [B_y,B_m] :
% 11.41/11.15 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_acyclicI,axiom,
% 11.41/11.15 ! [V_r_2,T_b] :
% 11.41/11.15 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 11.41/11.15 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Image__Int__eq,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 11.41/11.15 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 11.41/11.15 => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 11.41/11.15 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
% 11.41/11.15 => ( ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 11.41/11.15 => ! [B_y] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Qa_2))
% 11.41/11.15 => B_y = B_x ) )
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_single__valued__rel__comp,axiom,
% 11.41/11.15 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 11.41/11.15 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 11.41/11.15 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 11.41/11.15 => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_single__valued__subset,axiom,
% 11.41/11.15 ! [V_s_2,V_r_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 11.41/11.15 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 11.41/11.15 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_single__valued__Id__on,axiom,
% 11.41/11.15 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_single__valued__Id,axiom,
% 11.41/11.15 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_single__valued__rel__pow,axiom,
% 11.41/11.15 ! [V_n_2,V_R_2,T_b] :
% 11.41/11.15 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 11.41/11.15 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_single__valued__def,axiom,
% 11.41/11.15 ! [V_r_2,T_c,T_b] :
% 11.41/11.15 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 11.41/11.15 <=> ! [B_x,B_y] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2))
% 11.41/11.15 => ! [B_z] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2))
% 11.41/11.15 => B_y = B_z ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_single__valuedD,axiom,
% 11.41/11.15 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 11.41/11.15 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
% 11.41/11.15 => V_y_2 = V_z_2 ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_single__valued__confluent,axiom,
% 11.41/11.15 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 11.41/11.15 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.41/11.15 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rtrancl__Un__separatorE,axiom,
% 11.41/11.15 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
% 11.41/11.15 => ( ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 11.41/11.15 => ! [B_y] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Qa_2))
% 11.41/11.15 => B_x = B_y ) )
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rel__pow__Suc__E,axiom,
% 11.41/11.15 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 11.41/11.15 => ~ ! [B_y] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rel__pow__Suc__D2,axiom,
% 11.41/11.15 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 11.41/11.15 => ? [B_y] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 11.41/11.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rel__pow__Suc__E2,axiom,
% 11.41/11.15 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 11.41/11.15 => ~ ! [B_y] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_tranclD2,axiom,
% 11.41/11.15 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 11.41/11.15 => ? [B_z] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 11.41/11.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_tranclD,axiom,
% 11.41/11.15 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 11.41/11.15 => ? [B_z] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2))
% 11.41/11.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_IdE,axiom,
% 11.41/11.15 ! [V_p_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 11.41/11.15 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fold__empty,axiom,
% 11.41/11.15 ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 11.41/11.15
% 11.41/11.15 fof(fact_folding_Oeq__fold,axiom,
% 11.41/11.15 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fold__image__def,axiom,
% 11.41/11.15 ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fold__def,axiom,
% 11.41/11.15 ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_union__fold__insert,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fold__sup__insert,axiom,
% 11.41/11.15 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Osemilattice__sup(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fold__inf__insert,axiom,
% 11.41/11.15 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Osemilattice__inf(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_min__max_Ofold__inf__insert,axiom,
% 11.41/11.15 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_min__max_Ofold__sup__insert,axiom,
% 11.41/11.15 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 11.41/11.15 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 11.41/11.15 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_sup__SUPR__fold__sup,axiom,
% 11.41/11.15 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 11.41/11.15 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_sup__le__fold__sup,axiom,
% 11.41/11.15 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Osemilattice__sup(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fold__inf__le__inf,axiom,
% 11.41/11.15 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Osemilattice__inf(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 11.41/11.15 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 11.41/11.15 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fold1__eq__fold__idem,axiom,
% 11.41/11.15 ! [V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 11.41/11.15 ! [V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Olattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 11.41/11.15 ! [V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Olattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 11.41/11.15 ! [V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 11.41/11.15 ! [V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 11.41/11.15 ! [V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 11.41/11.15 ! [V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_minus__fold__remove,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_folding__one_Oeq__fold_H,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_SUPR__fold__sup,axiom,
% 11.41/11.15 ! [V_f_2,V_A_2,T_b,T_c] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fold1__eq__fold,axiom,
% 11.41/11.15 ! [V_a_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Groups_Oab__semigroup__mult(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.41/11.15 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Olattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Olattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Min_Oeq__fold_H,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Max_Oeq__fold_H,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 11.41/11.15 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 11.41/11.15 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 11.41/11.15 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 11.41/11.15 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm,axiom,
% 11.41/11.15 ! [T_b] :
% 11.41/11.15 ( class_Groups_Oab__semigroup__mult(T_b)
% 11.41/11.15 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 11.41/11.15 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 11.41/11.15 => V_y_2 = V_x_2 ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 11.41/11.15 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 11.41/11.15 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 11.41/11.15 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 11.41/11.15 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 11.41/11.15 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 11.41/11.15 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 11.41/11.15 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.41/11.15 => ? [B_y_H] :
% 11.41/11.15 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 11.41/11.15 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INFI__fold__inf,axiom,
% 11.41/11.15 ! [V_f_2,V_A_2,T_b,T_c] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF1__E,axiom,
% 11.41/11.15 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF1__D,axiom,
% 11.41/11.15 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__E,axiom,
% 11.41/11.15 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__D,axiom,
% 11.41/11.15 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF2__E,axiom,
% 11.41/11.15 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF2__D,axiom,
% 11.41/11.15 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_finite__INT,axiom,
% 11.41/11.15 ! [V_A_2,T_c,V_I_2,T_b] :
% 11.41/11.15 ( ? [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 11.41/11.15 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 11.41/11.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Compl__UN,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Compl__INT,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__simps_I9_J,axiom,
% 11.41/11.15 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__extend__simps_I9_J,axiom,
% 11.41/11.15 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_UN__extend__simps_I7_J,axiom,
% 11.41/11.15 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_UN__simps_I7_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Collect__ball__eq,axiom,
% 11.41/11.15 ! [V_Pa_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INFI__bool__eq,axiom,
% 11.41/11.15 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__extend__simps_I1_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.41/11.15 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 11.41/11.15 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__extend__simps_I2_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.41/11.15 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 11.41/11.15 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF__const,axiom,
% 11.41/11.15 ! [V_M_2,T_b,V_A_2,T_c] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 11.41/11.15 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__constant,axiom,
% 11.41/11.15 ! [V_c_2,T_c,T_b,V_A_2] :
% 11.41/11.15 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 11.41/11.15 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__empty,axiom,
% 11.41/11.15 ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Image__INT__subset,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__insert,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_le__INF__iff,axiom,
% 11.41/11.15 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__subset__iff,axiom,
% 11.41/11.15 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__simps_I5_J,axiom,
% 11.41/11.15 ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__extend__simps_I5_J,axiom,
% 11.41/11.15 ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__lower,axiom,
% 11.41/11.15 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__insert__distrib,axiom,
% 11.41/11.15 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__simps_I10_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__extend__simps_I10_J,axiom,
% 11.41/11.15 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__Int__distrib,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Pow__INT__eq,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF__commute,axiom,
% 11.41/11.15 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INFI__apply,axiom,
% 11.41/11.15 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__iff,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF__less__iff,axiom,
% 11.41/11.15 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 11.41/11.15 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 & class_Orderings_Olinorder(T_b) )
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
% 11.41/11.15 <=> ? [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.41/11.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__absorb,axiom,
% 11.41/11.15 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF__INT__eq,axiom,
% 11.41/11.15 ! [V_x_2,V_r_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 11.41/11.15 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF__INT__eq2,axiom,
% 11.41/11.15 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 11.41/11.15 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.41/11.15 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b] :
% 11.41/11.15 ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 11.41/11.15 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_vimage__INT,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_converse__INTER,axiom,
% 11.41/11.15 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Un__INT__distrib2,axiom,
% 11.41/11.15 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__extend__simps_I6_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Un__INT__distrib,axiom,
% 11.41/11.15 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__extend__simps_I7_J,axiom,
% 11.41/11.15 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__simps_I6_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__simps_I7_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__Un,axiom,
% 11.41/11.15 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF__subset,axiom,
% 11.41/11.15 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INTER__def,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__simps_I1_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.41/11.15 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 11.41/11.15 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__simps_I2_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.41/11.15 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 11.41/11.15 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__simps_I3_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.41/11.15 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 11.41/11.15 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__extend__simps_I3_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.41/11.15 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) )
% 11.41/11.15 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__extend__simps_I4_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.41/11.15 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 11.41/11.15 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF__leI,axiom,
% 11.41/11.15 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__greaterThan__UNIV,axiom,
% 11.41/11.15 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__simps_I4_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 11.41/11.15 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 11.41/11.15 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Image__INT__eq,axiom,
% 11.41/11.15 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 11.41/11.15 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 11.41/11.15 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 11.41/11.15 => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inf__INFI__fold__inf,axiom,
% 11.41/11.15 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__fold__inf,axiom,
% 11.41/11.15 ! [V_A_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__fold__sup,axiom,
% 11.41/11.15 ! [V_A_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_finite__Inter,axiom,
% 11.41/11.15 ! [V_M_2,T_b] :
% 11.41/11.15 ( ? [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 11.41/11.15 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 11.41/11.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_UnionI,axiom,
% 11.41/11.15 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_InterD,axiom,
% 11.41/11.15 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_InterE,axiom,
% 11.41/11.15 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INTER__eq__Inter__image,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__image__eq,axiom,
% 11.41/11.15 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__extend__simps_I8_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INT__simps_I8_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF1__iff,axiom,
% 11.41/11.15 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_INF2__iff,axiom,
% 11.41/11.15 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Un__Inter,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__empty,axiom,
% 11.41/11.15 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__eq,axiom,
% 11.41/11.15 ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__insert,axiom,
% 11.41/11.15 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__quotient,axiom,
% 11.41/11.15 ! [V_r_2,V_A_2,T_b] :
% 11.41/11.15 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.41/11.15 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__less__iff,axiom,
% 11.41/11.15 ! [V_a_2,V_S_2,T_b] :
% 11.41/11.15 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 & class_Orderings_Olinorder(T_b) )
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 11.41/11.15 <=> ? [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 11.41/11.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_less__Sup__iff,axiom,
% 11.41/11.15 ! [V_S_2,V_a_2,T_b] :
% 11.41/11.15 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 & class_Orderings_Olinorder(T_b) )
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 11.41/11.15 <=> ? [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 11.41/11.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__Pow__eq,axiom,
% 11.41/11.15 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2 ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Field__Union,axiom,
% 11.41/11.15 ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__lower,axiom,
% 11.41/11.15 ! [V_A_2,V_B_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__le__iff,axiom,
% 11.41/11.15 ! [V_b_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_le__Inf__iff,axiom,
% 11.41/11.15 ! [V_A_2,V_b_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__upper,axiom,
% 11.41/11.15 ! [V_A_2,V_B_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__mono,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__empty,axiom,
% 11.41/11.15 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__disjoint,axiom,
% 11.41/11.15 ! [V_A_2,V_C_2,T_b] :
% 11.41/11.15 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_finite__UnionD,axiom,
% 11.41/11.15 ! [V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 11.41/11.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__Inf,axiom,
% 11.41/11.15 ! [V_A_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__Sup,axiom,
% 11.41/11.15 ! [V_A_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_subset__Pow__Union,axiom,
% 11.41/11.15 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__anti__mono,axiom,
% 11.41/11.15 ! [V_A_2,V_B_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Domain__Union,axiom,
% 11.41/11.15 ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Range__Union,axiom,
% 11.41/11.15 ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sigma__Union,axiom,
% 11.41/11.15 ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_vimage__Union,axiom,
% 11.41/11.15 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Int__Union2,axiom,
% 11.41/11.15 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Int__Union,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_UN__simps_I8_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_UN__extend__simps_I8_J,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_image__Union,axiom,
% 11.41/11.15 ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__UNIV,axiom,
% 11.41/11.15 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__Un__distrib,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__insert,axiom,
% 11.41/11.15 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__image__eq,axiom,
% 11.41/11.15 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_UNION__eq__Union__image,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__upper,axiom,
% 11.41/11.15 ! [V_A_2,V_x_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__UNIV,axiom,
% 11.41/11.15 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__lower,axiom,
% 11.41/11.15 ! [V_A_2,V_x_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__Un__distrib,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__empty,axiom,
% 11.41/11.15 ! [T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__singleton,axiom,
% 11.41/11.15 ! [V_a_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__insert,axiom,
% 11.41/11.15 ! [V_A_2,V_a_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Int__Inter__image,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__UNIV,axiom,
% 11.41/11.15 ! [T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__singleton,axiom,
% 11.41/11.15 ! [V_a_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__empty,axiom,
% 11.41/11.15 ! [T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__UNIV,axiom,
% 11.41/11.15 ! [T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__insert,axiom,
% 11.41/11.15 ! [V_A_2,V_a_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Un__eq__Union,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Un__Union__image,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__Int__subset,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Int__eq__Inter,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__Un__subset,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__binary,axiom,
% 11.41/11.15 ! [V_b_2,V_a_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__binary,axiom,
% 11.41/11.15 ! [V_b_2,V_a_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_sup__Sup__fold__sup,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Sup__fin__Sup,axiom,
% 11.41/11.15 ! [V_A_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inf__Inf__fold__inf,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inf__fin__Inf,axiom,
% 11.41/11.15 ! [V_A_2,T_b] :
% 11.41/11.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_image__INT,axiom,
% 11.41/11.15 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 11.41/11.15 => ( ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 11.41/11.15 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_card__partition,axiom,
% 11.41/11.15 ! [V_k_2,V_C_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 11.41/11.15 => ( ! [B_c] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 11.41/11.15 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 11.41/11.15 => ( ! [B_c1] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 11.41/11.15 => ! [B_c2] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 11.41/11.15 => ( B_c1 != B_c2
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 11.41/11.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__def,axiom,
% 11.41/11.15 ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Union__def,axiom,
% 11.41/11.15 ! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_finite__Union,axiom,
% 11.41/11.15 ! [V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 11.41/11.15 => ( ! [B_M] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 11.41/11.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_insert__partition,axiom,
% 11.41/11.15 ! [V_F_2,V_x_2,T_b] :
% 11.41/11.15 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 11.41/11.15 => ( ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
% 11.41/11.15 => ! [B_xa] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
% 11.41/11.15 => ( B_x != B_xa
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 11.41/11.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inj__on__Inter,axiom,
% 11.41/11.15 ! [V_f_2,T_c,T_b,V_S_2] :
% 11.41/11.15 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 11.41/11.15 => ( ! [B_A] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 11.41/11.15 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 11.41/11.15 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Inter__subset,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,T_b] :
% 11.41/11.15 ( ! [B_X] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 11.41/11.15 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inj__on__INTER,axiom,
% 11.41/11.15 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 11.41/11.15 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => ( ! [B_i] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 11.41/11.15 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 11.41/11.15 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 11.41/11.15 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.15 => ~ ! [B_y] :
% 11.41/11.15 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 11.41/11.15 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 11.41/11.15 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 11.41/11.15 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_InterI,axiom,
% 11.41/11.15 ! [V_A_2,V_C_2,T_b] :
% 11.41/11.15 ( ! [B_X] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inf__le__fold__inf,axiom,
% 11.41/11.15 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Osemilattice__inf(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fold__sup__le__sup,axiom,
% 11.41/11.15 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Lattices_Osemilattice__sup(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => ( ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_wf__eq__minimal,axiom,
% 11.41/11.15 ! [V_r_2,T_b] :
% 11.41/11.15 ( c_Wellfounded_Owf(T_b,V_r_2)
% 11.41/11.15 <=> ! [B_Q] :
% 11.41/11.15 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 11.41/11.15 => ? [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 11.41/11.15 & ! [B_y] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 11.41/11.15 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_transfer__nat__int__set__cong,axiom,
% 11.41/11.15 ! [V_P_H_2,V_Pa_2] :
% 11.41/11.15 ( ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 11.41/11.15 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 11.41/11.15 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 11.41/11.15 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 11.41/11.15 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.41/11.15 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 11.41/11.15 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.41/11.15 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 11.41/11.15 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 11.41/11.15 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Int__Collect__mono,axiom,
% 11.41/11.15 ! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.41/11.15 => ( ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 11.41/11.15 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 11.41/11.15 => hBOOL(hAPP(V_Qa_2,B_x)) ) )
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Qa_2)))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_UnionE,axiom,
% 11.41/11.15 ! [V_C_2,V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 11.41/11.15 => ~ ! [B_X] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__upd__left,axiom,
% 11.41/11.15 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
% 11.41/11.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2)))
% 11.41/11.15 => c_Map_Omap__add(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_converseE,axiom,
% 11.41/11.15 ! [V_r_2,V_yx_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 11.41/11.15 => ~ ! [B_x,B_y] :
% 11.41/11.15 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__Some__iff,axiom,
% 11.41/11.15 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 11.41/11.15 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 11.41/11.15 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 11.41/11.15 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__SomeD,axiom,
% 11.41/11.15 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 11.41/11.15 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 11.41/11.15 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 11.41/11.15 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_dom__map__add,axiom,
% 11.41/11.15 ! [V_n_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_n_2)),c_Map_Odom(T_b,T_c,V_m_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 11.41/11.15 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 11.41/11.15 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 11.41/11.15 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 11.41/11.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 11.41/11.15 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 11.41/11.15 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
% 11.41/11.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
% 11.41/11.15 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_empty__map__add,axiom,
% 11.41/11.15 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)),V_m_2) = V_m_2 ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__empty,axiom,
% 11.41/11.15 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = V_m_2 ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__None,axiom,
% 11.41/11.15 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
% 11.41/11.15 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 11.41/11.15 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__find__right,axiom,
% 11.41/11.15 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
% 11.41/11.15 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
% 11.41/11.15 => hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__assoc,axiom,
% 11.41/11.15 ! [V_m3_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__add(T_b,T_c,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_m3_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__def,axiom,
% 11.41/11.15 ! [V_x_2,V_m2_2,V_m1_2,T_b,T_c] : hAPP(c_Map_Omap__add(T_c,T_b,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_b)),hAPP(V_m2_2,V_x_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__upd,axiom,
% 11.41/11.15 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inj__on__map__add__dom,axiom,
% 11.41/11.15 ! [V_m_H_2,V_m_2,T_c,T_b] :
% 11.41/11.15 ( c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),c_Map_Omap__add(T_b,T_c,V_m_2,V_m_H_2),c_Map_Odom(T_b,T_c,V_m_H_2))
% 11.41/11.15 <=> c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),V_m_H_2,c_Map_Odom(T_b,T_c,V_m_H_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__comm,axiom,
% 11.41/11.15 ! [V_m2_2,V_m1_2,T_c,T_b] :
% 11.41/11.15 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m1_2)),c_Map_Odom(T_b,T_c,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 => c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2) = c_Map_Omap__add(T_b,T_c,V_m2_2,V_m1_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_finite__range__map__of__map__add,axiom,
% 11.41/11.15 ! [V_l_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 11.41/11.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__add(T_c,T_b,V_f_2,c_Map_Omap__of(T_c,T_b,V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_rel__compE,axiom,
% 11.41/11.15 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
% 11.41/11.15 => ~ ! [B_x,B_y,B_z] :
% 11.41/11.15 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_finite__dom__map__of,axiom,
% 11.41/11.15 ! [V_l_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_l_2)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_finite__range__map__of,axiom,
% 11.41/11.15 ! [V_xys_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__of(T_c,T_b,V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__add__map__of__foldr,axiom,
% 11.41/11.15 ! [V_ps_2,V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,V_ps_2)) = c_List_Ofoldr(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)))))),c_Option_Ooption_OSome(T_c))),V_ps_2,V_m_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_,axiom,
% 11.41/11.15 ! [V_y_2,V_x_2,T_b] : c_Smallcheck_Oorelse(T_b,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,V_y_2,c_Option_Ooption_OSome(T_b)),V_x_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_full__small__int__def,axiom,
% 11.41/11.15 ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_small_H_Osimps,axiom,
% 11.41/11.15 ! [V_f_2,V_i_2,V_d_2] :
% 11.41/11.15 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 11.41/11.15 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 11.41/11.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 11.41/11.15 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_small_H_Opsimps,axiom,
% 11.41/11.15 ! [V_i_2,V_d_2,V_f_2] :
% 11.41/11.15 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))))
% 11.41/11.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 11.41/11.15 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 11.41/11.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 11.41/11.15 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_small__int__def,axiom,
% 11.41/11.15 ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_small__prod__def,axiom,
% 11.41/11.15 ! [V_d_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( ( class_Smallcheck_Osmall(T_c)
% 11.41/11.15 & class_Smallcheck_Osmall(T_b) )
% 11.41/11.15 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_b,T_c)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_b),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),c_Smallcheck_Osmall__class_Osmall(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c)))),V_d_2)),V_d_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_small_H_Opinduct,axiom,
% 11.41/11.15 ! [V_Pa_2,V_a2_2,V_a1_2,V_a0_2] :
% 11.41/11.15 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2))))
% 11.41/11.15 => ( ! [B_f,B_d,B_i] :
% 11.41/11.15 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i))))
% 11.41/11.15 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 11.41/11.15 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 11.41/11.15 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
% 11.41/11.15 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),B_i)) ) )
% 11.41/11.15 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_body__def,axiom,
% 11.41/11.15 c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__mapk__SomeI,axiom,
% 11.41/11.15 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.41/11.15 => ( hAPP(c_Map_Omap__of(T_b,T_d,V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2)
% 11.41/11.15 => hAPP(c_Map_Omap__of(T_c,T_d,hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_b),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__comp__def,axiom,
% 11.41/11.15 ! [V_k_2,V_g_2,V_f_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_c,c_Option_Ooption_ONone(T_b),V_f_2),hAPP(V_g_2,V_k_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inj__mapI,axiom,
% 11.41/11.15 ! [V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.41/11.15 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__comp__simps_I2_J,axiom,
% 11.41/11.15 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
% 11.41/11.15 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2)
% 11.41/11.15 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__comp__Some__iff,axiom,
% 11.41/11.15 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 11.41/11.15 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2)
% 11.41/11.15 <=> ? [B_k_H] :
% 11.41/11.15 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 11.41/11.15 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__comp__simps_I1_J,axiom,
% 11.41/11.15 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
% 11.41/11.15 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 11.41/11.15 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_d) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_List_Omap_Oidentity,axiom,
% 11.41/11.15 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_List_Omap_Oid,axiom,
% 11.41/11.15 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__ident,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__injective,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 11.41/11.15 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 11.41/11.15 => V_xs_2 = V_ys_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inj__mapD,axiom,
% 11.41/11.15 ! [V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 11.41/11.15 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inj__map__eq__map,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 11.41/11.15 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 11.41/11.15 <=> V_xs_2 = V_ys_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inj__map,axiom,
% 11.41/11.15 ! [V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 11.41/11.15 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_List_Omap_Ocomp,axiom,
% 11.41/11.15 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__comp__map,axiom,
% 11.41/11.15 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_List_Omap_Ocompositionality,axiom,
% 11.41/11.15 ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__map,axiom,
% 11.41/11.15 ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_foldr__map,axiom,
% 11.41/11.15 ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__comp__empty_I2_J,axiom,
% 11.41/11.15 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__comp__empty_I1_J,axiom,
% 11.41/11.15 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c)),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__comp__None__iff,axiom,
% 11.41/11.15 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 11.41/11.15 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 11.41/11.15 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
% 11.41/11.15 | ? [B_k_H] :
% 11.41/11.15 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 11.41/11.15 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__map,axiom,
% 11.41/11.15 ! [V_xs_2,V_f_2,T_d,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),c_Map_Omap__of(T_b,T_d,V_xs_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__map__keys,axiom,
% 11.41/11.15 ! [V_m_2,T_c,V_xs_2,T_b] :
% 11.41/11.15 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2)
% 11.41/11.15 => c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),T_c,T_b),c_Option_Othe(T_c)),V_m_2))),V_xs_2)) = V_m_2 ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_finite__set,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__map,axiom,
% 11.41/11.15 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__eq__conv,axiom,
% 11.41/11.15 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 11.41/11.15 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_option__map__comp,axiom,
% 11.41/11.15 ! [V_opt_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_opt_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Option_Omap_Ocompositionality,axiom,
% 11.41/11.15 ! [V_option_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_option_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Option_Omap_Ocomp,axiom,
% 11.41/11.15 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Option_Omap(T_b,T_d),V_g_2)) = hAPP(c_Option_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_option__map__o__sum__case,axiom,
% 11.41/11.15 ! [V_h_2,V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),tc_sum(T_b,T_c),hAPP(c_Option_Omap(T_e,T_d),V_f_2)),c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_e),T_c,V_g_2,V_h_2)) = c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_d),T_c,hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_b,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_g_2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_c,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_h_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_dom__option__map,axiom,
% 11.41/11.15 ! [V_m_2,V_f_2,T_d,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),T_b),c_Option_Omap(T_d,T_c)),V_f_2)),V_m_2)) = c_Map_Odom(T_b,T_d,V_m_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_infinite__UNIV__listI,axiom,
% 11.41/11.15 ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Option_Omap_Oidentity,axiom,
% 11.41/11.15 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Option_Omap_Oid,axiom,
% 11.41/11.15 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_option__map__eq__Some,axiom,
% 11.41/11.15 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 11.41/11.15 <=> ? [B_z] :
% 11.41/11.15 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z)
% 11.41/11.15 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_option__map__Some,axiom,
% 11.41/11.15 ! [V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_option__map__is__None,axiom,
% 11.41/11.15 ! [V_opt_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
% 11.41/11.15 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_option__map__None,axiom,
% 11.41/11.15 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),c_Option_Ooption_ONone(T_c)) = c_Option_Ooption_ONone(T_b) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_option__map__o__empty,axiom,
% 11.41/11.15 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_d,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c))),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_option__map__o__map__upd,axiom,
% 11.41/11.15 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_d)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_d),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_b_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inj__on__map__eq__map,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 11.41/11.15 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 11.41/11.15 <=> V_xs_2 = V_ys_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__inj__on,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 11.41/11.15 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
% 11.41/11.15 => V_xs_2 = V_ys_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__fun__upd,axiom,
% 11.41/11.15 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 11.41/11.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => hAPP(hAPP(c_List_Omap(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_inj__on__mapI,axiom,
% 11.41/11.15 ! [V_A_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2)))
% 11.41/11.15 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__eq__dom,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 11.41/11.15 ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 11.41/11.15 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__SomeD,axiom,
% 11.41/11.15 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xs_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__is__SomeD,axiom,
% 11.41/11.15 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_dom__map__of__conv__image__fst,axiom,
% 11.41/11.15 ! [V_xys_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__eq__None__iff,axiom,
% 11.41/11.15 ! [V_x_2,V_xys_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
% 11.41/11.15 <=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2)))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Option_Omap__def,axiom,
% 11.41/11.15 ! [V_f_2,T_c,T_b] : hAPP(c_Option_Omap(T_b,T_c),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_c),T_b,c_Option_Ooption_ONone(T_c),hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_WT__bodies__def,axiom,
% 11.41/11.15 ( c_Com_OWT__bodies
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__map__restrict,axiom,
% 11.41/11.15 ! [V_ks_2,V_f_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_b,T_c,hAPP(c_Fun_Ocomp(T_c,tc_Option_Ooption(T_c),T_b,c_Option_Ooption_OSome(T_c)),V_f_2),hAPP(c_List_Oset(T_b),V_ks_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_ran__distinct,axiom,
% 11.41/11.15 ! [V_al_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_al_2)))
% 11.41/11.15 => c_Map_Oran(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_al_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__map__of__compr,axiom,
% 11.41/11.15 ! [V_xs_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))
% 11.41/11.15 => hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),c_Map_Omap__of(T_b,T_c,V_xs_2)))),c_Option_Ooption_OSome(T_c)))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct__map,axiom,
% 11.41/11.15 ! [V_xs_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 11.41/11.15 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 11.41/11.15 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__inject__set,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))
% 11.41/11.15 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2)))
% 11.41/11.15 => ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 11.41/11.15 <=> hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__is__SomeI,axiom,
% 11.41/11.15 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)))
% 11.41/11.15 => hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__eq__Some__iff,axiom,
% 11.41/11.15 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 11.41/11.15 => ( hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2)
% 11.41/11.15 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Some__eq__map__of__iff,axiom,
% 11.41/11.15 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 11.41/11.15 => ( hAPP(c_Option_Ooption_OSome(T_c),V_y_2) = hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2)
% 11.41/11.15 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_greaterThanLessThan__upto,axiom,
% 11.41/11.15 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_weak__map__of__SomeI,axiom,
% 11.41/11.15 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_l_2)))
% 11.41/11.15 => ? [B_x] : hAPP(c_Map_Omap__of(T_b,T_c,V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_x) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__upto,axiom,
% 11.41/11.15 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_atLeastAtMost__upto,axiom,
% 11.41/11.15 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct__upto,axiom,
% 11.41/11.15 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_atLeastLessThan__upto,axiom,
% 11.41/11.15 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_greaterThanAtMost__upto,axiom,
% 11.41/11.15 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_nat__list__def,axiom,
% 11.41/11.15 ! [V_l_2] :
% 11.41/11.15 ( c_List_Onat__list(V_l_2)
% 11.41/11.15 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__remove1__eq,axiom,
% 11.41/11.15 ! [V_x_2,V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.15 => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__remove1__subset,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_remove1__idem,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_notin__set__remove1,axiom,
% 11.41/11.15 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_in__set__remove1,axiom,
% 11.41/11.15 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 11.41/11.15 ( V_a_2 != V_b_2
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
% 11.41/11.15 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_remove1__commute,axiom,
% 11.41/11.15 ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct__remove1,axiom,
% 11.41/11.15 ! [V_x,V_xs,T_a] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 11.41/11.15 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_sorted__list__of__set__remove,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__zip__map,axiom,
% 11.41/11.15 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 11.41/11.15 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_x_2)) )
% 11.41/11.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct__zipI1,axiom,
% 11.41/11.15 ! [V_ys,T_b,V_xs,T_a] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 11.41/11.15 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct__zipI2,axiom,
% 11.41/11.15 ! [V_xs,T_b,V_ys,T_a] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 11.41/11.15 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_zip__same__conv__map,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_zip__map__fst__snd,axiom,
% 11.41/11.15 ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2 ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__zip__map2,axiom,
% 11.41/11.15 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__zip__map,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_in__set__zipE,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 11.41/11.15 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__zip__rightD,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__zip__leftD,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_zip__same,axiom,
% 11.41/11.15 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
% 11.41/11.15 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 & V_a_2 = V_b_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_zip__map2,axiom,
% 11.41/11.15 ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_zip__map1,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_zip__map__map,axiom,
% 11.41/11.15 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_sorted__list__of__set__insert,axiom,
% 11.41/11.15 ! [V_x_2,V_A_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__zip__upd,axiom,
% 11.41/11.15 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 11.41/11.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 11.41/11.15 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 11.41/11.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
% 11.41/11.15 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_z_2))
% 11.41/11.15 => c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2)) ) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_length__zip,axiom,
% 11.41/11.15 ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__insort,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_c)
% 11.41/11.15 => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_insort__left__comm,axiom,
% 11.41/11.15 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_insort__key__left__comm,axiom,
% 11.41/11.15 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 11.41/11.15 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_length__insort,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_c)
% 11.41/11.15 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_neq__if__length__neq,axiom,
% 11.41/11.15 ! [V_ys,V_xs,T_a] :
% 11.41/11.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)
% 11.41/11.15 => V_xs != V_ys ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_fun__left__comm__insort,axiom,
% 11.41/11.15 ! [T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_lexn__length,axiom,
% 11.41/11.15 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
% 11.41/11.15 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 11.41/11.15 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__eq__imp__length__eq,axiom,
% 11.41/11.15 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
% 11.41/11.15 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_length__map,axiom,
% 11.41/11.15 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_remove1__insort,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_card__length,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct__card,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.15 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_card__distinct,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] :
% 11.41/11.15 ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 11.41/11.15 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__zip__inject,axiom,
% 11.41/11.15 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 11.41/11.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 11.41/11.15 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 11.41/11.15 => ( c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))
% 11.41/11.15 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__fst__zip,axiom,
% 11.41/11.15 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 11.41/11.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 11.41/11.15 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__snd__zip,axiom,
% 11.41/11.15 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 11.41/11.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 11.41/11.15 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct__insort,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_c)
% 11.41/11.15 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
% 11.41/11.15 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_length__pos__if__in__set,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_zip__eq__conv,axiom,
% 11.41/11.15 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 11.41/11.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 11.41/11.15 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 11.41/11.15 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2
% 11.41/11.15 & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2 ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_lenlex__conv,axiom,
% 11.41/11.15 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_lenlex__def,axiom,
% 11.41/11.15 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_finite__lists__length__eq,axiom,
% 11.41/11.15 ! [V_n_2,V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_list__eq__iff__zip__eq,axiom,
% 11.41/11.15 ! [T_b,V_ys_2,V_xs_2] :
% 11.41/11.15 ( V_xs_2 = V_ys_2
% 11.41/11.15 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 11.41/11.15 & ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__zip__is__None,axiom,
% 11.41/11.15 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 11.41/11.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 11.41/11.15 => ( hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_c)
% 11.41/11.15 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__zip__is__Some,axiom,
% 11.41/11.15 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 11.41/11.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 <=> ? [B_y] : hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),B_y) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_length__remove1,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.15 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 11.41/11.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_dom__map__of__zip,axiom,
% 11.41/11.15 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 11.41/11.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 11.41/11.15 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.15 => c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_b),V_xs_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_finite__lists__length__le,axiom,
% 11.41/11.15 ! [V_n_2,V_A_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Nitpick_Ocard_H__def,axiom,
% 11.41/11.15 ! [V_A_2,T_b] :
% 11.41/11.15 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) )
% 11.41/11.15 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel__iff__zip,axiom,
% 11.41/11.15 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 11.41/11.15 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 11.41/11.15 & ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel__rtrancl__refl,axiom,
% 11.41/11.15 ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel__eq__len,axiom,
% 11.41/11.15 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 11.41/11.15 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel__rtrancl__trans,axiom,
% 11.41/11.15 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel__mono,axiom,
% 11.41/11.15 ! [V_s_2,V_r_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrelp__listrel__eq,axiom,
% 11.41/11.15 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 11.41/11.15 ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
% 11.41/11.15 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_lexn_Osimps_I2_J,axiom,
% 11.41/11.15 ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_impossible__Cons,axiom,
% 11.41/11.15 ! [V_x,V_ys,V_xs,T_a] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
% 11.41/11.15 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__ConsD,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
% 11.41/11.15 => ( V_y_2 = V_x_2
% 11.41/11.15 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_zip__Cons__Cons,axiom,
% 11.41/11.15 ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__subset__Cons,axiom,
% 11.41/11.15 ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_foldr_Osimps_I2_J,axiom,
% 11.41/11.15 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrelp_OCons,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 11.41/11.15 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 11.41/11.15 => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrelp_Oequations_I2_J,axiom,
% 11.41/11.15 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 11.41/11.15 ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
% 11.41/11.15 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 11.41/11.15 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_list_Oinject,axiom,
% 11.41/11.15 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 11.41/11.15 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
% 11.41/11.15 <=> ( V_a_2 = V_a_H_2
% 11.41/11.15 & V_list_2 = V_list_H_2 ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_not__Cons__self2,axiom,
% 11.41/11.15 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 11.41/11.15
% 11.41/11.15 fof(fact_not__Cons__self,axiom,
% 11.41/11.15 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map_Osimps_I2_J,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_remove1_Osimps_I2_J,axiom,
% 11.41/11.15 ! [V_xs,T_a,V_y,V_x] :
% 11.41/11.15 ( ( V_x = V_y
% 11.41/11.15 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 11.41/11.15 & ( V_x != V_y
% 11.41/11.15 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_insort__key_Osimps_I2_J,axiom,
% 11.41/11.15 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 11.41/11.15 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) )
% 11.41/11.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 11.41/11.15 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct_Osimps_I2_J,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 11.41/11.15 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of__Cons__code_I2_J,axiom,
% 11.41/11.15 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 11.41/11.15 ( ( V_l = V_k
% 11.41/11.15 => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) )
% 11.41/11.15 & ( V_l != V_k
% 11.41/11.15 => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Map_Omap__of(T_b,T_c,V_ps),V_k) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_list_Osize_I4_J,axiom,
% 11.41/11.15 ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel_OCons,axiom,
% 11.41/11.15 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__of_Osimps_I2_J,axiom,
% 11.41/11.15 ! [V_ps_2,V_p_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__of(T_b,T_c,V_ps_2)),hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Option_Ooption_OSome(T_c),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Cons__in__lex,axiom,
% 11.41/11.15 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
% 11.41/11.15 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 11.41/11.15 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
% 11.41/11.15 | ( V_x_2 = V_y_2
% 11.41/11.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel__Cons,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__Cons__def,axiom,
% 11.41/11.15 ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel__Cons1,axiom,
% 11.41/11.15 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 11.41/11.15 => ~ ! [B_y,B_ys] :
% 11.41/11.15 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel__Cons2,axiom,
% 11.41/11.15 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
% 11.41/11.15 => ~ ! [B_x,B_xs] :
% 11.41/11.15 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_length__sublist,axiom,
% 11.41/11.15 ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_pick_Osimps,axiom,
% 11.41/11.15 ! [V_xs,V_x,T_a,V_i] :
% 11.41/11.15 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
% 11.41/11.15 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) )
% 11.41/11.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
% 11.41/11.15 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct__sublistI,axiom,
% 11.41/11.15 ! [V_I_2,V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.15 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_in__set__sublistD,axiom,
% 11.41/11.15 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_notin__set__sublistI,axiom,
% 11.41/11.15 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__sublist__subset,axiom,
% 11.41/11.15 ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_select__weight__cons__zero,axiom,
% 11.41/11.15 ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_pick__member,axiom,
% 11.41/11.15 ! [V_xs_2,T_b,V_i_2] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__simps_I2_J,axiom,
% 11.41/11.15 ! [V_xs,V_x,T_a] :
% 11.41/11.15 ( class_Groups_Omonoid__add(T_a)
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__subtractf,axiom,
% 11.41/11.15 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( class_Groups_Oab__group__add(T_b)
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__const__mult,axiom,
% 11.41/11.15 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 11.41/11.15 ( class_Rings_Osemiring__0(T_b)
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__mult__const,axiom,
% 11.41/11.15 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( class_Rings_Osemiring__0(T_b)
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__addf,axiom,
% 11.41/11.15 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__0,axiom,
% 11.41/11.15 ! [V_xs_2,T_c,T_b] :
% 11.41/11.15 ( class_Groups_Omonoid__add(T_b)
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__abs,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] :
% 11.41/11.15 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_uminus__listsum__map,axiom,
% 11.41/11.15 ! [V_xs_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( class_Groups_Oab__group__add(T_b)
% 11.41/11.15 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] :
% 11.41/11.15 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.41/11.15 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_select__weight__def,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 11.41/11.15 ! [V_f_2,V_xs_2,T_b,T_c] :
% 11.41/11.15 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.41/11.15 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 11.41/11.15 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 11.41/11.15 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.41/11.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 11.41/11.15 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 11.41/11.15 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__triv,axiom,
% 11.41/11.15 ! [V_xs_2,V_r_2,T_c,T_b] :
% 11.41/11.15 ( class_Rings_Osemiring__1(T_b)
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__map__remove1,axiom,
% 11.41/11.15 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 11.41/11.15 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.41/11.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_select__weight__member,axiom,
% 11.41/11.15 ! [V_s_2,V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 11.41/11.15 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 11.41/11.15 ! [V_f_2,V_A_2,T_b,T_c] :
% 11.41/11.15 ( class_Groups_Ocomm__monoid__add(T_c)
% 11.41/11.15 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) )
% 11.41/11.15 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.15 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_upto_Opsimps,axiom,
% 11.41/11.15 ! [V_j_2,V_i_2] :
% 11.41/11.15 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2)))
% 11.41/11.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 11.41/11.15 => c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) )
% 11.41/11.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 11.41/11.15 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel__Nil2,axiom,
% 11.41/11.15 ! [V_r_2,V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
% 11.41/11.15 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrel__Nil1,axiom,
% 11.41/11.15 ! [V_r_2,V_xs_2,T_b] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 11.41/11.15 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 11.41/11.15 ! [V_ns_2] :
% 11.41/11.15 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.15 <=> ! [B_x] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 11.41/11.15 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listsum__simps_I1_J,axiom,
% 11.41/11.15 ! [T_a] :
% 11.41/11.15 ( class_Groups_Omonoid__add(T_a)
% 11.41/11.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_Nil__is__map__conv,axiom,
% 11.41/11.15 ! [V_xs_2,V_f_2,T_c,T_b] :
% 11.41/11.15 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 11.41/11.15 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map_Osimps_I1_J,axiom,
% 11.41/11.15 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_map__is__Nil__conv,axiom,
% 11.41/11.15 ! [V_xs_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 11.41/11.15 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrelp_ONil,axiom,
% 11.41/11.15 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_listrelp_Oequations_I1_J,axiom,
% 11.41/11.15 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_insort__not__Nil,axiom,
% 11.41/11.15 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_c)
% 11.41/11.15 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_distinct_Osimps_I1_J,axiom,
% 11.41/11.15 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_remove1_Osimps_I1_J,axiom,
% 11.41/11.15 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_foldr_Osimps_I1_J,axiom,
% 11.41/11.15 ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2 ).
% 11.41/11.15
% 11.41/11.15 fof(fact_upto__empty,axiom,
% 11.41/11.15 ! [V_i,V_j] :
% 11.41/11.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 11.41/11.15 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_zip_Osimps_I1_J,axiom,
% 11.41/11.15 ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_zip__Nil,axiom,
% 11.41/11.15 ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_length__0__conv,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] :
% 11.41/11.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.15 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_list_Osize_I3_J,axiom,
% 11.41/11.15 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_sorted__list__of__set__empty,axiom,
% 11.41/11.15 ! [T_b] :
% 11.41/11.15 ( class_Orderings_Olinorder(T_b)
% 11.41/11.15 => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 11.41/11.15 ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__empty2,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] :
% 11.41/11.15 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 11.41/11.15 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_set__empty,axiom,
% 11.41/11.15 ! [V_xs_2,T_b] :
% 11.41/11.15 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 11.41/11.15 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.15
% 11.41/11.15 fof(fact_list_Osimps_I3_J,axiom,
% 11.41/11.16 ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list_Osimps_I2_J,axiom,
% 11.41/11.16 ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_insort__key_Osimps_I1_J,axiom,
% 11.41/11.16 ! [V_x_2,V_f_2,T_b,T_c] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_c)
% 11.41/11.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sublist__empty,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sublist__nil,axiom,
% 11.41/11.16 ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__greater__0__conv,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel_ONil,axiom,
% 11.41/11.16 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Nil__notin__lex,axiom,
% 11.41/11.16 ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Nil2__notin__lex,axiom,
% 11.41/11.16 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upto_Osimps,axiom,
% 11.41/11.16 ! [V_j,V_i] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 11.41/11.16 => c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 11.41/11.16 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sublist__singleton,axiom,
% 11.41/11.16 ! [V_x_2,T_b,V_A_2] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 11.41/11.16 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 11.41/11.16 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upto__rec__number__of,axiom,
% 11.41/11.16 ! [V_n,V_m] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 11.41/11.16 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 11.41/11.16 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel__Nil,axiom,
% 11.41/11.16 ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__Cons__sing__Nil,axiom,
% 11.41/11.16 ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_select__weigth__select,axiom,
% 11.41/11.16 ! [T_b,V_xs_2] :
% 11.41/11.16 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 11.41/11.16 => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_select,axiom,
% 11.41/11.16 ! [V_s_2,T_b,V_xs_2] :
% 11.41/11.16 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__of_Osimps_I1_J,axiom,
% 11.41/11.16 ! [V_x_1,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b,c_List_Olist_ONil(tc_prod(T_a,T_b))),V_x_1) = c_Option_Ooption_ONone(T_b) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__of__Cons__code_I1_J,axiom,
% 11.41/11.16 ! [V_k,T_a,T_b] : hAPP(c_Map_Omap__of(T_b,T_a,c_List_Olist_ONil(tc_prod(T_b,T_a))),V_k) = c_Option_Ooption_ONone(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_anamorph_Osimps,axiom,
% 11.41/11.16 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 11.41/11.16 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.41/11.16 => hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) )
% 11.41/11.16 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 11.41/11.16 => hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listset_Osimps_I1_J,axiom,
% 11.41/11.16 ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listset_Osimps_I2_J,axiom,
% 11.41/11.16 ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_zip__Cons1,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_zip__Cons,axiom,
% 11.41/11.16 ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list_Osimps_I5_J,axiom,
% 11.41/11.16 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list_Osimps_I4_J,axiom,
% 11.41/11.16 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2 ).
% 11.41/11.16
% 11.41/11.16 fof(fact_select__def,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_pick__same,axiom,
% 11.41/11.16 ! [V_xs_2,T_b,V_l_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth_Osimps,axiom,
% 11.41/11.16 ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__Cons__0,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__Cons__Suc,axiom,
% 11.41/11.16 ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__map,axiom,
% 11.41/11.16 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_all__set__conv__all__nth,axiom,
% 11.41/11.16 ! [V_Pa_2,V_xs_2,T_b] :
% 11.41/11.16 ( ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 11.41/11.16 <=> ! [B_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__conv__nth,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.16 <=> ! [B_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => ! [B_j] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => ( B_i != B_j
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__eq__iff__index__eq,axiom,
% 11.41/11.16 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
% 11.41/11.16 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__eq__iff__nth__eq,axiom,
% 11.41/11.16 ! [T_b,V_ys_2,V_xs_2] :
% 11.41/11.16 ( V_xs_2 = V_ys_2
% 11.41/11.16 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 11.41/11.16 & ! [B_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__zip,axiom,
% 11.41/11.16 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_elem__le__listsum__nat,axiom,
% 11.41/11.16 ! [V_ns,V_k] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_in__set__conv__nth,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 <=> ? [B_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__mem,axiom,
% 11.41/11.16 ! [V_xs_2,T_b,V_n_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__Cons_H,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a,V_n] :
% 11.41/11.16 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 11.41/11.16 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__conv__nth,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__Cons__number__of,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a,V_v] :
% 11.41/11.16 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x )
% 11.41/11.16 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listsum__setsum__nth,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.41/11.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__sublist,axiom,
% 11.41/11.16 ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel__iff__nth,axiom,
% 11.41/11.16 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 11.41/11.16 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 11.41/11.16 & ! [B_n] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__zip,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_insort__insert__insort__key,axiom,
% 11.41/11.16 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 11.41/11.16 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__list__update,axiom,
% 11.41/11.16 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 11.41/11.16 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__id,axiom,
% 11.41/11.16 ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__list__update__neq,axiom,
% 11.41/11.16 ! [V_x,V_xs,T_a,V_j,V_i] :
% 11.41/11.16 ( V_i != V_j
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__nonempty,axiom,
% 11.41/11.16 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 11.41/11.16 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update_Osimps_I1_J,axiom,
% 11.41/11.16 ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__code_I1_J,axiom,
% 11.41/11.16 ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_zip__update,axiom,
% 11.41/11.16 ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_update__zip,axiom,
% 11.41/11.16 ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__list__update,axiom,
% 11.41/11.16 ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__swap,axiom,
% 11.41/11.16 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 11.41/11.16 ( V_i != V_i_H
% 11.41/11.16 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__overwrite,axiom,
% 11.41/11.16 ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__insort__insert,axiom,
% 11.41/11.16 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_c)
% 11.41/11.16 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.16 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__beyond,axiom,
% 11.41/11.16 ! [V_x,V_i,V_xs,T_a] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i))
% 11.41/11.16 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__update,axiom,
% 11.41/11.16 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__code_I3_J,axiom,
% 11.41/11.16 ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__code_I2_J,axiom,
% 11.41/11.16 ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update_Osimps_I2_J,axiom,
% 11.41/11.16 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__update__subsetI,axiom,
% 11.41/11.16 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__update__subset__insert,axiom,
% 11.41/11.16 ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__list__update,axiom,
% 11.41/11.16 ! [V_x,V_j,V_xs,T_a,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => ( ( V_i = V_j
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x )
% 11.41/11.16 & ( V_i != V_j
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__same__conv,axiom,
% 11.41/11.16 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 11.41/11.16 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__list__update__eq,axiom,
% 11.41/11.16 ! [V_x,V_xs,T_a,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__update__memI,axiom,
% 11.41/11.16 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_insort__insert__triv,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__insort__insert,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listsum__update__nat,axiom,
% 11.41/11.16 ! [V_n,V_ns,V_k] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
% 11.41/11.16 => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_insort__insert__key__triv,axiom,
% 11.41/11.16 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 11.41/11.16 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_insort__insert__insort,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sublist__Cons,axiom,
% 11.41/11.16 ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__cons__cons,axiom,
% 11.41/11.16 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
% 11.41/11.16 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 11.41/11.16 | ( V_a_2 = V_b_2
% 11.41/11.16 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__append__length,axiom,
% 11.41/11.16 ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__append__length__plus,axiom,
% 11.41/11.16 ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_zip__append,axiom,
% 11.41/11.16 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 11.41/11.16 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us)
% 11.41/11.16 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs)
% 11.41/11.16 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__append1,axiom,
% 11.41/11.16 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__append,axiom,
% 11.41/11.16 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__length,axiom,
% 11.41/11.16 ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append1__eq__conv,axiom,
% 11.41/11.16 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
% 11.41/11.16 <=> ( V_xs_2 = V_ys_2
% 11.41/11.16 & V_x_2 = V_y_2 ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Cons__eq__append__conv,axiom,
% 11.41/11.16 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
% 11.41/11.16 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 11.41/11.16 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 11.41/11.16 | ? [B_ys_H] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 11.41/11.16 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__eq__Cons__conv,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 11.41/11.16 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 11.41/11.16 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 11.41/11.16 | ? [B_ys_H] :
% 11.41/11.16 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 11.41/11.16 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__append__left__rightI,axiom,
% 11.41/11.16 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Cons__eq__appendI,axiom,
% 11.41/11.16 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 11.41/11.16 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 11.41/11.16 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__Cons,axiom,
% 11.41/11.16 ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listsum__append,axiom,
% 11.41/11.16 ! [V_ys,V_xs,T_a] :
% 11.41/11.16 ( class_Groups_Omonoid__add(T_a)
% 11.41/11.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__append,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__append,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_remove1__append,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__assoc,axiom,
% 11.41/11.16 ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__eq__append__conv2,axiom,
% 11.41/11.16 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_ts_2)
% 11.41/11.16 <=> ? [B_us] :
% 11.41/11.16 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 11.41/11.16 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 )
% 11.41/11.16 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 11.41/11.16 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_same__append__eq,axiom,
% 11.41/11.16 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
% 11.41/11.16 <=> V_ys_2 = V_zs_2 ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__same__eq,axiom,
% 11.41/11.16 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
% 11.41/11.16 <=> V_ys_2 = V_zs_2 ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__eq__appendI,axiom,
% 11.41/11.16 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 11.41/11.16 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 11.41/11.16 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__of__append,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_ys_2),c_Map_Omap__of(T_b,T_c,V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldr__append,axiom,
% 11.41/11.16 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__append__leftI,axiom,
% 11.41/11.16 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_eq__Nil__appendI,axiom,
% 11.41/11.16 ! [T_a,V_ys,V_xs] :
% 11.41/11.16 ( V_xs = V_ys
% 11.41/11.16 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__self__conv2,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 11.41/11.16 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__self__conv,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 11.41/11.16 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__is__Nil__conv,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 11.41/11.16 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 11.41/11.16 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_self__append__conv2,axiom,
% 11.41/11.16 ! [V_xs_2,T_b,V_ys_2] :
% 11.41/11.16 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 11.41/11.16 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_self__append__conv,axiom,
% 11.41/11.16 ! [V_ys_2,T_b,V_xs_2] :
% 11.41/11.16 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 11.41/11.16 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__Nil2,axiom,
% 11.41/11.16 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Nil__is__append__conv,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 11.41/11.16 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 11.41/11.16 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__Nil,axiom,
% 11.41/11.16 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__append,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 11.41/11.16 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.16 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 11.41/11.16 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__append,axiom,
% 11.41/11.16 ! [V_ys,V_xs,T_a,V_n] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__update__append,axiom,
% 11.41/11.16 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__Nil__right,axiom,
% 11.41/11.16 ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sublist__append,axiom,
% 11.41/11.16 ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__lex,axiom,
% 11.41/11.16 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
% 11.41/11.16 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 11.41/11.16 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__upds__append1,axiom,
% 11.41/11.16 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 11.41/11.16 => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__take__index__conv,axiom,
% 11.41/11.16 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 11.41/11.16 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))
% 11.41/11.16 & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2 )
% 11.41/11.16 | ? [B_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))))
% 11.41/11.16 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 11.41/11.16 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__append,axiom,
% 11.41/11.16 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_fun__upds__append2__drop,axiom,
% 11.41/11.16 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 11.41/11.16 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_fun__upds__append__drop,axiom,
% 11.41/11.16 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 11.41/11.16 => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__upds__Nil1,axiom,
% 11.41/11.16 ! [V_bs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,c_List_Olist_ONil(T_b),V_bs_2) = V_m_2 ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__upds__Nil2,axiom,
% 11.41/11.16 ! [V_as_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,c_List_Olist_ONil(T_c)) = V_m_2 ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__Nil,axiom,
% 11.41/11.16 ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__eq__Nil,axiom,
% 11.41/11.16 ! [V_xs_2,V_n_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 11.41/11.16 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__0,axiom,
% 11.41/11.16 ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sublist__upt__eq__take,axiom,
% 11.41/11.16 ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__zip,axiom,
% 11.41/11.16 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__take,axiom,
% 11.41/11.16 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__add__upds,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__upds(T_b,T_c,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__take,axiom,
% 11.41/11.16 ! [V_i,V_xs,T_a] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 11.41/11.16 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__take__subset,axiom,
% 11.41/11.16 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__take__subset__set__take,axiom,
% 11.41/11.16 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_in__set__takeD,axiom,
% 11.41/11.16 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__upds__apply__nontin,axiom,
% 11.41/11.16 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => hAPP(c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__map,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__Suc__Cons,axiom,
% 11.41/11.16 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__1__Cons,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__upd__upds__conv__if,axiom,
% 11.41/11.16 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
% 11.41/11.16 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
% 11.41/11.16 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_dom__map__upds,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))),c_Map_Odom(T_b,T_c,V_m_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__all,axiom,
% 11.41/11.16 ! [V_n,V_xs,T_a] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__take,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__take,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_n,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__upds__Cons,axiom,
% 11.41/11.16 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__Cons,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__Cons_H,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a,V_n] :
% 11.41/11.16 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 11.41/11.16 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__upds__list__update2__drop,axiom,
% 11.41/11.16 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_i_2))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 11.41/11.16 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__upds__twist,axiom,
% 11.41/11.16 ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
% 11.41/11.16 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
% 11.41/11.16 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__Cons__number__of,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a,V_v] :
% 11.41/11.16 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 11.41/11.16 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_restrict__map__upds,axiom,
% 11.41/11.16 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_D_2))
% 11.41/11.16 => c_Map_Orestrict__map(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_b),V_xs_2))),V_xs_2,V_ys_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__Suc__conv__app__nth,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 11.41/11.16 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
% 11.41/11.16 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 11.41/11.16 & V_x_2 = V_y_2 )
% 11.41/11.16 | ( V_xs_2 = V_ys_2
% 11.41/11.16 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__append__leftD,axiom,
% 11.41/11.16 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
% 11.41/11.16 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Cons__acc__listrel1I,axiom,
% 11.41/11.16 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 11.41/11.16 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel1__mono,axiom,
% 11.41/11.16 ! [V_s_2,V_r_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel1__converse,axiom,
% 11.41/11.16 ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 11.41/11.16 ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 11.41/11.16 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel1I2,axiom,
% 11.41/11.16 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 11.41/11.16 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel1__eq__len,axiom,
% 11.41/11.16 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 11.41/11.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 11.41/11.16 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 11.41/11.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_not__Nil__listrel1,axiom,
% 11.41/11.16 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_not__listrel1__Nil,axiom,
% 11.41/11.16 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__listrel1I,axiom,
% 11.41/11.16 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 11.41/11.16 & V_us_2 = V_vs_2 )
% 11.41/11.16 | ( V_xs_2 = V_ys_2
% 11.41/11.16 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_in__listrel1__converse,axiom,
% 11.41/11.16 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 11.41/11.16 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 11.41/11.16 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 11.41/11.16 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Cons__listrel1__Cons,axiom,
% 11.41/11.16 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
% 11.41/11.16 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 11.41/11.16 & V_xs_2 = V_ys_2 )
% 11.41/11.16 | ( V_x_2 = V_y_2
% 11.41/11.16 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel1I1,axiom,
% 11.41/11.16 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel1__subset__listrel,axiom,
% 11.41/11.16 ! [V_r_H_2,V_r_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
% 11.41/11.16 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel1I,axiom,
% 11.41/11.16 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 11.41/11.16 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
% 11.41/11.16 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel1__iff__update,axiom,
% 11.41/11.16 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 11.41/11.16 <=> ? [B_y,B_n] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2))
% 11.41/11.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel1E,axiom,
% 11.41/11.16 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 11.41/11.16 => ~ ! [B_x,B_y] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 11.41/11.16 => ! [B_us,B_vs] :
% 11.41/11.16 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 11.41/11.16 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate1__def,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upd__conv__take__nth__drop,axiom,
% 11.41/11.16 ! [V_a,V_xs,T_a,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__eq__conv__conj,axiom,
% 11.41/11.16 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 11.41/11.16 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
% 11.41/11.16 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__append,axiom,
% 11.41/11.16 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__via__drop,axiom,
% 11.41/11.16 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__drop,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__rotate1,axiom,
% 11.41/11.16 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__1__Cons,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__Suc__Cons,axiom,
% 11.41/11.16 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__map,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_in__set__dropD,axiom,
% 11.41/11.16 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__rotate1,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__drop__subset,axiom,
% 11.41/11.16 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__drop,axiom,
% 11.41/11.16 ! [V_i,V_xs,T_a] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 11.41/11.16 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct1__rotate,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 11.41/11.16 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__drop,axiom,
% 11.41/11.16 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__0,axiom,
% 11.41/11.16 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__zip,axiom,
% 11.41/11.16 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate1__is__Nil__conv,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 11.41/11.16 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__Nil,axiom,
% 11.41/11.16 ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__eq__Nil,axiom,
% 11.41/11.16 ! [V_xs_2,V_n_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 11.41/11.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__all,axiom,
% 11.41/11.16 ! [V_n,V_xs,T_a] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
% 11.41/11.16 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__drop__subset__set__drop,axiom,
% 11.41/11.16 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__drop,axiom,
% 11.41/11.16 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__take,axiom,
% 11.41/11.16 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__take__drop__id,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__Cons,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__Cons_H,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a,V_n] :
% 11.41/11.16 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) )
% 11.41/11.16 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__drop,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_i,V_n] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__eq__append__conv__if,axiom,
% 11.41/11.16 ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
% 11.41/11.16 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
% 11.41/11.16 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)
% 11.41/11.16 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
% 11.41/11.16 => ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2
% 11.41/11.16 & hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2 ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__drop_H,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__simps,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_b,T_a] :
% 11.41/11.16 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 11.41/11.16 & hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__Cons__number__of,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a,V_v] :
% 11.41/11.16 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) )
% 11.41/11.16 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__add,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_j,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate1__length01,axiom,
% 11.41/11.16 ! [V_xs,T_a] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 11.41/11.16 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_zip__append2,axiom,
% 11.41/11.16 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_zip__append1,axiom,
% 11.41/11.16 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_id__take__nth__drop,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__hd__drop,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_n] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_hd__drop__conv__nth,axiom,
% 11.41/11.16 ! [V_n,T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_hd__map,axiom,
% 11.41/11.16 ! [V_f_2,T_c,T_b,V_xs_2] :
% 11.41/11.16 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 11.41/11.16 => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_hd_Osimps,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ).
% 11.41/11.16
% 11.41/11.16 fof(fact_hd__append,axiom,
% 11.41/11.16 ! [V_ys,T_a,V_xs] :
% 11.41/11.16 ( ( V_xs = c_List_Olist_ONil(T_a)
% 11.41/11.16 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) )
% 11.41/11.16 & ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_hd__append2,axiom,
% 11.41/11.16 ! [V_ys,T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_hd__in__set,axiom,
% 11.41/11.16 ! [T_b,V_xs_2] :
% 11.41/11.16 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_hd__conv__nth,axiom,
% 11.41/11.16 ! [T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate1__hd__tl,axiom,
% 11.41/11.16 ! [T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_hd__rotate__conv__nth,axiom,
% 11.41/11.16 ! [V_n,T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__Suc,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_tl__drop,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__tl,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_tl__append2,axiom,
% 11.41/11.16 ! [V_ys,T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__conv__mod,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__rotate,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_tl_Osimps_I2_J,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__tl,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__map,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__rotate,axiom,
% 11.41/11.16 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__tl,axiom,
% 11.41/11.16 ! [V_xs,T_a] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 11.41/11.16 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__rotate,axiom,
% 11.41/11.16 ! [V_xs_2,V_n_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 11.41/11.16 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__rotate,axiom,
% 11.41/11.16 ! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__is__Nil__conv,axiom,
% 11.41/11.16 ! [V_xs_2,V_n_2,T_b] :
% 11.41/11.16 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 11.41/11.16 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_tl_Osimps_I1_J,axiom,
% 11.41/11.16 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__tl,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__def,axiom,
% 11.41/11.16 ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate1__rotate__swap,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__Suc,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_tl__append,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate0,axiom,
% 11.41/11.16 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__add,axiom,
% 11.41/11.16 ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__id,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_n] :
% 11.41/11.16 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__length01,axiom,
% 11.41/11.16 ! [V_n,V_xs,T_a] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 11.41/11.16 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__tl,axiom,
% 11.41/11.16 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_tl__take,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__Suc,axiom,
% 11.41/11.16 ! [V_n,T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__drop__take,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_fold1__set,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 11.41/11.16 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 11.41/11.16 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list_Osize_I2_J,axiom,
% 11.41/11.16 ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldl__Nil,axiom,
% 11.41/11.16 ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2 ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldr__conv__foldl,axiom,
% 11.41/11.16 ! [V_a_2,V_xs_2,T_b] :
% 11.41/11.16 ( class_Groups_Oab__semigroup__add(T_b)
% 11.41/11.16 => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldl__absorb0,axiom,
% 11.41/11.16 ! [V_zs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Groups_Omonoid__add(T_b)
% 11.41/11.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldl__assoc,axiom,
% 11.41/11.16 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Groups_Osemigroup__add(T_b)
% 11.41/11.16 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_start__le__sum,axiom,
% 11.41/11.16 ! [V_ns_2,V_n_2,V_m_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldl__map,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__size__map,axiom,
% 11.41/11.16 ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldl__Cons,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldl__append,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listsum__foldl,axiom,
% 11.41/11.16 ! [T_b] :
% 11.41/11.16 ( class_Groups_Omonoid__add(T_b)
% 11.41/11.16 => c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldl__foldr1__lemma,axiom,
% 11.41/11.16 ! [V_xs_2,V_a_2,T_b] :
% 11.41/11.16 ( class_Groups_Omonoid__add(T_b)
% 11.41/11.16 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldl__foldr1,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( class_Groups_Omonoid__add(T_b)
% 11.41/11.16 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sum__eq__0__conv,axiom,
% 11.41/11.16 ! [V_ns_2,V_m_2] :
% 11.41/11.16 ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 & ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 11.41/11.16 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list_Osize_I1_J,axiom,
% 11.41/11.16 ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 11.41/11.16 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 11.41/11.16 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 11.41/11.16 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Sup__set__fold,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.16 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Inf__set__fold,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.16 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Sup__fin__set__fold,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Lattices_Olattice(T_b)
% 11.41/11.16 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Inf__fin__set__fold,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Lattices_Olattice(T_b)
% 11.41/11.16 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Min__fin__set__fold,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Max__fin__set__fold,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_SUPR__set__fold,axiom,
% 11.41/11.16 ! [V_f_2,V_xs_2,T_c,T_b] :
% 11.41/11.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.16 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_INFI__set__fold,axiom,
% 11.41/11.16 ! [V_f_2,V_xs_2,T_c,T_b] :
% 11.41/11.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 11.41/11.16 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__size__estimation,axiom,
% 11.41/11.16 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__size__estimation_H,axiom,
% 11.41/11.16 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__upds__fold__map__upd,axiom,
% 11.41/11.16 ! [V_vs_2,V_ks_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),T_c))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c))))),c_Option_Ooption_OSome(T_c))),V_m_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_ks_2),V_vs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_elem__le__sum,axiom,
% 11.41/11.16 ! [V_ns_2,V_n_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__size__conv__listsum,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel__subset,axiom,
% 11.41/11.16 ! [V_A_2,V_r_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lists__accI,axiom,
% 11.41/11.16 ! [V_r_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lists_ONil,axiom,
% 11.41/11.16 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listrel__refl__on,axiom,
% 11.41/11.16 ! [V_r_2,V_A_2,T_b] :
% 11.41/11.16 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 11.41/11.16 => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_equiv__listrel,axiom,
% 11.41/11.16 ! [V_r_2,V_A_2,T_b] :
% 11.41/11.16 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 11.41/11.16 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__in__lists__conv,axiom,
% 11.41/11.16 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
% 11.41/11.16 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 11.41/11.16 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lists__mono,axiom,
% 11.41/11.16 ! [V_B_2,V_A_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lists__UNIV,axiom,
% 11.41/11.16 ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Cons__in__lists__iff,axiom,
% 11.41/11.16 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
% 11.41/11.16 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 11.41/11.16 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_in__lists__conv__set,axiom,
% 11.41/11.16 ! [V_A_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 11.41/11.16 <=> ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lists__eq__set,axiom,
% 11.41/11.16 ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lists__empty,axiom,
% 11.41/11.16 ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lists__accD,axiom,
% 11.41/11.16 ! [V_r_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__append__rightI,axiom,
% 11.41/11.16 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 11.41/11.16 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__Nil__left,axiom,
% 11.41/11.16 ! [V_r_2,V_y_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 11.41/11.16 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__list__update,axiom,
% 11.41/11.16 ! [V_x,V_k,T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 11.41/11.16 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listsum__mono,axiom,
% 11.41/11.16 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 11.41/11.16 ( ( class_Groups_Omonoid__add(T_c)
% 11.41/11.16 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 11.41/11.16 => ( ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__appendL,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_ys] :
% 11.41/11.16 ( V_ys = c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__appendR,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_ys] :
% 11.41/11.16 ( V_ys != c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__append,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_ys] :
% 11.41/11.16 ( ( V_ys = c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 11.41/11.16 & ( V_ys != c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__ConsL,axiom,
% 11.41/11.16 ! [V_x,T_a,V_xs] :
% 11.41/11.16 ( V_xs = c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__ConsR,axiom,
% 11.41/11.16 ! [V_x,T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last_Osimps,axiom,
% 11.41/11.16 ! [V_x,T_a,V_xs] :
% 11.41/11.16 ( ( V_xs = c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 11.41/11.16 & ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__map,axiom,
% 11.41/11.16 ! [V_f_2,T_c,T_b,V_xs_2] :
% 11.41/11.16 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 11.41/11.16 => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__in__set,axiom,
% 11.41/11.16 ! [T_b,V_as_2] :
% 11.41/11.16 ( V_as_2 != c_List_Olist_ONil(T_b)
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__snoc,axiom,
% 11.41/11.16 ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__drop,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_n] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__conv__nth,axiom,
% 11.41/11.16 ! [T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__linear,axiom,
% 11.41/11.16 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 11.41/11.16 ( ! [B_a,B_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2))
% 11.41/11.16 | B_a = B_b
% 11.41/11.16 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2)) )
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 11.41/11.16 | V_x_2 = V_y_2
% 11.41/11.16 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lexord__irreflexive,axiom,
% 11.41/11.16 ! [V_y_2,V_r_2,T_b] :
% 11.41/11.16 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
% 11.41/11.16 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_lists_Osimps,axiom,
% 11.41/11.16 ! [V_A_2,V_a_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 11.41/11.16 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 11.41/11.16 | ? [B_a,B_l] :
% 11.41/11.16 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 11.41/11.16 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 11.41/11.16 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_list__size__pointwise,axiom,
% 11.41/11.16 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 11.41/11.16 ( ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_butlast__take,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_n] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__take__lemma,axiom,
% 11.41/11.16 ! [V_ys,V_xs,T_a,V_k] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
% 11.41/11.16 => ( ! [B_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__butlast,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__butlast,axiom,
% 11.41/11.16 ! [T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 11.41/11.16 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_butlast_Osimps_I1_J,axiom,
% 11.41/11.16 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_in__set__butlastD,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_butlast_Osimps_I2_J,axiom,
% 11.41/11.16 ! [V_x,T_a,V_xs] :
% 11.41/11.16 ( ( V_xs = c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 11.41/11.16 & ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_butlast__append,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_ys] :
% 11.41/11.16 ( ( V_ys = c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 11.41/11.16 & ( V_ys != c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__butlast,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_butlast__drop,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_in__set__butlast__appendI,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 11.41/11.16 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_butlast__snoc,axiom,
% 11.41/11.16 ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__butlast,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_n] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__butlast,axiom,
% 11.41/11.16 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_butlast__conv__take,axiom,
% 11.41/11.16 ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_butlast__list__update,axiom,
% 11.41/11.16 ! [V_x,V_xs,T_a,V_k] :
% 11.41/11.16 ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 11.41/11.16 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs) )
% 11.41/11.16 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 11.41/11.16 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_snoc__eq__iff__butlast,axiom,
% 11.41/11.16 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
% 11.41/11.16 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 11.41/11.16 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 11.41/11.16 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_append__butlast__last__id,axiom,
% 11.41/11.16 ! [T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose__aux__max,axiom,
% 11.41/11.16 ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_partition__set,axiom,
% 11.41/11.16 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 11.41/11.16 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 11.41/11.16 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__filter__map,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__is__subset,axiom,
% 11.41/11.16 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__filter__le,axiom,
% 11.41/11.16 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__append,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sum__length__filter__compl,axiom,
% 11.41/11.16 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter_Osimps_I2_J,axiom,
% 11.41/11.16 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 11.41/11.16 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 11.41/11.16 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 11.41/11.16 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__id__conv,axiom,
% 11.41/11.16 ! [V_xs_2,V_Pa_2,T_b] :
% 11.41/11.16 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
% 11.41/11.16 <=> ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__insort__triv,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_c)
% 11.41/11.16 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 11.41/11.16 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__filter,axiom,
% 11.41/11.16 ! [V_Pa_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.16 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_remove1__filter__not,axiom,
% 11.41/11.16 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 11.41/11.16 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 11.41/11.16 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__remove1,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,V_Qa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Qa_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__filter,axiom,
% 11.41/11.16 ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Qa_2)),V_Pa_2)),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_partition__filter1,axiom,
% 11.41/11.16 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__empty__conv,axiom,
% 11.41/11.16 ! [V_xs_2,V_Pa_2,T_b] :
% 11.41/11.16 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 11.41/11.16 <=> ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter_Osimps_I1_J,axiom,
% 11.41/11.16 ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__filter,axiom,
% 11.41/11.16 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_partition__filter__conv,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_partition__filter2,axiom,
% 11.41/11.16 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__map,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__filter__less,axiom,
% 11.41/11.16 ! [V_Pa_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__minus__filter__out,axiom,
% 11.41/11.16 ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_partition__P,axiom,
% 11.41/11.16 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 11.41/11.16 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 11.41/11.16 => ( ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 11.41/11.16 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 11.41/11.16 & ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 11.41/11.16 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_partition_Osimps_I1_J,axiom,
% 11.41/11.16 ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__in__sublist,axiom,
% 11.41/11.16 ! [V_s_2,V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.16 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_partition_Osimps_I2_J,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__filter__conv__card,axiom,
% 11.41/11.16 ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__filter__def,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),V_f_2)),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_b)))),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose__max__length,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__of__filter__in,axiom,
% 11.41/11.16 ! [V_Pa_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
% 11.41/11.16 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2)
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_k_2),V_z_2))
% 11.41/11.16 => hAPP(c_Map_Omap__of(T_c,T_b,hAPP(c_List_Ofilter(tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose__map__map,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__filter__simps_I1_J,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_b),T_b,c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose_Osimps_I1_J,axiom,
% 11.41/11.16 ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__filter__simps_I2_J,axiom,
% 11.41/11.16 ! [V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose__empty,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 11.41/11.16 <=> ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose_Osimps_I2_J,axiom,
% 11.41/11.16 ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sublist__shift__lemma__Suc,axiom,
% 11.41/11.16 ! [V_is_2,V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_select__weigth__drop__zero,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_pick__drop__zero,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__transpose,axiom,
% 11.41/11.16 ! [V_xs_2,T_b,V_i_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__transpose,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__filter__map__filter,axiom,
% 11.41/11.16 ! [V_xs_2,V_Pa_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = c_List_Omap__filter(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_c,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_c),c_If(tc_Option_Ooption(T_b))),V_Pa_2)),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_c),c_Option_Ooption_OSome(T_b)),V_f_2))),c_Option_Ooption_ONone(T_b)),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_insort__key__remove1,axiom,
% 11.41/11.16 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_c)
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 11.41/11.16 => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
% 11.41/11.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sublist__def,axiom,
% 11.41/11.16 ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted_ONil,axiom,
% 11.41/11.16 ! [T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__single,axiom,
% 11.41/11.16 ! [V_x,T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__same,axiom,
% 11.41/11.16 ! [V_xs_2,V_g_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__map__same,axiom,
% 11.41/11.16 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__filter,axiom,
% 11.41/11.16 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__upt,axiom,
% 11.41/11.16 ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__butlast,axiom,
% 11.41/11.16 ! [V_xs,T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upt__eq__Cons__conv,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 11.41/11.16 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 11.41/11.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 11.41/11.16 & V_i_2 = V_x_2
% 11.41/11.16 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2 ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_take__upt,axiom,
% 11.41/11.16 ! [V_n,V_m,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n))
% 11.41/11.16 => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upt__conv__Nil,axiom,
% 11.41/11.16 ! [V_i,V_j] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 11.41/11.16 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upt__eq__Nil__conv,axiom,
% 11.41/11.16 ! [V_j_2,V_i_2] :
% 11.41/11.16 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 11.41/11.16 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.41/11.16 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__many,axiom,
% 11.41/11.16 ! [V_zs,V_y,V_x,T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__many__eq,axiom,
% 11.41/11.16 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
% 11.41/11.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 11.41/11.16 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upt__add__eq__append,axiom,
% 11.41/11.16 ! [V_k,V_j,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upt__Suc,axiom,
% 11.41/11.16 ! [V_j,V_i] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upt__Suc__append,axiom,
% 11.41/11.16 ! [V_j,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__Cons,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 11.41/11.16 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 11.41/11.16 & ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__append,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 11.41/11.16 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 11.41/11.16 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 11.41/11.16 & ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => ! [B_xa] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_drop__upt,axiom,
% 11.41/11.16 ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__drop,axiom,
% 11.41/11.16 ! [V_n,V_xs,T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_hd__upt,axiom,
% 11.41/11.16 ! [V_j,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__insort__insert,axiom,
% 11.41/11.16 ! [V_x_2,V_xs_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upt__rec,axiom,
% 11.41/11.16 ! [V_j,V_i] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upt__conv__Cons,axiom,
% 11.41/11.16 ! [V_j,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__upt,axiom,
% 11.41/11.16 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_atLeastLessThan__upt,axiom,
% 11.41/11.16 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__distinct__set__unique,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 11.41/11.16 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 11.41/11.16 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 11.41/11.16 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 11.41/11.16 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__insort,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
% 11.41/11.16 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__upt,axiom,
% 11.41/11.16 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__remove1,axiom,
% 11.41/11.16 ! [V_a,V_xs,T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__upt,axiom,
% 11.41/11.16 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__upto,axiom,
% 11.41/11.16 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__list__of__set__range,axiom,
% 11.41/11.16 ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upt__0,axiom,
% 11.41/11.16 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted_Oequations_I1_J,axiom,
% 11.41/11.16 ! [T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__take,axiom,
% 11.41/11.16 ! [V_n,V_xs,T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__tl,axiom,
% 11.41/11.16 ! [V_xs,T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_upt__rec__number__of,axiom,
% 11.41/11.16 ! [V_n,V_m] :
% 11.41/11.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 11.41/11.16 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) )
% 11.41/11.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 11.41/11.16 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__insort__key,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
% 11.41/11.16 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__map__remove1,axiom,
% 11.41/11.16 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__Suc__upt,axiom,
% 11.41/11.16 ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__insort__insert__key,axiom,
% 11.41/11.16 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 11.41/11.16 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__upt,axiom,
% 11.41/11.16 ! [V_j,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__insort,axiom,
% 11.41/11.16 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 11.41/11.16 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 11.41/11.16 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__nth,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2 ).
% 11.41/11.16
% 11.41/11.16 fof(fact_atLeastAtMost__upt,axiom,
% 11.41/11.16 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_atLeast__upt,axiom,
% 11.41/11.16 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 11.41/11.16 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 11.41/11.16 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.41/11.16 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 11.41/11.16 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 11.41/11.16 ( class_Groups_Ocomm__monoid__add(T_b)
% 11.41/11.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__upt,axiom,
% 11.41/11.16 ! [V_j,V_k,V_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_greaterThanAtMost__upt,axiom,
% 11.41/11.16 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted_Oequations_I2_J,axiom,
% 11.41/11.16 ! [V_a1_2,V_a2_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 11.41/11.16 <=> ( ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 11.41/11.16 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_greaterThanLessThan__upt,axiom,
% 11.41/11.16 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__map__upt,axiom,
% 11.41/11.16 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__list__of__set,axiom,
% 11.41/11.16 ! [V_A_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 11.41/11.16 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 11.41/11.16 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 11.41/11.16 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_atMost__upto,axiom,
% 11.41/11.16 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_insort__remove1,axiom,
% 11.41/11.16 ! [V_xs_2,V_a_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 11.41/11.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__equals__nth__mono,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 11.41/11.16 <=> ! [B_j] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 11.41/11.16 => ! [B_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__nth__mono,axiom,
% 11.41/11.16 ! [V_j,V_i,V_xs,T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__sorted__distinct__set__unique,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_c)
% 11.41/11.16 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 11.41/11.16 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 11.41/11.16 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 11.41/11.16 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 11.41/11.16 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sublist__shift__lemma,axiom,
% 11.41/11.16 ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose__rectangle,axiom,
% 11.41/11.16 ! [V_n_2,T_b,V_xs_2] :
% 11.41/11.16 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 11.41/11.16 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.41/11.16 => ( ! [B_i] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 11.41/11.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 )
% 11.41/11.16 => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose_Opsimps_I2_J,axiom,
% 11.41/11.16 ! [V_xss_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
% 11.41/11.16 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose_Opsimps_I1_J,axiom,
% 11.41/11.16 ! [T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
% 11.41/11.16 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose__column,axiom,
% 11.41/11.16 ! [V_i_2,V_xs_2,T_b] :
% 11.41/11.16 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 11.41/11.16 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose__aux__filter__head,axiom,
% 11.41/11.16 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_inj__on__rev,axiom,
% 11.41/11.16 ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_filter__concat,axiom,
% 11.41/11.16 ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__concat,axiom,
% 11.41/11.16 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev_Osimps_I2_J,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__eq__Cons__iff,axiom,
% 11.41/11.16 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 11.41/11.16 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_concat_Osimps_I2_J,axiom,
% 11.41/11.16 ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_singleton__rev__conv,axiom,
% 11.41/11.16 ! [V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
% 11.41/11.16 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__singleton__conv,axiom,
% 11.41/11.16 ! [V_x_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
% 11.41/11.16 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Nil__eq__concat__conv,axiom,
% 11.41/11.16 ! [V_xss_2,T_b] :
% 11.41/11.16 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 11.41/11.16 <=> ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 11.41/11.16 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_concat__eq__Nil__conv,axiom,
% 11.41/11.16 ! [V_xss_2,T_b] :
% 11.41/11.16 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 11.41/11.16 <=> ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 11.41/11.16 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__is__Nil__conv,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 11.41/11.16 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_Nil__is__rev__conv,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 11.41/11.16 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_concat_Osimps_I1_J,axiom,
% 11.41/11.16 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev_Osimps_I1_J,axiom,
% 11.41/11.16 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_map__concat,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__map,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__concat,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_concat__conv__foldl,axiom,
% 11.41/11.16 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__foldl__cons,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldl__conv__concat,axiom,
% 11.41/11.16 ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_distinct__rev,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 11.41/11.16 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_concat__append,axiom,
% 11.41/11.16 ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__append,axiom,
% 11.41/11.16 ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__rev,axiom,
% 11.41/11.16 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_listsum__rev,axiom,
% 11.41/11.16 ! [V_xs,T_a] :
% 11.41/11.16 ( class_Groups_Ocomm__monoid__add(T_a)
% 11.41/11.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__rev__ident,axiom,
% 11.41/11.16 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__swap,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 11.41/11.16 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__is__rev__conv,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 11.41/11.16 <=> V_xs_2 = V_ys_2 ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldl__foldr,axiom,
% 11.41/11.16 ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldr__foldl,axiom,
% 11.41/11.16 ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__concat,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_set__rev,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_zip__rev,axiom,
% 11.41/11.16 ! [V_ys,T_b,V_xs,T_a] :
% 11.41/11.16 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)
% 11.41/11.16 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__filter,axiom,
% 11.41/11.16 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_hd__rev,axiom,
% 11.41/11.16 ! [T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_last__rev,axiom,
% 11.41/11.16 ! [T_a,V_xs] :
% 11.41/11.16 ( V_xs != c_List_Olist_ONil(T_a)
% 11.41/11.16 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__transpose,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__drop,axiom,
% 11.41/11.16 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__take,axiom,
% 11.41/11.16 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rotate__rev,axiom,
% 11.41/11.16 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose_Osimps_I3_J,axiom,
% 11.41/11.16 ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__nth,axiom,
% 11.41/11.16 ! [V_xs,T_a,V_n] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_concat__eq__concat__iff,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 11.41/11.16 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 11.41/11.16 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 11.41/11.16 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_concat__injective,axiom,
% 11.41/11.16 ! [V_ys_2,V_xs_2,T_b] :
% 11.41/11.16 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 11.41/11.16 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 11.41/11.16 => ( ! [B_x] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 11.41/11.16 => V_xs_2 = V_ys_2 ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_rev__update,axiom,
% 11.41/11.16 ! [V_y,V_xs,T_a,V_k] :
% 11.41/11.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_concat__map__singleton,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_sorted__rev__nth__mono,axiom,
% 11.41/11.16 ! [V_j,V_i,V_xs,T_a] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_a)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 11.41/11.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_foldr__max__sorted,axiom,
% 11.41/11.16 ! [V_y_2,V_xs_2,T_b] :
% 11.41/11.16 ( class_Orderings_Olinorder(T_b)
% 11.41/11.16 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 11.41/11.16 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 11.41/11.16 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 11.41/11.16 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 11.41/11.16 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose_Opsimps_I3_J,axiom,
% 11.41/11.16 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 11.41/11.16 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
% 11.41/11.16 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_length__transpose__sorted,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 11.41/11.16 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 11.41/11.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 11.41/11.16 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 11.41/11.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose__column__length,axiom,
% 11.41/11.16 ! [V_i_2,V_xs_2,T_b] :
% 11.41/11.16 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 11.41/11.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose__aux__filter__tail,axiom,
% 11.41/11.16 ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_nth__nth__transpose__sorted,axiom,
% 11.41/11.16 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 11.41/11.16 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 11.41/11.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
% 11.41/11.16 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transpose__transpose,axiom,
% 11.41/11.16 ! [V_xs_2,T_b] :
% 11.41/11.16 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 11.41/11.16 => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 11.41/11.16 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 11.41/11.16
% 11.41/11.16 fof(fact_takeWhile__map,axiom,
% 11.41/11.16 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 11.41/11.16
% 11.41/11.16 %----Arity declarations (203)
% 11.41/11.16 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 11.41/11.16 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Lattices_Obounded__lattice(T_1)
% 11.41/11.16 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 11.41/11.16 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Lattices_Obounded__lattice(T_1)
% 11.41/11.16 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Lattices_Obounded__lattice(T_1)
% 11.41/11.16 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Lattices_Olattice(T_1)
% 11.41/11.16 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Lattices_Olattice(T_1)
% 11.41/11.16 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Lattices_Odistrib__lattice(T_1)
% 11.41/11.16 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Lattices_Oboolean__algebra(T_1)
% 11.41/11.16 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Orderings_Opreorder,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Orderings_Opreorder(T_1)
% 11.41/11.16 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 11.41/11.16 ! [T_1,T_2] :
% 11.41/11.16 ( ( class_Finite__Set_Ofinite(T_2)
% 11.41/11.16 & class_Finite__Set_Ofinite(T_1) )
% 11.41/11.16 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Lattices_Olattice,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Lattices_Olattice(T_1)
% 11.41/11.16 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Orderings_Oorder,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Orderings_Oorder(T_1)
% 11.41/11.16 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Orderings_Otop,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Orderings_Otop(T_1)
% 11.41/11.16 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Orderings_Oord,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Orderings_Oord(T_1)
% 11.41/11.16 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Orderings_Obot,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Orderings_Obot(T_1)
% 11.41/11.16 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Groups_Ouminus,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Groups_Ouminus(T_1)
% 11.41/11.16 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_fun__Groups_Ominus,axiom,
% 11.41/11.16 ! [T_2,T_1] :
% 11.41/11.16 ( class_Groups_Ominus(T_1)
% 11.41/11.16 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 11.41/11.16 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 11.41/11.16 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 11.41/11.16 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 11.41/11.16 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 11.41/11.16 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 11.41/11.16 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 11.41/11.16 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 11.41/11.16 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 11.41/11.16 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 11.41/11.16 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 11.41/11.16 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 11.41/11.16 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 11.41/11.16 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 11.41/11.16 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 11.41/11.16 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 11.41/11.16 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 11.41/11.16 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 11.41/11.16 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 11.41/11.16 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 11.41/11.16 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 11.41/11.16 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 11.41/11.16 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 11.41/11.16 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 11.41/11.16 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 11.41/11.16 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 11.41/11.16 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 11.41/11.16 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 11.41/11.16 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 11.41/11.16 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 11.41/11.16 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 11.41/11.16 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 11.41/11.16 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 11.41/11.16 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 11.41/11.16 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 11.41/11.16 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 11.41/11.16 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 11.41/11.16 class_Orderings_Opreorder(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 11.41/11.16 class_Orderings_Olinorder(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 11.41/11.16 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 11.41/11.16 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 11.41/11.16 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 11.41/11.16 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 11.41/11.16 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 11.41/11.16 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 11.41/11.16 class_Lattices_Olattice(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 11.41/11.16 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 11.41/11.16 class_Divides_Oring__div(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 11.41/11.16 class_Rings_Omult__zero(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 11.41/11.16 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 11.41/11.16 class_Orderings_Oorder(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 11.41/11.16 class_Int_Oring__char__0(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 11.41/11.16 class_Int_Onumber__ring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 11.41/11.16 class_Rings_Osemiring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 11.41/11.16 class_Orderings_Oord(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 11.41/11.16 class_Groups_Ouminus(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 11.41/11.16 class_Groups_Osgn__if(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 11.41/11.16 class_Groups_Oabs__if(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 11.41/11.16 class_Rings_Oring__1(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 11.41/11.16 class_Groups_Ominus(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Power_Opower,axiom,
% 11.41/11.16 class_Power_Opower(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 11.41/11.16 class_Groups_Ozero(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Oring,axiom,
% 11.41/11.16 class_Rings_Oring(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 11.41/11.16 class_Rings_Oidom(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Int_Onumber,axiom,
% 11.41/11.16 class_Int_Onumber(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Groups_Oone,axiom,
% 11.41/11.16 class_Groups_Oone(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 11.41/11.16 class_Rings_Odvd(tc_Int_Oint) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 11.41/11.16 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 11.41/11.16 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 11.41/11.16 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 11.41/11.16 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 11.41/11.16 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 11.41/11.16 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 11.41/11.16 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 11.41/11.16 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 11.41/11.16 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 11.41/11.16 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 11.41/11.16 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 11.41/11.16 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 11.41/11.16 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 11.41/11.16 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 11.41/11.16 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 11.41/11.16 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 11.41/11.16 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 11.41/11.16 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 11.41/11.16 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 11.41/11.16 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 11.41/11.16 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 11.41/11.16 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 11.41/11.16 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 11.41/11.16 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 11.41/11.16 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 11.41/11.16 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 11.41/11.16 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 11.41/11.16 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 11.41/11.16 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 11.41/11.16 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 11.41/11.16 class_Lattices_Olattice(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 11.41/11.16 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 11.41/11.16 class_Orderings_Oorder(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 11.41/11.16 class_Rings_Osemiring(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 11.41/11.16 class_Orderings_Oord(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 11.41/11.16 class_Orderings_Obot(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 11.41/11.16 class_Groups_Ominus(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Power_Opower,axiom,
% 11.41/11.16 class_Power_Opower(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 11.41/11.16 class_Groups_Ozero(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 11.41/11.16 class_Int_Onumber(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 11.41/11.16 class_Groups_Oone(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 11.41/11.16 class_Rings_Odvd(tc_Nat_Onat) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 11.41/11.16 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 11.41/11.16 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 11.41/11.16 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 11.41/11.16 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 11.41/11.16 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 11.41/11.16 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 11.41/11.16 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 11.41/11.16 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 11.41/11.16 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 11.41/11.16 class_Lattices_Olattice(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 11.41/11.16 class_Orderings_Oorder(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 11.41/11.16 class_Orderings_Otop(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 11.41/11.16 class_Orderings_Oord(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 11.41/11.16 class_Orderings_Obot(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 11.41/11.16 class_Groups_Ouminus(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 11.41/11.16 class_Groups_Ominus(tc_HOL_Obool) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_String__Ochar__Finite__Set_Ofinite,axiom,
% 11.41/11.16 class_Finite__Set_Ofinite(tc_String_Ochar) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 11.41/11.16 ! [T_1,T_2] :
% 11.41/11.16 ( ( class_Finite__Set_Ofinite(T_2)
% 11.41/11.16 & class_Finite__Set_Ofinite(T_1) )
% 11.41/11.16 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 11.41/11.16 ! [T_1] :
% 11.41/11.16 ( class_Finite__Set_Ofinite(T_1)
% 11.41/11.16 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_String__Onibble__Finite__Set_Ofinite,axiom,
% 11.41/11.16 class_Finite__Set_Ofinite(tc_String_Onibble) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 11.41/11.16 ! [T_1,T_2] :
% 11.41/11.16 ( ( class_Finite__Set_Ofinite(T_2)
% 11.41/11.16 & class_Finite__Set_Ofinite(T_1) )
% 11.41/11.16 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_prod__Smallcheck_Osmall,axiom,
% 11.41/11.16 ! [T_1,T_2] :
% 11.41/11.16 ( ( class_Smallcheck_Osmall(T_2)
% 11.41/11.16 & class_Smallcheck_Osmall(T_1) )
% 11.41/11.16 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 11.41/11.16 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 11.41/11.16 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 11.41/11.16 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 11.41/11.16 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 11.41/11.16 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 11.41/11.16 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 11.41/11.16 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 11.41/11.16 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 11.41/11.16 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 11.41/11.16 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 11.41/11.16 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 11.41/11.16 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 11.41/11.16 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 11.41/11.16 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 11.41/11.16 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 11.41/11.16 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 11.41/11.16 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 11.41/11.16 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 11.41/11.16 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 11.41/11.16 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 11.41/11.16 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 11.41/11.16 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 11.41/11.16 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 11.41/11.16 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 11.41/11.16 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 11.41/11.16 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 11.41/11.16 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 11.41/11.16 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 11.41/11.16 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 11.41/11.16 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 11.41/11.16 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 11.41/11.16 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 11.41/11.16 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 11.41/11.16 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 11.41/11.16 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 11.41/11.16 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 11.41/11.16 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 11.41/11.16 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 11.41/11.16
% 11.41/11.16 %----Helper facts (20)
% 11.41/11.16 fof(help_c__COMBI__1,axiom,
% 11.41/11.16 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__COMBK__1,axiom,
% 11.41/11.16 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__COMBB__1,axiom,
% 11.41/11.16 ! [V_R_2,V_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__COMBC__1,axiom,
% 11.41/11.16 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__COMBS__1,axiom,
% 11.41/11.16 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fequal__1,axiom,
% 11.41/11.16 ! [V_y_2,V_x_2] :
% 11.41/11.16 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 11.41/11.16 | V_x_2 = V_y_2 ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fequal__2,axiom,
% 11.41/11.16 ! [V_y_2,V_x_2] :
% 11.41/11.16 ( V_x_2 != V_y_2
% 11.41/11.16 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fFalse__1,axiom,
% 11.41/11.16 ~ hBOOL(c_fFalse) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fTrue__1,axiom,
% 11.41/11.16 hBOOL(c_fTrue) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fNot__1,axiom,
% 11.41/11.16 ! [V_Pa_2] :
% 11.41/11.16 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2))
% 11.41/11.16 | ~ hBOOL(V_Pa_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fNot__2,axiom,
% 11.41/11.16 ! [V_Pa_2] :
% 11.41/11.16 ( ~ ~ hBOOL(V_Pa_2)
% 11.41/11.16 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fconj__1,axiom,
% 11.41/11.16 ! [V_Qa_2,V_Pa_2] :
% 11.41/11.16 ( ~ hBOOL(V_Pa_2)
% 11.41/11.16 | ~ hBOOL(V_Qa_2)
% 11.41/11.16 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fconj__2,axiom,
% 11.41/11.16 ! [V_Qa_2,V_Pa_2] :
% 11.41/11.16 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 11.41/11.16 | hBOOL(V_Pa_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fconj__3,axiom,
% 11.41/11.16 ! [V_Qa_2,V_Pa_2] :
% 11.41/11.16 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 11.41/11.16 | hBOOL(V_Qa_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fdisj__1,axiom,
% 11.41/11.16 ! [V_Qa_2,V_Pa_2] :
% 11.41/11.16 ( ~ hBOOL(V_Pa_2)
% 11.41/11.16 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fdisj__2,axiom,
% 11.41/11.16 ! [V_Pa_2,V_Qa_2] :
% 11.41/11.16 ( ~ hBOOL(V_Qa_2)
% 11.41/11.16 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fdisj__3,axiom,
% 11.41/11.16 ! [V_Qa_2,V_Pa_2] :
% 11.41/11.16 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
% 11.41/11.16 | hBOOL(V_Pa_2)
% 11.41/11.16 | hBOOL(V_Qa_2) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fimplies__1,axiom,
% 11.41/11.16 ! [V_Qa_2,V_Pa_2] :
% 11.41/11.16 ( hBOOL(V_Pa_2)
% 11.41/11.16 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fimplies__2,axiom,
% 11.41/11.16 ! [V_Pa_2,V_Qa_2] :
% 11.41/11.16 ( ~ hBOOL(V_Qa_2)
% 11.41/11.16 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 11.41/11.16
% 11.41/11.16 fof(help_c__fimplies__3,axiom,
% 11.41/11.16 ! [V_Qa_2,V_Pa_2] :
% 11.41/11.16 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
% 11.41/11.16 | ~ hBOOL(V_Pa_2)
% 11.41/11.16 | hBOOL(V_Qa_2) ) ).
% 11.41/11.16
% 11.41/11.16 %----Conjectures (1)
% 11.41/11.16 fof(conj_0,conjecture,
% 11.41/11.16 ! [B_Z,B_s] :
% 11.41/11.16 ( v_P(B_Z,B_s)
% 11.41/11.16 => ! [B_s_H] :
% 11.41/11.16 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),B_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_s_H)
% 11.41/11.16 => v_Q(B_Z,B_s_H) ) ) ).
% 11.41/11.16
% 11.41/11.16 %------------------------------------------------------------------------------
% 11.41/11.16 %-------------------------------------------
% 11.41/11.16 % Proof found
% 11.41/11.16 % SZS status Theorem for theBenchmark
% 11.41/11.16 % SZS output start Proof
% 11.41/11.17 %ClaNum:10051(EqnAxiom:2817)
% 11.41/11.17 %VarNum:77453(SingletonVarNum:23507)
% 11.41/11.17 %MaxLitNum:8
% 11.41/11.17 %MaxfuncDepth:13
% 11.41/11.17 %SharedTerms:1083
% 11.41/11.17 %goalClause: 3018 3470 4382
% 11.41/11.17 %singleGoalClaCount:3
% 11.41/11.17 [2821]P1(a859)
% 11.41/11.17 [2822]P1(a1)
% 11.41/11.17 [2823]P1(a108)
% 11.41/11.17 [2824]P85(a184)
% 11.41/11.17 [2825]P2(a859)
% 11.41/11.17 [2826]P2(a1)
% 11.41/11.17 [2827]P2(a108)
% 11.41/11.17 [2828]P63(a859)
% 11.41/11.17 [2829]P63(a1)
% 11.41/11.17 [2830]P63(a108)
% 11.41/11.17 [2831]P64(a859)
% 11.41/11.17 [2832]P64(a1)
% 11.41/11.17 [2833]P64(a108)
% 11.41/11.17 [2834]P67(a859)
% 11.41/11.17 [2835]P67(a1)
% 11.41/11.17 [2836]P67(a108)
% 11.41/11.17 [2837]P68(a859)
% 11.41/11.17 [2838]P68(a1)
% 11.41/11.17 [2839]P68(a108)
% 11.41/11.17 [2840]P69(a1)
% 11.41/11.17 [2841]P86(a859)
% 11.41/11.17 [2842]P86(a1)
% 11.41/11.17 [2843]P86(a108)
% 11.41/11.17 [2844]P111(a859)
% 11.41/11.17 [2845]P111(a1)
% 11.41/11.17 [2846]P112(a859)
% 11.41/11.17 [2847]P112(a1)
% 11.41/11.17 [2848]P112(a108)
% 11.41/11.17 [2849]P74(a859)
% 11.41/11.17 [2850]P74(a1)
% 11.41/11.17 [2851]P74(a108)
% 11.41/11.17 [2852]P80(a859)
% 11.41/11.17 [2853]P80(a1)
% 11.41/11.17 [2854]P80(a108)
% 11.41/11.17 [2855]P81(a859)
% 11.41/11.17 [2856]P81(a1)
% 11.41/11.17 [2857]P81(a108)
% 11.41/11.17 [2858]P113(a1)
% 11.41/11.17 [2859]P120(a859)
% 11.41/11.17 [2860]P120(a1)
% 11.41/11.17 [2861]P120(a108)
% 11.41/11.17 [2862]P87(a859)
% 11.41/11.17 [2863]P87(a1)
% 11.41/11.17 [2864]P87(a108)
% 11.41/11.17 [2865]P100(a859)
% 11.41/11.17 [2866]P100(a852)
% 11.41/11.17 [2867]P100(a1)
% 11.41/11.17 [2868]P100(a108)
% 11.41/11.17 [2869]P101(a859)
% 11.41/11.17 [2870]P101(a1)
% 11.41/11.17 [2871]P101(a108)
% 11.41/11.17 [2872]P104(a859)
% 11.41/11.17 [2873]P104(a852)
% 11.41/11.17 [2874]P104(a1)
% 11.41/11.17 [2875]P104(a108)
% 11.41/11.17 [2876]P103(a859)
% 11.41/11.17 [2877]P103(a852)
% 11.41/11.17 [2878]P103(a1)
% 11.41/11.17 [2879]P103(a108)
% 11.41/11.17 [2880]P123(a1)
% 11.41/11.17 [2881]P135(a1)
% 11.41/11.17 [2882]P114(a1)
% 11.41/11.17 [2883]P136(a1)
% 11.41/11.17 [2884]P105(a1)
% 11.41/11.17 [2885]P88(a1)
% 11.41/11.17 [2886]P70(a1)
% 11.41/11.17 [2887]P75(a859)
% 11.41/11.17 [2888]P75(a1)
% 11.41/11.17 [2889]P75(a108)
% 11.41/11.17 [2890]P71(a859)
% 11.41/11.17 [2891]P71(a1)
% 11.41/11.17 [2892]P71(a108)
% 11.41/11.17 [2893]P76(a859)
% 11.41/11.17 [2894]P76(a1)
% 11.41/11.17 [2895]P76(a108)
% 11.41/11.17 [2896]P65(a859)
% 11.41/11.17 [2897]P65(a1)
% 11.41/11.17 [2898]P65(a108)
% 11.41/11.17 [2899]P77(a1)
% 11.41/11.17 [2900]P3(a1)
% 11.41/11.17 [2901]P124(a859)
% 11.41/11.17 [2902]P124(a1)
% 11.41/11.17 [2903]P124(a108)
% 11.41/11.17 [2904]P137(a1)
% 11.41/11.17 [2905]P129(a859)
% 11.41/11.17 [2906]P129(a1)
% 11.41/11.17 [2907]P129(a108)
% 11.41/11.17 [2908]P140(a859)
% 11.41/11.17 [2909]P140(a1)
% 11.41/11.17 [2910]P140(a108)
% 11.41/11.17 [2911]P138(a859)
% 11.41/11.17 [2912]P138(a1)
% 11.41/11.17 [2913]P138(a108)
% 11.41/11.17 [2914]P110(a859)
% 11.41/11.17 [2915]P110(a1)
% 11.41/11.17 [2916]P110(a108)
% 11.41/11.17 [2917]P121(a1)
% 11.41/11.17 [2918]P122(a1)
% 11.41/11.17 [2919]P125(a859)
% 11.41/11.17 [2920]P125(a1)
% 11.41/11.17 [2921]P125(a108)
% 11.41/11.17 [2922]P118(a859)
% 11.41/11.17 [2923]P118(a1)
% 11.41/11.17 [2924]P118(a108)
% 11.41/11.17 [2925]P82(a1)
% 11.41/11.17 [2926]P126(a1)
% 11.41/11.17 [2927]P78(a859)
% 11.41/11.17 [2928]P78(a1)
% 11.41/11.17 [2929]P78(a108)
% 11.41/11.17 [2930]P130(a859)
% 11.41/11.17 [2931]P130(a1)
% 11.41/11.17 [2932]P130(a108)
% 11.41/11.17 [2933]P131(a1)
% 11.41/11.17 [2934]P133(a859)
% 11.41/11.17 [2935]P133(a1)
% 11.41/11.17 [2936]P133(a108)
% 11.41/11.17 [2937]P132(a859)
% 11.41/11.17 [2938]P132(a1)
% 11.41/11.17 [2939]P132(a108)
% 11.41/11.17 [2940]P127(a859)
% 11.41/11.17 [2941]P127(a1)
% 11.41/11.17 [2942]P127(a108)
% 11.41/11.17 [2943]P128(a1)
% 11.41/11.17 [2944]P91(a852)
% 11.41/11.17 [2945]P4(a859)
% 11.41/11.17 [2946]P4(a1)
% 11.41/11.17 [2947]P4(a108)
% 11.41/11.17 [2948]P5(a1)
% 11.41/11.17 [2949]P84(a852)
% 11.41/11.17 [2950]P84(a1)
% 11.41/11.17 [2951]P72(a859)
% 11.41/11.17 [2952]P72(a852)
% 11.41/11.17 [2953]P72(a1)
% 11.41/11.17 [2954]P72(a108)
% 11.41/11.17 [2955]P89(a1)
% 11.41/11.17 [2956]P90(a859)
% 11.41/11.17 [2957]P90(a1)
% 11.41/11.17 [2958]P90(a108)
% 11.41/11.17 [2959]P79(a1)
% 11.41/11.17 [2960]P134(a1)
% 11.41/11.17 [2961]P66(a1)
% 11.41/11.17 [2962]P106(a859)
% 11.41/11.17 [2963]P106(a1)
% 11.41/11.17 [2964]P106(a108)
% 11.41/11.17 [2965]P139(a859)
% 11.41/11.17 [2966]P139(a1)
% 11.41/11.17 [2967]P139(a108)
% 11.41/11.17 [2968]P115(a859)
% 11.41/11.17 [2969]P115(a1)
% 11.41/11.17 [2970]P115(a108)
% 11.41/11.17 [2971]P109(a1)
% 11.41/11.17 [2972]P93(a859)
% 11.41/11.17 [2973]P93(a852)
% 11.41/11.17 [2974]P93(a1)
% 11.41/11.17 [2975]P98(a859)
% 11.41/11.17 [2976]P98(a852)
% 11.41/11.17 [2977]P98(a1)
% 11.41/11.17 [2978]P6(a852)
% 11.41/11.17 [2979]P107(a852)
% 11.41/11.17 [2980]P94(a852)
% 11.41/11.17 [2981]P58(a852)
% 11.41/11.17 [2982]P58(a862)
% 11.41/11.17 [2983]P58(a863)
% 11.41/11.17 [2984]P58(a866)
% 11.41/11.17 [2985]P102(a859)
% 11.41/11.17 [2986]P102(a852)
% 11.41/11.17 [2987]P95(a852)
% 11.41/11.17 [2988]P99(a859)
% 11.41/11.17 [2989]P99(a852)
% 11.41/11.17 [2990]P99(a1)
% 11.41/11.17 [2991]P97(a859)
% 11.41/11.17 [2992]P97(a852)
% 11.41/11.17 [2993]P97(a1)
% 11.41/11.17 [2994]P73(a859)
% 11.41/11.17 [2995]P73(a1)
% 11.41/11.17 [2996]P73(a108)
% 11.41/11.17 [2997]P108(a859)
% 11.41/11.17 [2998]P141(a1)
% 11.41/11.17 [2999]P141(a863)
% 11.41/11.17 [3000]P83(a859)
% 11.41/11.17 [3001]P83(a1)
% 11.41/11.17 [3002]P83(a108)
% 11.41/11.17 [3003]P96(a852)
% 11.41/11.17 [3016]P35(a859,a247)
% 11.41/11.17 [3017]P35(a859,a336)
% 11.41/11.17 [3018]P144(a342,a783)
% 11.41/11.17 [4376]~E(a106,a92)
% 11.41/11.17 [4377]~E(a106,a92)
% 11.41/11.17 [4378]~P85(a185)
% 11.41/11.17 [4382]~P145(a342,a785)
% 11.41/11.17 [2818]E(f2(a1),a92)
% 11.41/11.17 [2819]E(f3(a108),a4)
% 11.41/11.17 [2820]E(f109(a108),a5)
% 11.41/11.17 [3004]E(f36(a25),f2(a859))
% 11.41/11.17 [3005]E(f93(a184),f2(a859))
% 11.41/11.17 [3006]E(f93(a185),f2(a859))
% 11.41/11.17 [3007]E(f186(a859),f110(a859))
% 11.41/11.17 [3008]E(f187(a859),f2(a859))
% 11.41/11.17 [3009]E(f246(a859),f111(a859))
% 11.41/11.17 [3010]E(f112(a1),f41(a1))
% 11.41/11.17 [3011]P7(f2(a1))
% 11.41/11.17 [3012]P7(f87(a1))
% 11.41/11.17 [3059]P85(f784(a26,a25))
% 11.41/11.17 [3060]P85(f784(a26,a25))
% 11.41/11.17 [3071]P35(f868(a859,a859),a47)
% 11.41/11.17 [3100]E(f172(a855,a853,a31),a32)
% 11.41/11.17 [3412]E(f339(a859,a859,a247,a247),a47)
% 11.41/11.17 [3470]P38(f784(a29,a871),a783,f2(a859),a785)
% 11.41/11.17 [4379]~E(f87(a1),f2(a1))
% 11.41/11.17 [3013]E(f145(f120(a1)),f120(a859))
% 11.41/11.17 [3014]E(f159(f2(a859)),f2(a859))
% 11.41/11.17 [3015]E(f6(f2(a108)),f2(a859))
% 11.41/11.17 [3022]E(f784(f88(a1),a92),a92)
% 11.41/11.17 [3025]E(f784(a114,f2(a1)),f2(a859))
% 11.41/11.17 [3026]E(f784(a5,f2(a859)),f2(a108))
% 11.41/11.17 [3027]E(f784(a160,f2(a859)),f87(a859))
% 11.41/11.17 [3028]E(f784(a114,f87(a1)),f87(a859))
% 11.41/11.17 [3029]E(f784(a5,f87(a859)),f87(a108))
% 11.41/11.17 [3030]E(f784(f113(a859),a92),f2(a859))
% 11.41/11.17 [3031]E(f784(f113(a1),a92),f2(a1))
% 11.41/11.17 [3032]E(f784(f113(a108),a92),f2(a108))
% 11.41/11.17 [3033]E(f784(a114,f2(a1)),f2(a859))
% 11.41/11.17 [3034]E(f784(f188(a853),a25),f2(a859))
% 11.41/11.17 [3035]E(f784(f188(a852),a184),f2(a859))
% 11.41/11.17 [3036]E(f784(f188(a852),a185),f2(a859))
% 11.41/11.17 [3037]E(f784(f113(a859),a92),f2(a859))
% 11.41/11.17 [3045]E(f784(f88(a1),f87(a1)),a106)
% 11.41/11.17 [3050]E(f784(f109(a1),f2(a859)),f2(a1))
% 11.41/11.17 [3051]E(f784(f109(a1),f87(a859)),f87(a1))
% 11.41/11.17 [3052]E(f784(f188(a859),f2(a859)),f2(a859))
% 11.41/11.17 [3053]E(f784(f188(a108),f2(a108)),f2(a859))
% 11.41/11.17 [3054]E(f784(f109(a1),f2(a859)),f2(a1))
% 11.41/11.17 [3055]E(f784(f109(a1),f87(a859)),f87(a1))
% 11.41/11.17 [3056]E(f784(f88(a1),f2(a1)),f2(a1))
% 11.41/11.17 [3067]E(f784(a114,f87(a1)),f784(a160,f2(a859)))
% 11.41/11.17 [3069]E(f337(f868(a859,a859),a47),a48)
% 11.41/11.17 [3070]E(f338(f868(a859,a859),a47),a49)
% 11.41/11.17 [3091]E(f784(f267(a859),f2(a859)),f187(f869(a859,a852)))
% 11.41/11.17 [3092]E(f784(f268(a859),f2(a859)),f249(f869(a859,a852)))
% 11.41/11.17 [3102]P37(f187(f869(a1,a852)))
% 11.41/11.17 [3137]E(f784(f784(f3(a108),f2(a108)),f87(a108)),f2(a108))
% 11.41/11.17 [3207]P85(f784(f784(f243(a1),a106),f2(a1)))
% 11.41/11.17 [3232]P85(f784(f784(f243(a1),f2(a1)),f87(a1)))
% 11.41/11.17 [3233]P85(f784(f784(f242(a1),f2(a1)),f2(a1)))
% 11.41/11.17 [3234]P85(f784(f784(f242(a1),f2(a1)),f87(a1)))
% 11.41/11.17 [3403]P85(f784(f71(a855),f175(a855,a853,a32)))
% 11.41/11.17 [3445]E(f784(f784(f291(a859,a859,a859),a336),f310(a859,a336)),a247)
% 11.41/11.17 [3487]P39(a1,a859,a114,f784(f242(a1),f2(a1)))
% 11.41/11.17 [3490]E(f784(f784(f54(a859,f869(a859,a852)),f249(f869(a859,a852))),f267(a859)),f249(f869(a859,a852)))
% 11.41/11.17 [3491]E(f784(f784(f54(a859,f869(a859,a852)),f249(f869(a859,a852))),f303(a859)),f249(f869(a859,a852)))
% 11.41/11.17 [3492]E(f784(f784(f54(a859,f869(a859,a852)),f249(f869(a859,a852))),f268(a859)),f249(f869(a859,a852)))
% 11.41/11.17 [3493]E(f784(f784(f55(a859,f869(a859,a852)),f249(f869(a859,a852))),f306(a859)),f187(f869(a859,a852)))
% 11.41/11.17 [3509]P26(a859,a1,f109(a1),f249(f869(a859,a852)))
% 11.41/11.17 [3522]P39(a859,a1,f109(a1),f784(f18(a852,a859),a184))
% 11.41/11.17 [3652]E(f784(f82(a859,a108,a1,a5),a114),f113(a108))
% 11.41/11.17 [3870]P54(a108,a859,a22,a5,f249(f869(a859,a852)))
% 11.41/11.17 [3878]P54(a1,f869(f868(a859,a859),a852),a116,a98,a107)
% 11.41/11.17 [4142]E(f262(a1,a1,a1,a1,f41(a1),f88(a1)),a66)
% 11.41/11.17 [4413]~E(f784(f113(a1),a106),f784(f113(a1),a92))
% 11.41/11.17 [4414]~P85(f784(a193,f2(a1)))
% 11.41/11.17 [4415]~P85(f784(a193,f87(a1)))
% 11.41/11.17 [4471]~P85(f784(f784(f243(a1),a92),f2(a1)))
% 11.41/11.17 [3083]E(f784(f784(f89(a1),a92),a106),a106)
% 11.41/11.17 [3084]E(f784(f784(f89(a1),a92),a92),a92)
% 11.41/11.17 [3085]E(f784(f784(f3(a1),a106),a106),a92)
% 11.41/11.17 [3099]E(f784(f109(a1),f784(a160,f2(a859))),f87(a1))
% 11.41/11.17 [3160]E(f784(f50(a863),f249(f869(a863,a852))),f87(a859))
% 11.41/11.17 [3181]P85(f784(a193,f784(f113(a1),a106)))
% 11.41/11.17 [3182]P85(f784(f784(f243(a1),a106),a92))
% 11.41/11.17 [3183]P85(f784(f784(f242(a1),a106),a106))
% 11.41/11.17 [3184]P85(f784(f784(f242(a1),a106),a92))
% 11.41/11.17 [3185]P85(f784(f784(f242(a1),a92),a92))
% 11.41/11.17 [3243]E(f784(f784(f312(a859),f2(a859)),f187(f869(a859,a852))),f784(f303(a859),f2(a859)))
% 11.41/11.17 [3299]P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),a92)))
% 11.41/11.17 [3312]E(f784(f313(a859,a859,a160),f249(f869(a859,a852))),f784(f306(a859),f2(a859)))
% 11.41/11.17 [3317]E(f784(f313(a1,a859,a114),f187(f869(a1,a852))),f187(f869(a859,a852)))
% 11.41/11.17 [3326]E(f784(f313(a859,a1,f109(a1)),f187(f869(a859,a852))),f187(f869(a1,a852)))
% 11.41/11.17 [3350]P9(f868(a859,a859),f249(f869(f868(a859,a859),a852)),a118)
% 11.41/11.17 [3659]E(f784(f82(a859,a1,a108,f109(a1)),a22),a23)
% 11.41/11.17 [3719]P35(a859,f784(f266(f868(a859,a859)),f784(f261(a859,a859,a852),f243(a859))))
% 11.41/11.17 [4462]~P85(f784(a193,f784(f113(a1),a92)))
% 11.41/11.17 [4463]~P85(f784(f784(f243(a1),a106),a106))
% 11.41/11.17 [4464]~P85(f784(f784(f243(a1),a92),a106))
% 11.41/11.17 [4465]~P85(f784(f784(f243(a1),a92),a92))
% 11.41/11.17 [4466]~P85(f784(f784(f242(a1),a92),a106))
% 11.41/11.17 [4481]~P85(f784(f71(a859),f249(f869(a859,a852))))
% 11.41/11.17 [4482]~P85(f784(f71(a1),f249(f869(a1,a852))))
% 11.41/11.17 [4307]E(f784(f261(a1,a1,a852),f784(f784(f10(f869(a1,a852),f869(a1,a852),a1),f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f243(a1),f2(a1))))),f784(f784(f9(a1,a1,f869(a1,a852)),f784(f784(f10(f869(a1,f869(a1,a852)),f869(a1,f869(a1,a852)),a1),f9(a1,a1,a852)),f784(f784(f10(f869(a1,a1),f869(a1,f869(a1,a852)),a1),f784(f10(a1,f869(a1,a852),a1),a343)),a222))),f87(a1)))),a218)
% 11.41/11.17 [3353]E(f784(f784(f3(a1),f784(f784(f89(a1),a106),a106)),a106),a106)
% 11.41/11.17 [3385]E(f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106),f784(f88(a1),a106))
% 11.41/11.17 [3427]E(f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106),f784(f784(f3(a1),a92),a106))
% 11.41/11.17 [3584]E(f784(f784(f69(f868(a859,a859)),f249(f869(f868(a859,a859),a852))),a118),a107)
% 11.41/11.17 [3923]E(f784(f313(f868(a866,a866),a862,f784(f261(a866,a866,a862),a314)),f784(f784(f258(a866,a866),f249(f869(a866,a852))),f784(f18(f869(a866,a852),a866),f249(f869(a866,a852))))),f249(f869(a862,a852)))
% 11.41/11.17 [3613]E(f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f87(a859))
% 11.41/11.17 [3614]E(f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f87(a1))
% 11.41/11.17 [3615]E(f784(f113(a108),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f87(a108))
% 11.41/11.17 [3616]E(f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f87(a859))
% 11.41/11.17 [3619]E(f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(a160,f2(a859)))
% 11.41/11.17 [4004]E(f784(f784(f110(f869(f868(f868(a859,a859),f868(a859,a859)),a852)),a47),f310(f868(a859,a859),f187(f869(f868(f868(a859,a859),f868(a859,a859)),a852)))),a79)
% 11.41/11.17 [4075]E(f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),f2(a859)),f2(a859))),f187(f869(f868(a859,a859),a852))))),f2(a1))
% 11.41/11.17 [4076]E(f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),f87(a859)),f2(a859))),f187(f869(f868(a859,a859),a852))))),f87(a1))
% 11.41/11.17 [4090]E(f784(f266(f868(a859,a859)),f784(f261(a859,a859,a852),f784(f784(f10(a859,f869(a859,a852),a859),f784(f9(a859,a859,a852),a343)),a160))),a336)
% 11.41/11.17 [4058]E(f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),f784(a160,f784(a160,f2(a859))))
% 11.41/11.17 [4059]E(f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),f784(a160,f784(a160,f2(a859))))
% 11.41/11.17 [4062]E(f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),f784(f784(f89(a859),f87(a859)),f87(a859)))
% 11.41/11.17 [4063]E(f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),f784(f50(a852),f249(f869(a852,a852))))
% 11.41/11.17 [4128]P7(f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))
% 11.41/11.17 [4201]P27(f869(f868(a859,a859),a852),f784(f784(f251(f869(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),a852),f869(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),a852)),a48),a80))
% 11.41/11.17 [4202]P27(f869(f868(a859,a859),a852),f784(f784(f251(f869(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),a852),f869(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),a852)),a49),a78))
% 11.41/11.17 [4239]E(f784(f784(f110(f869(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),a852)),f338(f868(a859,a859),a79)),f784(f784(f312(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),f187(f869(f868(a859,a859),a852))),f187(f869(f868(a859,a859),a852)))),f187(f869(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),a852)))),a78)
% 11.41/11.17 [4240]E(f784(f784(f110(f869(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),a852)),f337(f868(a859,a859),a79)),f784(f784(f312(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),f187(f869(f868(a859,a859),a852))),f187(f869(f868(a859,a859),a852)))),f187(f869(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),a852)))),a80)
% 11.41/11.17 [4130]E(f784(a114,f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(a160,f784(a160,f2(a859))))
% 11.41/11.17 [4177]E(f784(a114,f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))
% 11.41/11.17 [4178]E(f784(f109(a1),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))
% 11.41/11.17 [4211]P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.17 [4212]E(f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106)),f784(a160,f784(a160,f784(a160,f2(a859)))))
% 11.41/11.17 [4252]P7(f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106)))
% 11.41/11.17 [4278]E(f784(a114,f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106)))
% 11.41/11.17 [4279]E(f784(f109(a1),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106)))
% 11.41/11.17 [4293]P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))))
% 11.41/11.17 [3019]P8(x30191,a343)
% 11.41/11.17 [3413]P26(a859,a859,a160,x34131)
% 11.41/11.17 [3038]P35(a1,f115(x30381))
% 11.41/11.17 [3039]P35(a1,f117(x30391))
% 11.41/11.17 [3044]P36(x30441,f190(x30441))
% 11.41/11.17 [3088]P35(f869(x30881,a852),f309(x30881))
% 11.41/11.17 [3128]E(f60(a1,x31281,x31281),f2(a1))
% 11.41/11.17 [3178]P16(x31781,f869(x31781,a852),f312(x31781))
% 11.41/11.17 [4383]~E(f784(a29,x43831),a25)
% 11.41/11.17 [4384]~E(f784(a29,x43841),a25)
% 11.41/11.17 [4385]~E(f784(a160,x43851),x43851)
% 11.41/11.17 [4386]~E(f784(a160,x43861),x43861)
% 11.41/11.17 [4393]~E(f784(a160,x43931),f2(a859))
% 11.41/11.17 [4394]~E(f784(a160,x43941),f2(a859))
% 11.41/11.17 [4395]~E(f784(a160,x43951),f2(a859))
% 11.41/11.17 [4396]~E(f784(a160,x43961),f2(a859))
% 11.41/11.17 [4397]~E(f784(a160,x43971),f2(a859))
% 11.41/11.17 [4398]~E(f784(a160,x43981),f2(a859))
% 11.41/11.17 [3020]E(f44(f42(x30201)),f2(a859))
% 11.41/11.17 [3021]E(f44(f43(x30211)),f2(a859))
% 11.41/11.17 [3023]E(f784(f188(a859),x30231),x30231)
% 11.41/11.17 [3024]E(f784(f113(a1),x30241),x30241)
% 11.41/11.17 [3040]E(f784(a98,f346(x30401)),x30401)
% 11.41/11.17 [3041]E(f248(x30411,f2(a108)),f2(a108))
% 11.41/11.17 [3042]E(f784(f188(a867),x30421),f2(a859))
% 11.41/11.17 [3043]E(f784(f188(a862),x30431),f2(a859))
% 11.41/11.17 [3057]E(f121(x30571,f120(x30571)),f120(x30571))
% 11.41/11.17 [3061]E(f784(f188(a854),f42(x30611)),f2(a859))
% 11.41/11.17 [3062]E(f784(f188(a854),f43(x30621)),f2(a859))
% 11.41/11.17 [3063]E(f36(f784(a29,x30631)),f2(a859))
% 11.41/11.17 [3064]E(f784(f161(x30641),f120(x30641)),f120(x30641))
% 11.41/11.17 [3065]E(f784(f163(x30651),f120(x30651)),f120(x30651))
% 11.41/11.17 [3066]E(f784(f162(x30661),f120(x30661)),f120(x30661))
% 11.41/11.17 [3072]E(f784(f113(a1),x30721),f784(f112(a1),x30721))
% 11.41/11.17 [3073]E(f784(a5,f784(a22,x30731)),x30731)
% 11.41/11.17 [3074]E(f784(a5,f784(a22,x30741)),x30741)
% 11.41/11.17 [3075]E(f784(a22,f784(a5,x30751)),x30751)
% 11.41/11.17 [3076]E(f784(a98,f784(a116,x30761)),x30761)
% 11.41/11.17 [3077]P7(f784(f109(a1),x30771))
% 11.41/11.17 [3081]E(f784(f188(f864(x30811)),f190(x30811)),f2(a859))
% 11.41/11.17 [3082]E(f784(f188(f860(x30821)),f120(x30821)),f2(a859))
% 11.41/11.17 [3087]E(f784(f188(a853),f784(a29,x30871)),f2(a859))
% 11.41/11.17 [3097]E(f236(x30971,f190(x30971)),f187(f869(x30971,a852)))
% 11.41/11.17 [3105]E(f784(f784(f89(a859),x31051),f2(a859)),x31051)
% 11.41/11.17 [3106]E(f784(f784(f89(a1),x31061),f2(a1)),x31061)
% 11.41/11.17 [3107]E(f784(f784(f90(a859),x31071),f87(a859)),x31071)
% 11.41/11.17 [3108]E(f784(f784(f90(a1),x31081),f87(a1)),x31081)
% 11.41/11.17 [3109]E(f784(f784(f3(a859),x31091),f2(a859)),x31091)
% 11.41/11.17 [3110]E(f784(f784(f186(a859),x31101),f2(a859)),x31101)
% 11.41/11.17 [3111]E(f784(f784(f90(a859),x31111),f2(a859)),f2(a859))
% 11.41/11.17 [3112]E(f784(f784(f51(a1),x31121),f2(a1)),f2(a1))
% 11.41/11.17 [3113]E(f784(f784(f246(a859),x31131),f2(a859)),f2(a859))
% 11.41/11.17 [3119]E(f784(f164(x31191),f120(x31191)),f187(f869(x31191,a852)))
% 11.41/11.17 [3123]P85(f784(f132(x31231),f120(x31231)))
% 11.41/11.17 [3129]E(f784(f146(x31291,x31291),f7(x31291)),f41(f860(x31291)))
% 11.41/11.17 [3130]E(f784(f146(x31301,x31301),f41(x31301)),f41(f860(x31301)))
% 11.41/11.17 [3131]E(f784(f206(x31311,x31311),f7(x31311)),f41(f864(x31311)))
% 11.41/11.17 [3132]E(f784(f206(x31321,x31321),f41(x31321)),f41(f864(x31321)))
% 11.41/11.17 [3133]E(f60(a1,x31331,f2(a1)),x31331)
% 11.41/11.17 [3134]E(f784(f242(a859),f784(a160,x31341)),f784(f243(a859),x31341))
% 11.41/11.17 [3135]E(f784(f267(a859),f784(a160,x31351)),f784(f303(a859),x31351))
% 11.41/11.17 [3136]E(f784(f268(a859),f784(a160,x31361)),f784(f306(a859),x31361))
% 11.41/11.17 [3138]E(f60(a1,f2(a1),x31381),f2(a1))
% 11.41/11.17 [3145]E(f784(f784(f89(a859),x31451),f87(a859)),f784(a160,x31451))
% 11.41/11.17 [3155]E(f784(f304(a859,x31551),f2(a859)),f187(f869(a859,a852)))
% 11.41/11.17 [3165]E(f305(a859,f2(a859),x31651),f784(f303(a859),x31651))
% 11.41/11.17 [3210]E(f784(f784(f3(a859),f784(a160,x32101)),f87(a859)),x32101)
% 11.41/11.17 [3223]E(f62(f2(a1),x32231),f784(f784(f251(a1,a1),f2(a1)),f2(a1)))
% 11.41/11.17 [3227]E(f784(f784(f89(a859),f784(a22,x32271)),f2(a859)),f784(a22,x32271))
% 11.41/11.17 [3273]P85(f784(f784(f243(a859),x32731),f784(a160,x32731)))
% 11.41/11.17 [3287]P85(f784(f784(f243(a859),f2(a859)),f784(a160,x32871)))
% 11.41/11.17 [3297]E(f784(f784(f180(f860(x32971),f860(x32971)),f2(a859)),f161(x32971)),f41(f860(x32971)))
% 11.41/11.17 [3572]E(f784(f784(f3(a108),f784(a5,f784(a160,f784(a22,x35721)))),f87(a108)),x35721)
% 11.41/11.17 [3641]P85(f784(f784(f242(a1),f784(f88(a1),f784(f109(a1),x36411))),f2(a1)))
% 11.41/11.17 [3792]P85(f784(f784(f243(a1),f784(f88(a1),f784(f109(a1),f784(a160,x37921)))),f2(a1)))
% 11.41/11.17 [4421]~E(f249(f869(x44211,a852)),f187(f869(x44211,a852)))
% 11.41/11.17 [4472]~P85(f784(f784(f243(a859),x44721),f2(a859)))
% 11.41/11.17 [4473]~P85(f784(f784(f243(a859),x44731),f2(a859)))
% 11.41/11.17 [4474]~P85(f784(f784(f243(a859),x44741),f2(a859)))
% 11.41/11.17 [4490]~P85(f784(f784(f243(a1),f784(f109(a1),x44901)),f2(a1)))
% 11.41/11.17 [3086]E(f170(x30861,f120(f860(x30861))),f120(f860(x30861)))
% 11.41/11.17 [3089]E(f784(f784(f90(a1),a92),x30891),a92)
% 11.41/11.17 [3090]E(f784(f784(f89(a1),a92),x30901),x30901)
% 11.41/11.17 [3093]E(f784(a114,f784(f109(a1),x30931)),x30931)
% 11.41/11.17 [3094]E(f784(f784(f89(a1),x30941),a92),x30941)
% 11.41/11.17 [3095]E(f784(f784(f3(a1),x30951),a92),x30951)
% 11.41/11.17 [3098]E(f784(f784(f3(a859),x30981),x30981),f2(a859))
% 11.41/11.17 [3103]E(f784(f88(a1),f784(f88(a1),x31031)),x31031)
% 11.41/11.17 [3104]E(f784(f50(a859),f784(f267(a859),x31041)),x31041)
% 11.41/11.17 [3114]E(f784(f784(f89(a859),f2(a859)),x31141),x31141)
% 11.41/11.17 [3115]E(f784(f784(f89(a1),f2(a1)),x31151),x31151)
% 11.41/11.17 [3116]E(f784(f784(f90(a859),f87(a859)),x31161),x31161)
% 11.41/11.17 [3117]E(f784(f784(f90(a1),f87(a1)),x31171),x31171)
% 11.41/11.17 [3118]E(f784(f784(f186(a859),f2(a859)),x31181),x31181)
% 11.41/11.17 [3124]E(f784(f784(f90(a859),f2(a859)),x31241),f2(a859))
% 11.41/11.17 [3125]E(f784(f784(f51(a1),f2(a1)),x31251),f2(a1))
% 11.41/11.17 [3126]E(f784(f784(f3(a859),f2(a859)),x31261),f2(a859))
% 11.41/11.17 [3127]E(f784(f784(f246(a859),f2(a859)),x31271),f2(a859))
% 11.41/11.17 [3143]E(f784(f304(a859,f2(a859)),x31431),f784(f267(a859),x31431))
% 11.41/11.17 [3144]E(f784(f784(f90(a1),a106),x31441),f784(f88(a1),x31441))
% 11.41/11.17 [3146]E(f784(a114,f784(f113(a1),x31461)),f784(f113(a859),x31461))
% 11.41/11.17 [3147]E(f784(a114,f784(f113(a1),x31471)),f784(f113(a859),x31471))
% 11.41/11.17 [3148]E(f784(a22,f784(f113(a108),x31481)),f784(f113(a859),x31481))
% 11.41/11.17 [3149]E(f784(f50(a859),f784(f303(a859),x31491)),f784(a160,x31491))
% 11.41/11.17 [3158]E(f784(f784(f89(a859),f87(a859)),x31581),f784(a160,x31581))
% 11.41/11.17 [3161]E(f784(f112(a1),f784(f109(a1),x31611)),f784(f109(a1),x31611))
% 11.41/11.17 [3162]E(f784(f84(a1),f784(f109(a1),x31621)),f784(f109(a1),x31621))
% 11.41/11.17 [3167]E(f784(f50(x31671),f187(f869(x31671,a852))),f2(a859))
% 11.41/11.17 [3169]E(f784(f784(f51(a859),x31691),f784(a160,f2(a859))),x31691)
% 11.41/11.17 [3179]E(f60(a859,x31791,f784(a160,f2(a859))),f2(a859))
% 11.41/11.17 [3180]E(f60(a1,x31801,f784(f113(a1),a106)),f2(a1))
% 11.41/11.17 [3187]E(f784(f784(f89(a1),a106),x31871),f784(f784(f89(a1),x31871),a106))
% 11.41/11.17 [3195]E(f784(f784(f51(a1),x31951),f784(f113(a1),a106)),f784(f88(a1),x31951))
% 11.41/11.17 [3199]E(f134(a859,f784(f304(a859,x31991),f2(a859))),f120(a859))
% 11.41/11.17 [3200]E(f784(f784(f3(a1),x32001),f87(a1)),f784(f784(f89(a1),x32001),a106))
% 11.41/11.17 [3201]E(f784(f784(f89(a1),x32011),f87(a1)),f784(f784(f3(a1),x32011),a106))
% 11.41/11.17 [3202]P85(f784(f784(f194(a25),x32021),x32021))
% 11.41/11.17 [3203]P85(f784(f784(f194(a25),x32031),x32031))
% 11.41/11.17 [3204]P85(f784(f784(f242(a859),x32041),x32041))
% 11.41/11.17 [3205]P85(f784(f784(f242(a1),x32051),x32051))
% 11.41/11.17 [3206]P85(f784(f784(f289(a859),x32061),x32061))
% 11.41/11.17 [3211]E(f784(f88(a1),f784(f113(a1),x32111)),f784(f113(a1),f784(f88(a1),x32111)))
% 11.41/11.17 [3212]P85(f784(f71(a859),f784(f267(a859),x32121)))
% 11.41/11.17 [3213]P85(f784(f71(a859),f784(f303(a859),x32131)))
% 11.41/11.17 [3221]E(f152(x32211,f249(f869(x32211,a852))),f249(f869(f860(x32211),a852)))
% 11.41/11.17 [3225]P85(f784(f784(f242(a859),f2(a859)),x32251))
% 11.41/11.17 [3226]P85(f784(f784(f242(a859),f2(a859)),x32261))
% 11.41/11.17 [3237]E(f784(f784(f89(a859),f159(x32371)),f784(a160,f2(a859))),f159(f784(a160,x32371)))
% 11.41/11.17 [3238]E(f784(f266(x32381),f784(f18(a852,x32381),a184)),f249(f869(x32381,a852)))
% 11.41/11.17 [3239]E(f784(f266(x32391),f784(f18(a852,x32391),a185)),f187(f869(x32391,a852)))
% 11.41/11.17 [3242]E(f784(f784(f312(a859),x32421),f784(f267(a859),x32421)),f784(f267(a859),f784(a160,x32421)))
% 11.41/11.17 [3253]E(f784(f784(f89(a1),f87(a1)),f784(f109(a1),x32531)),f784(f109(a1),f784(a160,x32531)))
% 11.41/11.17 [3276]E(f187(f869(f868(x32761,x32761),a852)),f270(x32761,f187(f869(x32761,a852))))
% 11.41/11.17 [3277]E(f784(f311(x32771),f249(f869(x32771,a852))),f249(f869(f869(x32771,a852),a852)))
% 11.41/11.17 [3278]E(f784(f88(f869(x32781,a852)),f249(f869(x32781,a852))),f187(f869(x32781,a852)))
% 11.41/11.17 [3279]E(f784(f88(f869(x32791,a852)),f187(f869(x32791,a852))),f249(f869(x32791,a852)))
% 11.41/11.17 [3280]P85(f784(f71(x32801),f187(f869(x32801,a852))))
% 11.41/11.17 [3281]P85(f784(f71(x32811),f187(f869(x32811,a852))))
% 11.41/11.17 [3283]E(f784(f304(a859,x32831),f784(a160,x32831)),f784(f784(f312(a859),x32831),f187(f869(a859,a852))))
% 11.41/11.17 [3284]E(f94(f868(a859,a859),f63(x32841,f2(a859))),f784(f784(f251(a859,a859),f2(a859)),x32841))
% 11.41/11.17 [3298]E(f784(f784(f312(a859),f784(a160,x32981)),f784(f303(a859),x32981)),f784(f303(a859),f784(a160,x32981)))
% 11.41/11.17 [3303]P35(x33031,f187(f869(f868(x33031,x33031),a852)))
% 11.41/11.17 [3305]P85(f784(f784(f242(a1),f2(a1)),f784(f109(a1),x33051)))
% 11.41/11.17 [3306]P85(f784(f784(f242(a1),f2(a1)),f784(f109(a1),x33061)))
% 11.41/11.17 [3314]E(f784(f784(f89(a859),f784(f188(a859),x33141)),f784(a160,f2(a859))),f784(f188(a859),f784(a160,x33141)))
% 11.41/11.17 [3365]E(f784(f313(x33651,x33651,f41(x33651)),f249(f869(x33651,a852))),f249(f869(x33651,a852)))
% 11.41/11.17 [3420]P37(f784(f313(a859,a1,f109(a1)),x34201))
% 11.41/11.17 [3460]P46(x34601,f187(f869(x34601,a852)),f187(f869(f868(x34601,x34601),a852)))
% 11.41/11.17 [3484]E(f784(f784(f251(a1,a1),f784(f113(a1),a106)),f784(f784(f3(a1),x34841),f87(a1))),f65(f784(f113(a1),a106),x34841))
% 11.41/11.17 [3485]P85(f784(f784(f347(a859),f784(a22,x34851)),f249(f869(a859,a852))))
% 11.41/11.17 [3534]P57(x35341,f784(f18(f869(x35341,a852),x35341),f784(f18(a852,x35341),a185)))
% 11.41/11.17 [3543]E(f292(a859,f289(a859),x35431,x35431),f784(f784(f312(a859),x35431),f187(f869(a859,a852))))
% 11.41/11.17 [3713]E(f784(f136(f860(x37131),f860(x37131),f130(x37131),f120(x37131)),f120(f860(x37131))),f120(x37131))
% 11.41/11.17 [3733]P85(f784(f784(f347(f869(f868(a859,a859),a852)),f346(x37331)),a107))
% 11.41/11.17 [3756]P85(f784(f784(f347(f869(f868(a859,a859),a852)),f784(a116,x37561)),a107))
% 11.41/11.17 [3888]P26(x38881,f869(x38881,a852),f784(f784(f9(x38881,f869(x38881,a852),f869(x38881,a852)),f312(x38881)),f187(f869(x38881,a852))),f249(f869(x38881,a852)))
% 11.41/11.17 [4416]~E(f784(f784(f89(a1),x44161),x44161),a106)
% 11.41/11.17 [4417]~E(f784(f784(f89(a1),x44171),x44171),a106)
% 11.41/11.17 [4460]~E(f784(a5,f784(a160,f784(a22,x44601))),f2(a108))
% 11.41/11.17 [4461]~E(f784(a5,f784(a160,f784(a22,x44611))),f2(a108))
% 11.41/11.17 [4467]~P85(f784(a193,f784(f109(a1),x44671)))
% 11.41/11.17 [4469]~P85(f784(f784(f243(a859),x44691),x44691))
% 11.41/11.17 [4470]~P85(f784(f784(f243(a859),x44701),x44701))
% 11.41/11.17 [4483]~P85(f784(f784(f242(a859),f784(a160,x44831)),x44831))
% 11.41/11.17 [3228]E(f784(a114,f784(f88(a1),f784(f109(a1),x32281))),f2(a859))
% 11.41/11.17 [3231]E(f784(f784(f89(a1),f784(f88(a1),x32311)),x32311),f2(a1))
% 11.41/11.17 [3236]E(f784(f50(a1),f784(f304(a1,f2(a1)),x32361)),f784(a114,x32361))
% 11.41/11.17 [3246]E(f784(f784(f252(a859),f784(a160,f2(a859))),x32461),f784(a160,f2(a859)))
% 11.41/11.17 [3347]E(f784(f286(x33471),f187(f869(f868(x33471,x33471),a852))),f187(f869(x33471,a852)))
% 11.41/11.17 [3349]P85(f784(f71(a1),f784(f304(a1,f2(a1)),x33491)))
% 11.41/11.17 [3355]E(f53(f869(x33551,a852),f249(f869(f869(x33551,a852),a852))),f187(f869(x33551,a852)))
% 11.41/11.17 [3356]E(f53(f869(x33561,a852),f187(f869(f869(x33561,a852),a852))),f249(f869(x33561,a852)))
% 11.41/11.17 [3357]E(f52(f869(x33571,a852),f249(f869(f869(x33571,a852),a852))),f249(f869(x33571,a852)))
% 11.41/11.17 [3358]E(f52(f869(x33581,a852),f187(f869(f869(x33581,a852),a852))),f187(f869(x33581,a852)))
% 11.41/11.17 [3363]P85(f784(f784(f289(a859),f784(a160,f2(a859))),x33631))
% 11.41/11.17 [3401]E(f784(f784(f312(f860(x34011)),f120(x34011)),f187(f869(f860(x34011),a852))),f153(x34011,f120(f869(x34011,a852))))
% 11.41/11.17 [3402]E(f784(f784(f312(f860(x34021)),f120(x34021)),f187(f869(f860(x34021),a852))),f152(x34021,f187(f869(x34021,a852))))
% 11.41/11.17 [3433]E(f784(f784(f89(a1),f784(f88(a1),x34331)),f784(f88(a1),x34331)),f784(f88(a1),f784(f784(f89(a1),x34331),x34331)))
% 11.41/11.17 [3444]E(f784(f784(f89(a859),f6(x34441)),f784(a160,f2(a859))),f6(f784(a5,f784(a160,f784(a22,x34441)))))
% 11.41/11.17 [3476]E(f784(f50(a1),f784(f313(a859,a1,f109(a1)),x34761)),f784(f50(a859),x34761))
% 11.41/11.17 [3479]P85(f784(f784(f242(a859),x34791),f784(f784(f90(a859),x34791),x34791)))
% 11.41/11.17 [3515]E(f784(f313(a1,a859,a114),f305(a1,f2(a1),f784(f109(a1),x35151))),f784(f303(a859),x35151))
% 11.41/11.17 [3529]E(f784(f784(f51(a859),f784(a160,f2(a859))),f784(f113(a859),x35291)),f784(a114,f784(f784(f51(a1),f87(a1)),f784(f113(a1),x35291))))
% 11.41/11.17 [3531]E(f784(f164(a859),f134(a859,f784(f304(a859,f2(a859)),f784(a160,x35311)))),f784(f303(a859),x35311))
% 11.41/11.17 [3532]E(f784(f784(f89(a859),f784(f188(a108),x35321)),f784(a160,f2(a859))),f784(f188(a108),f784(a5,f784(a160,f784(a22,x35321)))))
% 11.41/11.17 [3548]E(f784(f313(a1,a859,a114),f784(f313(a859,a1,f109(a1)),x35481)),x35481)
% 11.41/11.17 [3577]E(f784(f784(f312(a859),f2(a859)),f784(f313(a859,a859,a160),f784(f267(a859),x35771))),f784(f267(a859),f784(a160,x35771)))
% 11.41/11.17 [3583]P52(x35831,x35831,f310(x35831,f187(f869(f868(x35831,x35831),a852))))
% 11.41/11.17 [3589]P85(f784(a193,f784(f88(a1),f784(f109(a1),f784(a160,x35891)))))
% 11.41/11.17 [3600]E(f784(f784(f3(f869(a859,a852)),f784(f268(a859),x36001)),f784(f784(f312(a859),x36001),f187(f869(a859,a852)))),f784(f268(a859),f784(a160,x36001)))
% 11.41/11.17 [3617]E(f784(f784(f89(a1),f784(f784(f3(a1),a92),x36171)),f784(f784(f3(a1),a92),x36171)),f784(f784(f3(a1),a92),f784(f784(f89(a1),x36171),x36171)))
% 11.41/11.17 [3620]P46(x36201,f249(f869(x36201,a852)),f310(x36201,f187(f869(f868(x36201,x36201),a852))))
% 11.41/11.17 [3631]E(f784(f784(f312(f869(x36311,a852)),f187(f869(x36311,a852))),f187(f869(f869(x36311,a852),a852))),f784(f311(x36311),f187(f869(x36311,a852))))
% 11.41/11.17 [3660]E(f784(f784(f3(f869(a859,a852)),f784(f306(a859),x36601)),f784(f784(f312(a859),f784(a160,x36601)),f187(f869(a859,a852)))),f784(f306(a859),f784(a160,x36601)))
% 11.41/11.17 [3669]E(f784(f784(f312(f864(x36691)),f190(x36691)),f784(f313(x36691,f864(x36691),f237(x36691)),f249(f869(x36691,a852)))),f249(f869(f864(x36691),a852)))
% 11.41/11.17 [3768]E(f784(f113(a859),f784(f784(f89(a1),x37681),x37681)),f784(f784(f95(a859,a859),f784(f113(a859),x37681)),f784(f784(f20(a859,a859,a859),f89(a859)),f7(a859))))
% 11.41/11.17 [4153]P16(x41531,f869(x41531,a852),f784(f784(f10(f869(x41531,a852),f869(f869(x41531,a852),f869(x41531,a852)),x41531),f784(f9(f869(x41531,a852),f869(x41531,a852),f869(x41531,a852)),f3(f869(x41531,a852)))),f784(f784(f9(x41531,f869(x41531,a852),f869(x41531,a852)),f312(x41531)),f187(f869(x41531,a852)))))
% 11.41/11.17 [4238]E(f784(f266(f868(a1,a1)),f784(f261(a1,a1,a852),f784(f784(f10(f869(a1,a852),f869(a1,a852),a1),f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),x42381)))),f243(a1)))),f117(x42381))
% 11.41/11.17 [4270]E(f784(f266(f868(a1,a1)),f784(f261(a1,a1,a852),f784(f784(f20(a1,f869(a1,a852),f869(a1,a852)),f784(f784(f10(f869(a852,a852),f869(f869(a1,a852),f869(a1,a852)),a1),f10(a852,a852,a1)),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),x42701)))),f243(a1)))),f115(x42701))
% 11.41/11.17 [4322]E(f784(f266(f868(f869(x43221,a852),f869(x43221,a852))),f784(f261(f869(x43221,a852),f869(x43221,a852),a852),f784(f784(f9(f869(x43221,a852),f869(f869(x43221,a852),a852),f869(f869(x43221,a852),a852)),f784(f784(f10(f869(f869(x43221,a852),f869(a852,a852)),f869(f869(f869(x43221,a852),a852),f869(f869(x43221,a852),a852)),f869(x43221,a852)),f20(f869(x43221,a852),a852,a852)),f784(f784(f10(f869(f869(x43221,a852),a852),f869(f869(x43221,a852),f869(a852,a852)),f869(x43221,a852)),f784(f10(a852,f869(a852,a852),f869(x43221,a852)),a344)),f243(f869(x43221,a852))))),f71(x43221)))),f309(x43221))
% 11.41/11.17 [4487]~P85(f784(f71(f860(x44871)),f249(f869(f860(x44871),a852))))
% 11.41/11.17 [4500]~P85(f784(f784(f242(a1),f2(a1)),f784(f88(a1),f784(f109(a1),f784(a160,x45001)))))
% 11.41/11.17 [3379]E(f784(f784(f3(a1),f784(f784(f89(a1),x33791),a106)),a106),x33791)
% 11.41/11.17 [3395]E(f784(f164(a859),f134(a859,f784(f304(a859,f2(a859)),x33951))),f784(f267(a859),x33951))
% 11.41/11.17 [3591]E(f784(f269(x35911,x35911),f310(x35911,f187(f869(f868(x35911,x35911),a852)))),f249(f869(x35911,a852)))
% 11.41/11.17 [3592]E(f784(f271(x35921,x35921),f310(x35921,f187(f869(f868(x35921,x35921),a852)))),f249(f869(x35921,a852)))
% 11.41/11.17 [3637]E(f784(f784(f89(a1),f784(f784(f89(a1),f87(a1)),x36371)),x36371),f784(f784(f3(a1),f784(f784(f89(a1),x36371),x36371)),a106))
% 11.41/11.17 [3687]E(f784(f288(x36871,x36871),f310(x36871,f187(f869(f868(x36871,x36871),a852)))),f310(x36871,f187(f869(f868(x36871,x36871),a852))))
% 11.41/11.17 [3736]P85(f784(f784(f242(a859),x37361),f784(f784(f90(a859),x37361),f784(f784(f90(a859),x37361),x37361))))
% 11.41/11.17 [3822]E(f784(f784(f291(x38221,x38221,x38221),f187(f869(f868(x38221,x38221),a852))),f310(x38221,f187(f869(f868(x38221,x38221),a852)))),f187(f869(f868(x38221,x38221),a852)))
% 11.41/11.17 [4008]P85(f784(f71(a859),f784(f266(a859),f784(f784(f9(a859,a859,a852),f243(a859)),x40081))))
% 11.41/11.17 [4009]P85(f784(f71(a859),f784(f266(a859),f784(f784(f9(a859,a859,a852),f242(a859)),x40091))))
% 11.41/11.17 [4289]E(f784(f266(f868(x42891,x42891)),f784(f784(f10(f869(x42891,a852),a852,f868(x42891,x42891)),f96(x42891)),f784(f784(f9(f868(x42891,x42891),f869(x42891,f868(x42891,x42891)),f869(x42891,a852)),f784(f784(f10(f869(f868(x42891,x42891),a852),f869(f869(x42891,f868(x42891,x42891)),f869(x42891,a852)),f868(x42891,x42891)),f10(f868(x42891,x42891),a852,x42891)),a343)),f784(f784(f20(x42891,x42891,f868(x42891,x42891)),f251(x42891,x42891)),f7(x42891))))),f310(x42891,f187(f869(f868(x42891,x42891),a852))))
% 11.41/11.17 [4488]~E(f784(f784(f3(a1),f784(f784(f89(a1),x44881),x44881)),a106),a92)
% 11.41/11.17 [4489]~E(f784(f784(f3(a1),f784(f784(f89(a1),x44891),x44891)),a106),a92)
% 11.41/11.17 [4491]~E(f784(f784(f89(a1),f784(f784(f89(a1),f87(a1)),x44911)),x44911),f2(a1))
% 11.41/11.17 [3780]E(f784(f784(f89(a1),f784(f784(f3(a1),a106),x37801)),f784(f784(f3(a1),a106),x37801)),f784(f784(f3(a1),a106),f784(f784(f3(a1),f784(f784(f89(a1),x37801),x37801)),a106)))
% 11.41/11.17 [3895]E(f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),a106),x38951)),f784(f784(f3(a1),a106),x38951))),a106),f784(f784(f3(a1),a106),f784(f784(f89(a1),x38951),x38951)))
% 11.41/11.17 [3930]E(f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f89(a1),x39301),a106)),f784(f784(f89(a1),x39301),a106))),a106),f784(f784(f89(a1),f784(f784(f89(a1),x39301),x39301)),a106))
% 11.41/11.17 [3968]E(f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),a106),x39681)),f784(f784(f3(a1),a106),x39681))),a106),f784(f784(f3(a1),a92),f784(f784(f3(a1),f784(f784(f89(a1),x39681),x39681)),a106)))
% 11.41/11.17 [4071]E(f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x40711),f2(a859))),f187(f869(f868(a859,a859),a852))))),f784(f109(a1),x40711))
% 11.41/11.17 [4080]E(f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),f350(x40801)),f503(x40801))),f187(f869(f868(a859,a859),a852))))),x40801)
% 11.41/11.17 [4113]E(f784(f266(a1),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),f2(a1)))),x41131)),f784(f313(a859,a1,f109(a1)),f784(f266(a859),f784(f784(f10(a1,a852,a859),x41131),f109(a1)))))
% 11.41/11.17 [4161]P37(f784(f266(a1),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),f2(a1)))),x41611)))
% 11.41/11.17 [4181]P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),x41811),f187(f869(f868(a859,a859),a852)))),a80))
% 11.41/11.17 [4187]E(f784(f313(a1,a859,a114),f784(f266(a1),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),f2(a1)))),f784(f784(f10(a859,a852,a1),x41871),a114)))),f784(f266(a859),x41871))
% 11.41/11.17 [4336]E(f316(a859,f784(f784(f54(f868(a859,a859),f869(a859,a852)),f784(a116,x43361)),f784(f261(a859,a859,f869(a859,a852)),f784(f784(f9(a859,f869(a859,a852),f869(a859,f869(a859,a852))),f784(f784(f10(f869(a859,f869(f869(a859,a852),f869(a859,a852))),f869(f869(a859,a852),f869(a859,f869(a859,a852))),a859),f9(a859,f869(a859,a852),f869(a859,a852))),f784(f784(f10(f869(a859,a859),f869(a859,f869(f869(a859,a852),f869(a859,a852))),a859),f784(f10(a859,f869(f869(a859,a852),f869(a859,a852)),a859),f312(a859))),f3(a859)))),f187(f869(a859,a852)))))),f784(a114,x43361))
% 11.41/11.17 [3823]E(f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),x38231),x38231)),a106)),a106),f784(f784(f89(a1),x38231),x38231))
% 11.41/11.17 [3871]E(f784(f784(f3(a1),f784(f784(f3(a1),f784(f784(f89(a1),x38711),x38711)),a106)),a106),f784(f784(f89(a1),f784(f784(f3(a1),x38711),a106)),f784(f784(f3(a1),x38711),a106)))
% 11.41/11.17 [4088]E(f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f89(a1),f784(f88(a1),x40881)),a106)),f784(f784(f89(a1),f784(f88(a1),x40881)),a106))),a106),f784(f88(a1),f784(f784(f3(a1),f784(f784(f89(a1),x40881),x40881)),a106)))
% 11.41/11.17 [4131]E(f784(f784(f89(a859),x41311),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(a160,f784(a160,x41311)))
% 11.41/11.17 [4132]E(f784(f784(f90(a859),x41321),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f784(f89(a859),x41321),x41321))
% 11.41/11.17 [4133]E(f784(f784(f51(a859),f784(f784(f89(a859),x41331),x41331)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x41331)
% 11.41/11.17 [4214]E(f60(a859,f784(a160,f784(a160,x42141)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f60(a859,x42141,f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.17 [4352]E(f784(a98,f784(f784(f54(f868(a859,a859),f869(f868(a859,a859),a852)),f784(a116,x43521)),f784(f261(a859,a859,f869(f868(a859,a859),a852)),f784(f784(f10(f869(a859,f869(f868(a859,a859),a852)),f869(a859,f869(f868(a859,a859),a852)),a859),f784(f10(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852),a859),f287(f868(a859,a859),f868(a859,a859),a118))),f784(f784(f9(a859,f869(f868(a859,a859),a852),f869(a859,f869(f868(a859,a859),a852))),f784(f784(f10(f869(a859,f869(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f869(f869(f868(a859,a859),a852),f869(a859,f869(f868(a859,a859),a852))),a859),f9(a859,f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f10(f869(a859,f868(a859,a859)),f869(a859,f869(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),a859),f784(f10(f868(a859,a859),f869(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),a859),f312(f868(a859,a859)))),f784(f9(a859,a859,f868(a859,a859)),f251(a859,a859))))),f187(f869(f868(a859,a859),a852))))))),f784(f88(a1),x43521))
% 11.41/11.17 [4209]E(f784(f784(f89(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x42091),f784(a160,f784(a160,x42091)))
% 11.41/11.17 [4210]E(f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x42101),f784(f784(f89(a859),x42101),x42101))
% 11.41/11.17 [4243]E(f784(f784(f51(a859),f784(a160,f784(a160,x42431))),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(a160,f784(f784(f51(a859),x42431),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.17 [4294]E(f784(f784(f89(a859),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),x42941),f784(a160,f784(a160,f784(a160,x42941))))
% 11.41/11.17 [4373]E(f784(f261(a1,a1,f868(a1,a1)),f784(f784(f20(a1,f869(a1,f868(a1,a1)),f869(a1,f868(a1,a1))),f784(f784(f10(f869(a1,f869(f868(a1,a1),f868(a1,a1))),f869(f869(a1,f868(a1,a1)),f869(a1,f868(a1,a1))),a1),f20(a1,f868(a1,a1),f868(a1,a1))),f784(f784(f10(f869(a1,f868(a1,a1)),f869(a1,f869(f868(a1,a1),f868(a1,a1))),a1),f784(f20(a1,f868(a1,a1),f869(f868(a1,a1),f868(a1,a1))),f784(f784(f10(a852,f869(f868(a1,a1),f869(f868(a1,a1),f868(a1,a1))),a1),f105(f868(a1,a1))),f784(f784(f10(a1,a852,a1),f784(f242(a1),f2(a1))),f784(f784(f9(a1,a1,a1),f3(a1)),x43731))))),f784(f784(f9(a1,f869(a1,a1),f869(a1,f868(a1,a1))),f784(f784(f10(f869(a1,f868(a1,a1)),f869(f869(a1,a1),f869(a1,f868(a1,a1))),a1),f10(a1,f868(a1,a1),a1)),f784(f784(f10(a1,f869(a1,f868(a1,a1)),a1),f251(a1,a1)),f784(f784(f9(a1,a1,a1),f784(f784(f10(a1,f869(a1,a1),a1),f89(a1)),f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))),f87(a1))))),f784(f784(f9(a1,a1,a1),f3(a1)),x43731))))),f784(f784(f10(a1,f869(a1,f868(a1,a1)),a1),f251(a1,a1)),f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))),f58(x43731))
% 11.41/11.17 [3422]P38(a25,x34221,x34222,x34221)
% 11.41/11.17 [3423]P38(a25,x34231,x34232,x34231)
% 11.41/11.17 [3080]P15(a1,f169(x30801,x30802))
% 11.41/11.17 [3175]P46(x31751,x31752,f270(x31751,x31752))
% 11.41/11.17 [3176]P52(x31761,x31761,f270(x31761,x31762))
% 11.41/11.17 [3447]P26(x34471,x34471,f7(x34471),x34472)
% 11.41/11.17 [3448]P26(x34481,x34481,f41(x34481),x34482)
% 11.41/11.17 [3454]P33(x34541,x34542,f120(x34541),f120(x34541))
% 11.41/11.17 [3455]P33(x34551,x34552,f120(x34551),f120(x34551))
% 11.41/11.17 [3456]P26(x34561,f864(x34561),f237(x34561),x34562)
% 11.41/11.17 [3465]P26(f860(x34651),f860(x34651),f162(x34651),x34652)
% 11.41/11.17 [4380]~E(f43(x43801),f42(x43802))
% 11.41/11.17 [4381]~E(f43(x43811),f42(x43812))
% 11.41/11.17 [4387]~E(f30(x43871,x43872),a25)
% 11.41/11.17 [4388]~E(f38(x43881,x43882),a25)
% 11.41/11.17 [4389]~E(f37(x43891,x43892),a25)
% 11.41/11.17 [4390]~E(f30(x43901,x43902),a25)
% 11.41/11.17 [4391]~E(f38(x43911,x43912),a25)
% 11.41/11.17 [4392]~E(f37(x43921,x43922),a25)
% 11.41/11.17 [3046]E(f784(f7(x30461),x30462),x30462)
% 11.41/11.17 [3047]E(f784(f266(x30471),x30472),x30472)
% 11.41/11.17 [3048]E(f784(f41(x30481),x30482),x30482)
% 11.41/11.17 [3049]E(f784(f41(x30491),x30492),x30492)
% 11.41/11.17 [3058]E(f784(f191(x30581),x30582),f122(x30581))
% 11.41/11.17 [3068]E(f36(f30(x30681,x30682)),f2(a859))
% 11.41/11.17 [3078]E(f94(x30781,f784(a343,x30782)),x30782)
% 11.41/11.17 [3079]E(f99(x30791,f784(a343,x30792)),x30792)
% 11.41/11.17 [3096]E(f784(f188(a853),f30(x30961,x30962)),f2(a859))
% 11.41/11.17 [3101]E(f784(f131(x31011,x31012),f120(x31011)),f120(x31011))
% 11.41/11.17 [3120]E(f310(x31201,f310(x31201,x31202)),f310(x31201,x31202))
% 11.41/11.17 [3141]E(f784(f784(f130(x31411),x31412),f120(x31411)),x31412)
% 11.41/11.17 [3150]E(f784(f784(f165(x31501),x31502),f120(x31501)),f120(x31501))
% 11.41/11.17 [3151]E(f784(f784(f133(x31511),x31512),f120(x31511)),f120(x31511))
% 11.41/11.17 [3153]E(f238(x31531,x31532,f190(x31531)),f2(a859))
% 11.41/11.17 [3154]E(f147(x31541,x31542,f120(x31541)),f2(a859))
% 11.41/11.17 [3156]E(f154(x31561,x31562,f120(x31561)),f120(x31561))
% 11.41/11.17 [3157]E(f166(x31571,f120(x31571),x31572),f120(x31571))
% 11.41/11.17 [3163]E(f784(f269(x31631,x31631),f270(x31631,x31632)),x31632)
% 11.41/11.17 [3164]E(f784(f271(x31641,x31641),f270(x31641,x31642)),x31642)
% 11.41/11.17 [3172]P85(f784(a26,f30(x31721,x31722)))
% 11.41/11.17 [3173]P85(f784(a26,f30(x31731,x31732)))
% 11.41/11.17 [3174]E(f784(f288(x31741,x31741),f270(x31741,x31742)),f270(x31741,x31742))
% 11.41/11.17 [3186]E(f310(f860(x31861),f149(x31861,x31862)),f150(x31861,f310(x31861,x31862)))
% 11.41/11.17 [3188]P85(f784(f132(a1),f169(x31881,x31882)))
% 11.41/11.17 [3197]E(f784(f269(x31971,x31971),f310(x31971,x31972)),f249(f869(x31971,a852)))
% 11.41/11.17 [3198]E(f784(f271(x31981,x31981),f310(x31981,x31982)),f249(f869(x31981,a852)))
% 11.41/11.17 [3208]E(f784(f164(a1),f169(x32081,x32082)),f305(a1,x32081,x32082))
% 11.41/11.17 [3209]E(f784(f164(a1),f169(x32091,x32092)),f305(a1,x32091,x32092))
% 11.41/11.17 [3224]P53(x32241,f187(f869(x32241,a852)),x32242)
% 11.41/11.17 [3229]E(f784(f260(a1,a1),f61(x32291,x32292)),f60(a1,x32291,x32292))
% 11.41/11.17 [3230]E(f784(f304(a859,x32301),f784(a160,x32302)),f305(a859,x32301,x32302))
% 11.41/11.17 [3257]E(f305(a859,f784(a160,x32571),x32572),f307(a859,x32571,x32572))
% 11.41/11.17 [3260]P46(x32601,f249(f869(x32601,a852)),f310(x32601,x32602))
% 11.41/11.17 [3325]E(f784(f784(f3(a859),x33251),f784(a160,x33252)),f784(f50(a859),f308(a859,x33252,x33251)))
% 11.41/11.17 [3380]E(f158(x33801,x33802,f120(x33801)),f784(f784(f251(f860(x33801),f860(x33801)),f120(x33801)),f120(x33801)))
% 11.41/11.17 [3399]E(f784(f261(x33991,x33992,f868(x33991,x33992)),f251(x33991,x33992)),f41(f868(x33991,x33992)))
% 11.41/11.17 [3404]P85(f784(f784(f347(f860(x34041)),f120(x34041)),f152(x34041,x34042)))
% 11.41/11.17 [3405]E(f784(f188(f860(x34051)),f121(x34051,x34052)),f784(f784(f3(a859),f784(f188(f860(x34051)),x34052)),f87(a859)))
% 11.41/11.17 [3414]P85(f784(f71(a859),f305(a859,x34141,x34142)))
% 11.41/11.17 [3415]P85(f784(f71(a859),f307(a859,x34151,x34152)))
% 11.41/11.17 [3416]P85(f784(f71(a859),f308(a859,x34161,x34162)))
% 11.41/11.17 [3417]P85(f784(f71(a1),f305(a1,x34171,x34172)))
% 11.41/11.17 [3418]P85(f784(f71(a1),f307(a1,x34181,x34182)))
% 11.41/11.17 [3419]P85(f784(f71(a1),f308(a1,x34191,x34192)))
% 11.41/11.17 [3528]E(f784(f313(a859,a859,a160),f305(a859,x35281,x35282)),f305(a859,f784(a160,x35281),f784(a160,x35282)))
% 11.41/11.17 [3545]E(f784(f784(f291(x35451,x35451,x35451),f310(x35451,x35452)),f310(x35451,x35452)),f310(x35451,x35452))
% 11.41/11.17 [3575]E(f784(f784(f251(a1,a1),f784(f784(f51(a1),x35751),x35752)),f60(a1,x35751,x35752)),f61(x35751,x35752))
% 11.41/11.17 [3576]E(f784(f784(f251(a108,a108),f784(f784(f51(a108),x35761),x35762)),f60(a108,x35761,x35762)),f24(x35761,x35762))
% 11.41/11.17 [3604]E(f784(f784(f251(a859,a859),f784(f784(f51(a859),x36041),x36042)),f60(a859,x36041,x36042)),f94(f868(a859,a859),f63(x36041,x36042)))
% 11.41/11.17 [3656]P85(f784(f784(f243(a859),f784(f784(f3(a859),x36561),x36562)),f784(a160,x36561)))
% 11.41/11.17 [3755]E(f784(f784(f89(a1),f784(f784(f90(a1),x37551),f784(f784(f51(a1),x37552),x37551))),f60(a1,x37552,x37551)),x37552)
% 11.41/11.17 [3759]E(f784(f784(f54(a859,f869(f868(f860(x37591),f860(x37591)),a852)),f249(f869(a859,a852))),f137(x37591,x37592)),f139(x37591,x37592))
% 11.41/11.17 [3982]P85(f784(f784(f347(f868(f860(x39821),f860(x39821))),f784(f784(f251(f860(x39821),f860(x39821)),f120(x39821)),f120(x39821))),f150(x39821,x39822)))
% 11.41/11.17 [4143]E(f262(x41431,x41431,x41432,x41432,f41(x41431),f41(x41432)),f41(f868(x41431,x41432)))
% 11.41/11.17 [4144]E(f262(x41441,x41441,x41442,x41442,f7(x41441),f7(x41442)),f41(f868(x41441,x41442)))
% 11.41/11.17 [4145]E(f262(x41451,x41451,x41452,x41452,f41(x41451),f41(x41452)),f41(f868(x41451,x41452)))
% 11.41/11.17 [4146]E(f262(x41461,x41461,x41462,x41462,f41(x41461),f41(x41462)),f41(f868(x41461,x41462)))
% 11.41/11.17 [4399]~E(f784(f237(x43991),x43992),f190(x43991))
% 11.41/11.17 [4400]~E(f784(f237(x44001),x44002),f190(x44001))
% 11.41/11.17 [4418]~P36(x44181,f784(f237(x44181),x44182))
% 11.41/11.17 [3139]E(f784(f241(x31391),f784(f237(x31391),x31392)),x31392)
% 11.41/11.17 [3140]E(f784(f162(x31401),f784(f162(x31401),x31402)),x31402)
% 11.41/11.17 [3142]E(f784(f784(f133(x31421),f2(a859)),x31422),x31422)
% 11.41/11.17 [3152]E(f784(f784(f165(x31521),f2(a859)),x31522),f120(x31521))
% 11.41/11.17 [3159]E(f784(f784(f130(x31591),f120(x31591)),x31592),x31592)
% 11.41/11.17 [3166]E(f784(f188(f864(x31661)),f784(f237(x31661),x31662)),f2(a859))
% 11.41/11.17 [3168]E(f52(f869(x31681,a852),f784(f311(x31681),x31682)),x31682)
% 11.41/11.17 [3170]E(f784(f164(x31701),f784(f161(x31701),x31702)),f784(f164(x31701),x31702))
% 11.41/11.17 [3171]E(f784(f164(x31711),f784(f162(x31711),x31712)),f784(f164(x31711),x31712))
% 11.41/11.17 [3177]E(f784(f784(f3(a108),x31771),x31772),f784(f784(a4,x31771),x31772))
% 11.41/11.17 [3189]E(f784(f188(a862),f784(f784(a314,x31891),x31892)),f2(a859))
% 11.41/11.17 [3191]E(f784(f784(f89(a859),x31911),x31912),f784(f784(f89(a859),x31912),x31911))
% 11.41/11.17 [3192]E(f784(f784(f89(a1),x31921),x31922),f784(f784(f89(a1),x31922),x31921))
% 11.41/11.17 [3193]E(f784(f784(f90(a859),x31931),x31932),f784(f784(f90(a859),x31932),x31931))
% 11.41/11.17 [3194]E(f784(f784(f90(a1),x31941),x31942),f784(f784(f90(a1),x31942),x31941))
% 11.41/11.17 [3216]E(f784(f784(f180(x32161,x32161),f2(a859)),x32162),f41(x32161))
% 11.41/11.17 [3217]E(f784(f188(f860(x32171)),f784(f161(x32171),x32172)),f784(f188(f860(x32171)),x32172))
% 11.41/11.17 [3218]E(f784(f188(f860(x32181)),f784(f162(x32181),x32182)),f784(f188(f860(x32181)),x32182))
% 11.41/11.17 [3219]E(f166(x32191,x32192,f187(f869(a859,a852))),f120(x32191))
% 11.41/11.17 [3220]E(f784(f784(f146(x32201,x32201),f7(x32201)),x32202),x32202)
% 11.41/11.17 [3222]E(f784(f250(a1,a1),f61(x32221,x32222)),f784(f784(f51(a1),x32221),x32222))
% 11.41/11.17 [3240]E(f36(f37(x32401,x32402)),f784(f784(f89(a859),f36(x32402)),f784(a160,f2(a859))))
% 11.41/11.17 [3241]E(f784(f286(x32411),f784(f288(x32411,x32411),x32412)),f784(f286(x32411),x32412))
% 11.41/11.17 [3245]P85(f784(f71(x32451),f784(f164(x32451),x32452)))
% 11.41/11.17 [3251]E(f784(f784(f89(a1),x32511),f784(f88(a1),x32512)),f784(f784(f3(a1),x32511),x32512))
% 11.41/11.17 [3252]E(f784(f784(f89(a1),x32521),f784(f88(a1),x32522)),f784(f784(f3(a1),x32521),x32522))
% 11.41/11.17 [3258]P25(x32581,x32582,f187(f869(f858(x32581),a852)))
% 11.41/11.17 [3259]P25(x32591,x32592,f187(f869(f858(x32591),a852)))
% 11.41/11.17 [3263]E(f784(f313(x32631,x32631,f7(x32631)),x32632),x32632)
% 11.41/11.17 [3264]E(f784(f313(x32641,x32641,f41(x32641)),x32642),x32642)
% 11.41/11.17 [3265]E(f784(f315(x32651,x32651,f7(x32651)),x32652),x32652)
% 11.41/11.17 [3266]E(f784(f315(x32661,x32661,f41(x32661)),x32662),x32662)
% 11.41/11.17 [3267]P85(f784(f249(f869(x32671,a852)),x32672))
% 11.41/11.17 [3269]E(f784(f50(a859),f784(f304(a859,x32691),x32692)),f784(f784(f3(a859),x32692),x32691))
% 11.41/11.17 [3270]E(f784(f304(a859,f784(a160,x32701)),x32702),f308(a859,x32701,x32702))
% 11.41/11.17 [3282]E(f784(f784(f312(x32821),x32822),f187(f869(x32821,a852))),f784(f266(x32821),f784(a343,x32822)))
% 11.41/11.17 [3288]E(f784(f784(f312(x32881),x32882),f187(f869(x32881,a852))),f236(x32881,f784(f237(x32881),x32882)))
% 11.41/11.17 [3290]E(f310(x32901,f784(f288(x32901,x32901),x32902)),f784(f288(x32901,x32901),f310(x32901,x32902)))
% 11.41/11.17 [3294]E(f784(f784(f89(a859),f784(a160,x32941)),x32942),f784(f784(f89(a859),x32941),f784(a160,x32942)))
% 11.41/11.17 [3295]E(f784(f784(f3(a859),f784(a160,x32951)),f784(a160,x32952)),f784(f784(f3(a859),x32951),x32952))
% 11.41/11.17 [3302]E(f784(f50(a859),f307(a859,x33021,x33022)),f784(f784(f3(a859),x33022),x33021))
% 11.41/11.17 [3311]P35(x33111,f784(f784(f290(a859,x33111),a247),x33112))
% 11.41/11.17 [3313]P15(a859,f134(a859,f784(f304(a859,x33131),x33132)))
% 11.41/11.17 [3315]P85(f784(f71(a859),f784(f304(a859,x33151),x33152)))
% 11.41/11.17 [3316]P85(f784(f71(a1),f784(f304(a1,x33161),x33162)))
% 11.41/11.17 [3318]E(f784(f288(f860(x33181),f860(x33181)),f149(x33181,x33182)),f149(x33181,f784(f288(x33181,x33181),x33182)))
% 11.41/11.17 [3319]E(f784(f188(a853),f37(x33191,x33192)),f784(f784(f89(a859),f784(f188(a853),x33192)),f784(a160,f2(a859))))
% 11.41/11.17 [3321]E(f784(f304(a1,x33211),f784(f784(f89(a1),x33212),f87(a1))),f305(a1,x33211,x33212))
% 11.41/11.17 [3324]E(f784(f784(f51(a1),f784(f88(a1),x33241)),f784(f88(a1),x33242)),f784(f784(f51(a1),x33241),x33242))
% 11.41/11.17 [3332]E(f177(x33321,x33322,f784(f18(f864(x33322),x33321),f190(x33322))),f187(f869(x33322,a852)))
% 11.41/11.17 [3333]E(f175(x33331,x33332,f784(f18(f864(x33332),x33331),f190(x33332))),f187(f869(x33331,a852)))
% 11.41/11.17 [3334]E(f784(f784(f180(f868(x33341,x33341),a852),f87(a859)),x33342),x33342)
% 11.41/11.17 [3336]E(f784(f784(f3(f869(x33361,a852)),x33362),f187(f869(x33361,a852))),x33362)
% 11.41/11.17 [3337]E(f784(f784(f110(f869(x33371,a852)),x33372),f187(f869(x33371,a852))),x33372)
% 11.41/11.17 [3338]E(f784(f784(f111(f869(x33381,a852)),x33382),f249(f869(x33381,a852))),x33382)
% 11.41/11.17 [3339]E(f784(f250(a859,a859),f94(f868(a859,a859),f63(x33391,x33392))),f784(f784(f51(a859),x33391),x33392))
% 11.41/11.17 [3345]E(f317(x33451,f784(a23,x33452),f784(f88(a1),f784(a23,x33452))),f784(f784(f320(a1),x33451),x33452))
% 11.41/11.17 [3346]E(f305(a1,f784(f784(f89(a1),x33461),f87(a1)),x33462),f307(a1,x33461,x33462))
% 11.41/11.17 [3351]E(f784(f260(a859,a859),f94(f868(a859,a859),f63(x33511,x33512))),f60(a859,x33511,x33512))
% 11.41/11.17 [3359]E(f318(x33591,f784(a23,x33592),f784(f88(a1),f784(a23,x33592))),f319(a1,x33591,x33592))
% 11.41/11.17 [3361]P85(f784(f784(f347(x33611),x33612),f249(f869(x33611,a852))))
% 11.41/11.17 [3362]P85(f784(f784(f347(x33621),x33622),f249(f869(x33621,a852))))
% 11.41/11.17 [3366]E(f784(f784(f3(a859),f784(a160,x33661)),x33662),f784(f50(a859),f305(a859,x33662,x33661)))
% 11.41/11.17 [3391]E(f784(f784(f3(f869(x33911,a852)),x33912),f249(f869(x33911,a852))),f187(f869(x33911,a852)))
% 11.41/11.17 [3392]E(f784(f784(f110(f869(x33921,a852)),x33922),f249(f869(x33921,a852))),f249(f869(x33921,a852)))
% 11.41/11.17 [3393]E(f784(f784(f111(f869(x33931,a852)),x33932),f187(f869(x33931,a852))),f187(f869(x33931,a852)))
% 11.41/11.17 [3406]E(f60(a1,f784(f109(a1),x34061),f784(f109(a1),x34062)),f784(f109(a1),f60(a859,x34061,x34062)))
% 11.41/11.17 [3407]E(f60(a1,f784(f109(a1),x34071),f784(f109(a1),x34072)),f784(f109(a1),f60(a859,x34071,x34072)))
% 11.41/11.17 [3408]E(f60(a1,f784(f88(a1),x34081),f784(f88(a1),x34082)),f784(f88(a1),f60(a1,x34081,x34082)))
% 11.41/11.17 [3421]E(f784(f188(f860(x34211)),f784(f163(x34211),x34212)),f784(f784(f3(a859),f784(f188(f860(x34211)),x34212)),f87(a859)))
% 11.41/11.17 [3449]E(f784(f784(f51(a1),f60(a1,x34491,x34492)),x34492),f2(a1))
% 11.41/11.17 [3458]E(f784(a5,f60(a859,f784(a22,x34581),f784(a22,x34582))),f60(a108,x34581,x34582))
% 11.41/11.17 [3495]E(f784(a5,f784(f784(f89(a859),f784(a22,x34951)),f784(a22,x34952))),f784(f784(f89(a108),x34951),x34952))
% 11.41/11.17 [3496]E(f784(a5,f784(f784(f90(a859),f784(a22,x34961)),f784(a22,x34962))),f784(f784(f90(a108),x34961),x34962))
% 11.41/11.17 [3497]E(f784(a5,f784(f784(f51(a859),f784(a22,x34971)),f784(a22,x34972))),f784(f784(f51(a108),x34971),x34972))
% 11.41/11.17 [3498]E(f784(a5,f784(f784(f3(a859),f784(a22,x34981)),f784(a22,x34982))),f784(f784(f3(a108),x34981),x34982))
% 11.41/11.17 [3507]E(f784(f313(a859,a859,a160),f784(f304(a859,x35071),x35072)),f784(f304(a859,f784(a160,x35071)),f784(a160,x35072)))
% 11.41/11.17 [3533]P85(f784(f63(x35331,x35332),f94(f868(a859,a859),f63(x35331,x35332))))
% 11.41/11.17 [3550]E(f784(f784(f89(a859),f784(f784(f89(a859),f36(x35501)),f36(x35502))),f784(a160,f2(a859))),f36(f38(x35501,x35502)))
% 11.41/11.17 [3551]E(f60(a859,f784(a160,f60(a859,x35511,x35512)),x35512),f60(a859,f784(a160,x35511),x35512))
% 11.41/11.17 [3565]E(f784(f784(f55(f869(x35651,a852),f869(x35651,a852)),x35652),f7(f869(x35651,a852))),f53(f869(x35651,a852),x35652))
% 11.41/11.17 [3566]E(f784(f784(f54(f869(x35661,a852),f869(x35661,a852)),x35662),f7(f869(x35661,a852))),f52(f869(x35661,a852),x35662))
% 11.41/11.17 [3569]P85(f784(f784(f347(f869(x35691,a852)),x35692),f784(f311(x35691),x35692)))
% 11.41/11.17 [3574]E(f60(a1,f784(f88(a1),f60(a1,x35741,x35742)),x35742),f60(a1,f784(f88(a1),x35741),x35742))
% 11.41/11.17 [3585]P85(f784(f784(f242(f869(x35851,a852)),x35852),f249(f869(x35851,a852))))
% 11.41/11.17 [3587]E(f784(f784(f291(x35871,x35871,x35871),f310(x35871,x35872)),f310(x35871,f310(x35871,x35872))),f310(x35871,x35872))
% 11.41/11.17 [3588]E(f784(f784(f110(f869(x35881,a852)),f784(f271(x35881,x35881),x35882)),f784(f269(x35881,x35881),x35882)),f784(f286(x35881),x35882))
% 11.41/11.17 [3610]E(f327(x36101,x36102,f249(f869(x36101,a852)),f249(f869(x36102,a852))),f249(f869(f870(x36101,x36102),a852)))
% 11.41/11.17 [3661]P85(f784(f784(f242(a859),f60(a859,x36611,x36612)),x36611))
% 11.41/11.17 [3685]P85(f784(f784(f242(a1),f784(f88(a1),f784(f109(a1),x36851))),f784(f109(a1),x36852)))
% 11.41/11.17 [3710]P85(f784(f784(f347(f869(x37101,a852)),f187(f869(x37101,a852))),f784(f311(x37101),x37102)))
% 11.41/11.17 [3715]E(f310(x37151,f784(f784(f291(x37151,x37151,x37151),x37152),f310(x37151,x37152))),f310(x37151,x37152))
% 11.41/11.17 [3717]E(f784(f784(f291(x37171,x37171,x37171),f310(x37171,x37172)),x37172),f784(f784(f291(x37171,x37171,x37171),x37172),f310(x37171,x37172)))
% 11.41/11.17 [3718]E(f784(f784(f291(x37181,x37181,x37181),f310(x37181,x37182)),x37182),f784(f784(f291(x37181,x37181,x37181),x37182),f310(x37181,x37182)))
% 11.41/11.17 [3720]E(f784(a114,f784(f784(f89(a1),f784(f784(f3(a1),x37201),x37202)),f87(a1))),f784(f50(a1),f305(a1,x37202,x37201)))
% 11.41/11.17 [3737]E(f784(f269(x37371,x37371),f784(f784(f291(x37371,x37371,x37371),x37372),f310(x37371,x37372))),f784(f269(x37371,x37371),x37372))
% 11.41/11.17 [3738]E(f784(f271(x37381,x37381),f784(f784(f291(x37381,x37381,x37381),x37382),f310(x37381,x37382))),f784(f271(x37381,x37381),x37382))
% 11.41/11.17 [3751]E(f784(f784(f89(a859),f784(f784(f89(a859),f784(f188(a853),x37511)),f784(f188(a853),x37512))),f784(a160,f2(a859))),f784(f188(a853),f38(x37511,x37512)))
% 11.41/11.17 [3763]P26(a859,a859,f784(f784(f9(a859,a859,a859),f89(a859)),x37631),x37632)
% 11.41/11.17 [3765]P15(a859,f784(f162(a859),f784(f784(f146(f860(x37651),a859),f188(f860(x37651))),f170(x37651,x37652))))
% 11.41/11.17 [3812]P85(f784(f784(f243(a1),f784(f88(a1),f784(f109(a1),f784(a160,x38121)))),f784(f109(a1),x38122)))
% 11.41/11.17 [3852]E(f784(f136(f860(x38521),x38521,f784(f9(x38521,f860(x38521),f860(x38521)),f144(x38521)),f120(x38521)),x38522),f784(f162(x38521),x38522))
% 11.41/11.17 [3902]P85(f784(f784(f242(f869(f868(f860(x39021),f860(x39021)),a852)),f150(x39021,x39022)),f310(f860(x39021),f149(x39021,x39022))))
% 11.41/11.17 [3934]P85(f784(f63(x39341,x39342),f784(f784(f251(a859,a859),f784(f784(f51(a859),x39341),x39342)),f60(a859,x39341,x39342))))
% 11.41/11.17 [3945]P85(f784(f784(f242(f869(f868(f860(x39451),f860(x39451)),a852)),f149(x39451,f310(x39451,x39452))),f310(f860(x39451),f149(x39451,x39452))))
% 11.41/11.17 [4173]E(f784(f784(f263(f868(a108,a108),a108,f868(a108,a108),f868(x41731,f868(a108,a108))),f274(f784(f157(a108),f784(f784(f146(f868(a108,x41731),a108),f250(a108,x41731)),x41732)))),f784(f784(f10(x41731,f869(f868(a108,a108),f868(x41731,f868(a108,a108))),a108),f251(x41731,f868(a108,a108))),f275(x41731,x41732))),f273(x41731,x41732))
% 11.41/11.17 [4318]E(f60(a859,f784(f784(f89(a859),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),x43181),f784(f113(a859),x43182)),f60(a859,f784(a160,f784(a160,f784(a160,x43181))),f784(f113(a859),x43182)))
% 11.41/11.17 [4332]E(f784(f784(f51(a859),f784(f784(f89(a859),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),x43321)),f784(f113(a859),x43322)),f784(f784(f51(a859),f784(a160,f784(a160,f784(a160,x43321)))),f784(f113(a859),x43322)))
% 11.41/11.17 [4351]E(f784(f261(f869(f868(x43511,x43511),a852),f869(f868(x43511,x43511),a852),f869(f869(x43512,x43511),f868(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852)))),f784(f784(f9(f869(f868(x43511,x43511),a852),f869(f869(f868(x43511,x43511),a852),f869(f869(x43512,x43511),f869(f868(x43512,x43512),a852))),f869(f869(f868(x43511,x43511),a852),f869(f869(x43512,x43511),f868(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852))))),f784(f784(f10(f869(f869(f869(x43512,x43511),f869(f868(x43512,x43512),a852)),f869(f869(x43512,x43511),f868(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852)))),f869(f869(f869(f868(x43511,x43511),a852),f869(f869(x43512,x43511),f869(f868(x43512,x43512),a852))),f869(f869(f868(x43511,x43511),a852),f869(f869(x43512,x43511),f868(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852))))),f869(f868(x43511,x43511),a852)),f10(f869(f869(x43512,x43511),f869(f868(x43512,x43512),a852)),f869(f869(x43512,x43511),f868(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852))),f869(f868(x43511,x43511),a852))),f784(f784(f10(f869(f869(x43512,x43511),f869(f869(f868(x43512,x43512),a852),f868(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852)))),f869(f869(f869(x43512,x43511),f869(f868(x43512,x43512),a852)),f869(f869(x43512,x43511),f868(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852)))),f869(f868(x43511,x43511),a852)),f20(f869(x43512,x43511),f869(f868(x43512,x43512),a852),f868(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852)))),f784(f784(f10(f869(f869(x43512,x43511),f869(f868(x43512,x43512),a852)),f869(f869(x43512,x43511),f869(f869(f868(x43512,x43512),a852),f868(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852)))),f869(f868(x43511,x43511),a852)),f784(f10(f869(f868(x43512,x43512),a852),f869(f869(f868(x43512,x43512),a852),f868(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852))),f869(x43512,x43511)),f251(f869(f868(x43512,x43512),a852),f869(f868(x43512,x43512),a852)))),f290(x43511,x43512))))),f290(x43511,x43512))),f83(x43511,x43512))
% 11.41/11.17 [4468]~E(f784(f311(x44681),x44682),f187(f869(f869(x44681,a852),a852)))
% 11.41/11.17 [4485]~P85(f784(f784(f347(x44851),x44852),f187(f869(x44851,a852))))
% 11.41/11.17 [4486]~P85(f784(f784(f347(x44861),x44862),f187(f869(x44861,a852))))
% 11.41/11.17 [4495]~P85(f784(f784(f243(f869(x44951,a852)),x44952),f187(f869(x44951,a852))))
% 11.41/11.17 [3272]E(f784(f784(f3(a859),x32721),f784(f784(f89(a859),x32721),x32722)),f2(a859))
% 11.41/11.17 [3274]E(f784(f784(f110(f869(x32741,a852)),x32742),x32742),x32742)
% 11.41/11.17 [3275]E(f784(f784(f111(f869(x32751,a852)),x32752),x32752),x32752)
% 11.41/11.17 [3304]E(f784(f784(f3(f869(x33041,a852)),x33042),x33042),f187(f869(x33041,a852)))
% 11.41/11.17 [3307]E(f784(f137(x33071,x33072),f2(a859)),f187(f869(f868(f860(x33071),f860(x33071)),a852)))
% 11.41/11.17 [3308]E(f784(f784(f89(a859),x33081),f784(a160,x33082)),f784(a160,f784(f784(f89(a859),x33081),x33082)))
% 11.41/11.17 [3320]E(f195(f784(f109(a1),x33201),f784(f109(a1),x33202)),f784(f109(a1),f784(f784(f3(a859),x33201),x33202)))
% 11.41/11.17 [3323]E(f784(f784(f51(a1),f784(f88(a1),x33231)),x33232),f784(f784(f51(a1),x33231),f784(f88(a1),x33232)))
% 11.41/11.17 [3327]E(f784(f50(a1),f784(f304(a1,x33271),x33272)),f784(a114,f784(f784(f3(a1),x33272),x33271)))
% 11.41/11.17 [3330]E(f784(f784(f89(a859),f784(a160,x33301)),x33302),f784(a160,f784(f784(f89(a859),x33301),x33302)))
% 11.41/11.17 [3335]E(f784(f88(f869(x33351,a852)),f784(f88(f869(x33351,a852)),x33352)),x33352)
% 11.41/11.17 [3348]E(f170(x33481,f784(f784(f144(f860(x33481)),f120(x33481)),x33482)),f170(x33481,x33482))
% 11.41/11.17 [3352]E(f784(f784(f89(a859),x33521),f784(f784(f90(a859),x33521),x33522)),f784(f784(f90(a859),x33521),f784(a160,x33522)))
% 11.41/11.17 [3360]E(f784(f784(a4,f784(a5,x33601)),f784(a5,x33602)),f784(a5,f784(f784(f3(a859),x33601),x33602)))
% 11.41/11.17 [3370]E(f784(f784(f252(a1),f784(f109(a1),x33701)),x33702),f784(f109(a1),f784(f784(f252(a859),x33701),x33702)))
% 11.41/11.17 [3371]E(f784(f784(f90(a1),f784(f88(a1),x33711)),x33712),f784(f88(a1),f784(f784(f90(a1),x33711),x33712)))
% 11.41/11.17 [3372]E(f784(f784(f252(a1),f784(f109(a1),x33721)),x33722),f784(f109(a1),f784(f784(f252(a859),x33721),x33722)))
% 11.41/11.17 [3373]E(f784(f784(f252(a1),f784(f109(a1),x33731)),x33732),f784(f109(a1),f784(f784(f252(a859),x33731),x33732)))
% 11.41/11.17 [3374]E(f784(f784(f89(a108),f784(a5,x33741)),f784(a5,x33742)),f784(a5,f784(f784(f89(a859),x33741),x33742)))
% 11.41/11.17 [3375]E(f784(f784(f90(a108),f784(a5,x33751)),f784(a5,x33752)),f784(a5,f784(f784(f90(a859),x33751),x33752)))
% 11.41/11.17 [3376]E(f784(f784(f246(a859),f784(a160,x33761)),f784(a160,x33762)),f784(a160,f784(f784(f246(a859),x33761),x33762)))
% 11.41/11.17 [3377]E(f784(f784(f186(a859),f784(a160,x33771)),f784(a160,x33772)),f784(a160,f784(f784(f186(a859),x33771),x33772)))
% 11.41/11.17 [3382]E(f784(f164(a859),f134(a859,f784(f304(a859,x33821),x33822))),f784(f304(a859,x33821),x33822))
% 11.41/11.17 [3383]E(f784(f164(a859),f134(a859,f784(f304(a859,x33831),x33832))),f784(f304(a859,x33831),x33832))
% 11.41/11.17 [3384]E(f316(x33841,f784(f784(f312(x33841),x33842),f187(f869(x33841,a852)))),x33842)
% 11.41/11.17 [3389]E(f784(f269(x33891,x33892),f187(f869(f868(x33891,x33892),a852))),f187(f869(x33892,a852)))
% 11.41/11.17 [3390]E(f784(f271(x33901,x33902),f187(f869(f868(x33901,x33902),a852))),f187(f869(x33901,a852)))
% 11.41/11.17 [3394]E(f784(a114,f784(f784(f3(a1),x33941),x33942)),f784(f50(a1),f307(a1,x33942,x33941)))
% 11.41/11.17 [3398]E(f784(f784(f89(a859),x33981),f784(f784(f90(a859),x33982),x33981)),f784(f784(f90(a859),f784(a160,x33982)),x33981))
% 11.41/11.17 [3400]E(f784(f784(f69(x34001),f187(f869(x34001,a852))),x34002),f187(f869(f869(x34001,a852),a852)))
% 11.41/11.17 [3409]E(f784(f188(f860(a859)),f134(a859,f784(f304(a859,x34091),x34092))),f784(f784(f3(a859),x34092),x34091))
% 11.41/11.17 [3428]E(f784(f784(f110(f869(x34281,a852)),f187(f869(x34281,a852))),x34282),x34282)
% 11.41/11.17 [3429]E(f784(f784(f111(f869(x34291,a852)),f249(f869(x34291,a852))),x34292),x34292)
% 11.41/11.17 [3430]E(f784(f784(f90(a1),f784(f109(a1),x34301)),f784(f109(a1),x34302)),f784(f109(a1),f784(f784(f90(a859),x34301),x34302)))
% 11.41/11.17 [3431]E(f784(f784(f51(a1),f784(f109(a1),x34311)),f784(f109(a1),x34312)),f784(f109(a1),f784(f784(f51(a859),x34311),x34312)))
% 11.41/11.17 [3432]E(f784(f784(f89(a1),f784(f88(a1),x34321)),f784(f88(a1),x34322)),f784(f88(a1),f784(f784(f89(a1),x34321),x34322)))
% 11.41/11.17 [3434]E(f784(f784(f89(a1),f784(f109(a1),x34341)),f784(f109(a1),x34342)),f784(f109(a1),f784(f784(f89(a859),x34341),x34342)))
% 11.41/11.17 [3435]E(f784(f784(f89(a1),f784(f109(a1),x34351)),f784(f109(a1),x34352)),f784(f109(a1),f784(f784(f89(a859),x34351),x34352)))
% 11.41/11.17 [3436]E(f784(f784(f89(a1),f784(f113(a1),x34361)),f784(f113(a1),x34362)),f784(f113(a1),f784(f784(f89(a1),x34361),x34362)))
% 11.41/11.17 [3437]E(f784(f784(f90(a1),f784(f109(a1),x34371)),f784(f109(a1),x34372)),f784(f109(a1),f784(f784(f90(a859),x34371),x34372)))
% 11.41/11.17 [3438]E(f784(f784(f90(a1),f784(f109(a1),x34381)),f784(f109(a1),x34382)),f784(f109(a1),f784(f784(f90(a859),x34381),x34382)))
% 11.41/11.17 [3439]E(f784(f784(f90(a1),f784(f113(a1),x34391)),f784(f113(a1),x34392)),f784(f113(a1),f784(f784(f90(a1),x34391),x34392)))
% 11.41/11.17 [3440]E(f784(f784(f51(a1),f784(f109(a1),x34401)),f784(f109(a1),x34402)),f784(f109(a1),f784(f784(f51(a859),x34401),x34402)))
% 11.41/11.17 [3459]E(f784(f784(f8(x34591,a859),f784(f18(a859,x34591),f87(a859))),x34592),f784(f50(x34591),x34592))
% 11.41/11.17 [3471]E(f784(f88(a1),f60(a1,f784(f88(a1),x34711),x34712)),f60(a1,x34711,f784(f88(a1),x34712)))
% 11.41/11.17 [3473]E(f784(f164(a1),f169(x34731,f784(f784(f3(a1),x34732),f87(a1)))),f784(f304(a1,x34731),x34732))
% 11.41/11.17 [3477]P85(f784(f784(f242(a859),x34771),f784(f784(f89(a859),x34772),x34771)))
% 11.41/11.17 [3478]P85(f784(f784(f242(a859),x34781),f784(f784(f89(a859),x34781),x34782)))
% 11.41/11.17 [3481]E(f784(f784(f3(f869(x34811,a852)),f187(f869(x34811,a852))),x34812),f187(f869(x34811,a852)))
% 11.41/11.17 [3482]E(f784(f784(f110(f869(x34821,a852)),f249(f869(x34821,a852))),x34822),f249(f869(x34821,a852)))
% 11.41/11.17 [3483]E(f784(f784(f111(f869(x34831,a852)),f187(f869(x34831,a852))),x34832),f187(f869(x34831,a852)))
% 11.41/11.17 [3488]E(f784(f784(f251(a1,a1),x34881),f784(f88(a1),x34882)),f784(a66,f784(f784(f251(a1,a1),x34881),x34882)))
% 11.41/11.17 [3489]E(f784(f304(a1,f784(f784(f89(a1),x34891),f87(a1))),x34892),f308(a1,x34891,x34892))
% 11.41/11.17 [3499]E(f784(f784(f90(a859),x34991),f784(f784(f51(a859),x34992),x34991)),f784(f784(f3(a859),x34992),f60(a859,x34992,x34991)))
% 11.41/11.17 [3500]E(f784(f784(f90(a1),x35001),f784(f784(f51(a1),x35002),x35001)),f784(f784(f3(a1),x35002),f60(a1,x35002,x35001)))
% 11.41/11.17 [3504]E(f784(f164(a1),f169(f784(f784(f89(a1),x35041),f87(a1)),x35042)),f307(a1,x35041,x35042))
% 11.41/11.17 [3508]P85(f784(f784(f242(f869(x35081,a852)),x35082),x35082))
% 11.41/11.17 [3513]E(f784(f784(f110(f869(x35131,a852)),x35132),f784(f88(f869(x35131,a852)),x35132)),f249(f869(x35131,a852)))
% 11.41/11.17 [3514]E(f784(f784(f111(f869(x35141,a852)),x35142),f784(f88(f869(x35141,a852)),x35142)),f187(f869(x35141,a852)))
% 11.41/11.17 [3520]E(f784(f784(f3(a859),f784(f784(f3(a859),x35201),f87(a859))),x35202),f784(f784(f3(a859),x35201),f784(a160,x35202)))
% 11.41/11.17 [3525]E(f784(f784(f3(f869(x35251,a852)),f249(f869(x35251,a852))),x35252),f784(f88(f869(x35251,a852)),x35252))
% 11.41/11.17 [3526]E(f784(f784(f3(a1),f784(f113(a1),x35261)),f784(f113(a1),x35262)),f784(f113(a1),f784(f784(f89(a1),x35261),f784(f88(a1),x35262))))
% 11.41/11.17 [3538]E(f784(f164(a859),f134(a859,f784(f304(a859,x35381),f784(a160,x35382)))),f305(a859,x35381,x35382))
% 11.41/11.17 [3567]E(f784(f784(f180(f868(x35671,x35671),a852),f2(a859)),x35672),f310(x35671,f187(f869(f868(x35671,x35671),a852))))
% 11.41/11.17 [3571]P85(f784(f132(a859),f134(a859,f784(f304(a859,x35711),x35712))))
% 11.41/11.17 [3586]E(f784(f313(a1,a859,a114),f305(a1,f784(f109(a1),x35861),f784(f109(a1),x35862))),f305(a859,x35861,x35862))
% 11.41/11.17 [3596]E(f182(a859,f2(a859),f7(a859),f784(f784(f3(a859),x35961),x35962)),f784(f784(f3(a859),x35961),f784(a160,x35962)))
% 11.41/11.17 [3597]E(f784(a114,f784(f784(f3(a1),x35971),f784(f784(f89(a1),x35972),f87(a1)))),f784(f50(a1),f308(a1,x35972,x35971)))
% 11.41/11.17 [3632]E(f784(f784(f146(a859,a859),a160),f134(a859,f784(f304(a859,x36321),x36322))),f134(a859,f784(f304(a859,f784(a160,x36321)),f784(a160,x36322))))
% 11.41/11.17 [3639]E(f784(f164(a1),f169(f784(f784(f89(a1),x36391),f87(a1)),f784(f784(f3(a1),x36392),f87(a1)))),f308(a1,x36391,x36392))
% 11.41/11.17 [3653]P85(f784(f784(f242(f869(x36531,a852)),f187(f869(x36531,a852))),x36532))
% 11.41/11.17 [3657]E(f94(x36571,f784(f784(f9(x36571,x36571,a852),a343),x36572)),x36572)
% 11.41/11.17 [3658]E(f99(x36581,f784(f784(f9(x36581,x36581,a852),a343),x36582)),x36582)
% 11.41/11.17 [3662]E(f784(f164(a859),f134(a859,f784(f304(a859,f784(a160,x36621)),f784(a160,x36622)))),f307(a859,x36621,x36622))
% 11.41/11.17 [3688]E(f784(f784(f258(x36881,x36882),f249(f869(x36881,a852))),f784(f18(f869(x36882,a852),x36881),f249(f869(x36882,a852)))),f249(f869(f868(x36881,x36882),a852)))
% 11.41/11.17 [3724]E(f784(f266(x37241),f784(f784(f10(a852,a852,x37241),a341),x37242)),f784(f88(f869(x37241,a852)),f784(f266(x37241),x37242)))
% 11.41/11.17 [3727]E(f784(f266(x37271),f784(f784(f9(x37271,x37271,a852),a343),x37272)),f784(f784(f312(x37271),x37272),f187(f869(x37271,a852))))
% 11.41/11.17 [3734]E(f784(f784(f89(a1),f784(f784(f89(a1),x37341),x37341)),f784(f784(f89(a1),x37342),x37342)),f784(f784(f89(a1),f784(f784(f89(a1),x37341),x37342)),f784(f784(f89(a1),x37341),x37342)))
% 11.41/11.17 [3735]E(f784(f784(f3(a1),f784(f784(f89(a1),x37351),x37351)),f784(f784(f89(a1),x37352),x37352)),f784(f784(f89(a1),f784(f784(f3(a1),x37351),x37352)),f784(f784(f3(a1),x37351),x37352)))
% 11.41/11.17 [3749]P85(f784(f784(f242(a859),f784(f50(x37491),f784(f164(x37491),x37492))),f784(f188(f860(x37491)),x37492)))
% 11.41/11.17 [3760]E(f784(f266(x37601),f784(f784(f9(x37601,f869(x37601,a852),a852),f347(x37601)),x37602)),x37602)
% 11.41/11.17 [3776]E(f784(f784(f165(x37761),f784(f784(f3(a859),f784(f188(f860(x37761)),x37762)),f87(a859))),x37762),f121(x37761,x37762))
% 11.41/11.17 [3799]E(f182(a859,f2(a859),f784(f784(f10(a859,a859,a859),a160),f784(f246(a859),x37991)),x37992),f784(f784(f246(a859),f784(a160,x37991)),x37992))
% 11.41/11.17 [3803]E(f52(f869(x38031,a852),f784(f313(f869(f868(x38031,x38031),a852),f869(x38031,a852),f286(x38031)),x38032)),f784(f286(x38031),f52(f869(f868(x38031,x38031),a852),x38032)))
% 11.41/11.17 [3804]E(f182(a859,f784(a160,x38041),f784(f784(f10(a859,a859,a859),a160),f784(f186(a859),x38041)),x38042),f784(f784(f186(a859),f784(a160,x38041)),x38042))
% 11.41/11.17 [3806]E(f784(f784(f251(a1,a1),f784(f784(f51(a1),f784(f84(a1),x38061)),f784(f84(a1),x38062))),f60(a1,f784(f84(a1),x38061),f784(f84(a1),x38062))),f68(x38061,x38062))
% 11.41/11.17 [3826]P85(f784(f784(f242(f869(f869(x38261,a852),a852)),x38262),f784(f311(x38261),f52(f869(x38261,a852),x38262))))
% 11.41/11.17 [3857]E(f784(f784(f54(x38571,f869(x38571,a852)),x38572),f784(f784(f9(x38571,f869(x38571,a852),f869(x38571,a852)),f312(x38571)),f187(f869(x38571,a852)))),x38572)
% 11.41/11.17 [3858]E(f784(f784(f291(x38581,x38581,x38581),f784(f288(x38581,x38581),x38582)),f310(x38581,f784(f288(x38581,x38581),x38582))),f784(f288(x38581,x38581),f784(f784(f291(x38581,x38581,x38581),x38582),f310(x38581,x38582))))
% 11.41/11.17 [3926]E(f784(f164(x39261),f784(f136(f860(x39261),f860(x39261),f130(x39261),f120(x39261)),x39262)),f784(f784(f54(f860(x39261),f869(x39261,a852)),f784(f164(f860(x39261)),x39262)),f164(x39261)))
% 11.41/11.17 [3956]E(f784(f784(f110(f869(f868(x39561,x39561),a852)),f310(x39561,f187(f869(f868(x39561,x39561),a852)))),f784(f784(f291(x39561,x39561,x39561),f310(x39561,x39562)),x39562)),f310(x39561,x39562))
% 11.41/11.17 [3993]E(f784(f784(f173(x39931,x39931),x39932),x39932),f784(f784(f146(x39931,f868(x39931,x39931)),f784(f784(f20(x39931,x39931,f868(x39931,x39931)),f251(x39931,x39931)),f7(x39931))),x39932))
% 11.41/11.17 [4107]E(f784(f136(a859,f860(x41071),f784(f9(f860(x41071),a859,a859),f784(f784(f10(a859,f869(a859,a859),f860(x41071)),f186(a859)),f188(f860(x41071)))),f2(a859)),f784(f162(f860(x41071)),x41072)),f784(f188(f860(f860(x41071))),f170(x41071,x41072)))
% 11.41/11.17 [4186]E(f784(f784(f290(f868(a859,f860(x41861)),f860(x41861)),f339(a859,f860(x41861),a247,f139(x41861,x41862))),f784(f784(f20(f860(x41861),f860(x41861),f868(a859,f860(x41861))),f784(f784(f10(a859,f869(f860(x41861),f868(a859,f860(x41861))),f860(x41861)),f251(a859,f860(x41861))),f188(f860(x41861)))),f7(f860(x41861)))),f140(x41861,x41862))
% 11.41/11.17 [4309]E(f784(f266(x43091),f784(f784(f10(f869(f869(x43091,a852),a852),a852,x43091),f97(f869(x43091,a852))),f784(f784(f10(f869(f869(x43091,a852),a852),f869(f869(x43091,a852),a852),x43091),f784(f20(f869(x43091,a852),a852,a852),f784(f784(f10(a852,f869(a852,a852),f869(x43091,a852)),a348),f784(f784(f9(f869(x43091,a852),f869(f869(x43091,a852),a852),a852),f347(f869(x43091,a852))),x43092)))),f347(x43091)))),f53(f869(x43091,a852),x43092))
% 11.41/11.17 [4496]~P85(f784(f784(f243(a1),f784(f109(a1),x44961)),f784(f88(a1),f784(f109(a1),x44962))))
% 11.41/11.17 [3396]E(f784(f784(f3(a859),f784(f784(f89(a859),x33961),x33962)),x33962),x33961)
% 11.41/11.17 [3397]E(f784(f784(f3(a859),f784(f784(f89(a859),x33971),x33972)),x33971),x33972)
% 11.41/11.17 [3472]E(f784(f784(f89(a859),f784(f784(f3(a859),x34721),x34722)),x34722),f784(f784(f186(a859),x34721),x34722))
% 11.41/11.17 [3573]E(f784(f784(f90(a859),f784(f784(f51(a859),x35731),x35732)),x35732),f784(f784(f3(a859),x35731),f60(a859,x35731,x35732)))
% 11.41/11.17 [3601]E(f784(f164(a859),f134(a859,f784(f304(a859,f784(a160,x36011)),x36012))),f308(a859,x36011,x36012))
% 11.41/11.17 [3609]E(f784(f109(a1),f221(f784(a114,f784(f84(a1),x36091)),f784(a114,f784(f84(a1),x36092)))),f784(f784(a222,x36091),x36092))
% 11.41/11.17 [3611]E(f784(f784(f110(f869(x36111,a852)),f784(f88(f869(x36111,a852)),x36112)),x36112),f249(f869(x36111,a852)))
% 11.41/11.17 [3612]E(f784(f784(f111(f869(x36121,a852)),f784(f88(f869(x36121,a852)),x36122)),x36122),f187(f869(x36121,a852)))
% 11.41/11.17 [3628]P85(f784(f784(f242(a859),f784(f784(f51(a859),x36281),x36282)),x36281))
% 11.41/11.17 [3629]P85(f784(f784(f242(a859),f784(f784(f3(a859),x36291),x36292)),x36291))
% 11.41/11.17 [3654]P85(f784(f784(f243(a859),x36541),f784(a160,f784(f784(f89(a859),x36542),x36541))))
% 11.41/11.17 [3655]P85(f784(f784(f243(a859),x36551),f784(a160,f784(f784(f89(a859),x36551),x36552))))
% 11.41/11.17 [3674]E(f784(f784(f90(a859),f784(a114,f784(f84(a1),x36741))),f784(a114,f784(f84(a1),x36742))),f784(a114,f784(f84(a1),f784(f784(f90(a1),x36741),x36742))))
% 11.41/11.17 [3681]E(f784(f784(f89(a1),f784(f784(f90(a1),x36811),x36812)),f784(f784(f90(a1),x36811),x36812)),f784(f784(f90(a1),f784(f784(f89(a1),x36811),x36811)),x36812))
% 11.41/11.17 [3684]P85(f784(f784(f242(a1),f2(a1)),f784(f784(f252(a1),f784(f84(a1),x36841)),x36842)))
% 11.41/11.17 [3754]E(f784(f287(f860(x37541),f860(x37541),f150(x37541,x37542)),f784(f784(f312(f860(x37541)),f120(x37541)),f187(f869(f860(x37541),a852)))),f784(f784(f312(f860(x37541)),f120(x37541)),f187(f869(f860(x37541),a852))))
% 11.41/11.17 [3772]E(f784(f784(f110(f869(f868(x37721,x37721),a852)),f310(x37721,x37722)),f310(x37721,f187(f869(f868(x37721,x37721),a852)))),f310(x37721,x37722))
% 11.41/11.17 [3788]E(f784(f784(f51(a1),f784(f113(a1),f784(f784(f89(a1),x37881),x37881))),f784(f113(a1),f784(f784(f89(a1),x37882),x37882))),f784(f784(f51(a1),f784(f113(a1),x37881)),f784(f113(a1),x37882)))
% 11.41/11.17 [3847]E(f784(f784(f252(a1),x38471),f784(f113(a859),f784(f784(f89(a1),x38472),x38472))),f784(f784(f95(a1,a1),f784(f784(f252(a1),x38471),f784(f113(a859),x38472))),f784(f784(f20(a1,a1,a1),f90(a1)),f7(a1))))
% 11.41/11.17 [3853]E(f784(f266(f869(x38531,a852)),f784(f784(f9(f869(x38531,a852),f869(x38531,a852),a852),f242(f869(x38531,a852))),x38532)),f784(f311(x38531),x38532))
% 11.41/11.17 [3901]E(f784(f313(a1,a1,f784(f784(f9(a1,a1,a1),f89(a1)),x39011)),f784(f304(a1,f2(a1)),f784(f784(f3(a1),x39012),x39011))),f784(f304(a1,x39011),x39012))
% 11.41/11.17 [3904]P47(x39041,f784(f784(f3(f869(f868(x39041,x39041),a852)),x39042),f310(x39041,f187(f869(f868(x39041,x39041),a852)))))
% 11.41/11.17 [3924]E(f784(f188(f860(x39241)),f784(f136(f860(x39241),f860(x39241),f130(x39241),f120(x39241)),x39242)),f784(f157(a859),f784(f784(f146(f860(x39241),a859),f188(f860(x39241))),x39242)))
% 11.41/11.17 [3928]P46(x39281,f249(f869(x39281,a852)),f784(f784(f110(f869(f868(x39281,x39281),a852)),x39282),f310(x39281,f187(f869(f868(x39281,x39281),a852)))))
% 11.41/11.17 [3967]P85(f784(f784(f347(f868(x39671,x39671)),f784(f784(f251(x39671,x39671),x39672),x39672)),f310(x39671,f187(f869(f868(x39671,x39671),a852)))))
% 11.41/11.17 [3972]E(f182(a859,f2(a859),f784(f784(f10(a859,a859,a859),a160),f784(f784(f9(a859,a859,a859),f246(a859)),x39721)),x39722),f784(f784(f246(a859),x39722),f784(a160,x39721)))
% 11.41/11.17 [3975]E(f182(a859,f784(a160,x39751),f784(f784(f10(a859,a859,a859),a160),f784(f784(f9(a859,a859,a859),f186(a859)),x39751)),x39752),f784(f784(f186(a859),x39752),f784(a160,x39751)))
% 11.41/11.17 [3978]E(f784(f313(x39781,f860(x39781),f784(f784(f9(x39781,f860(x39781),f860(x39781)),f144(x39781)),f120(x39781))),x39782),f167(x39781,x39782,f784(f784(f312(f860(x39781)),f120(x39781)),f187(f869(f860(x39781),a852)))))
% 11.41/11.17 [3979]E(f784(f784(f110(f869(f868(x39791,x39791),a852)),f784(f784(f291(x39791,x39791,x39791),x39792),f310(x39791,x39792))),f310(x39791,f187(f869(f868(x39791,x39791),a852)))),f310(x39791,x39792))
% 11.41/11.17 [3987]P85(f784(f784(f242(f869(f868(x39871,x39871),a852)),f270(x39871,x39872)),f784(f784(f258(x39871,x39871),x39872),f784(f18(f869(x39871,a852),x39871),x39872))))
% 11.41/11.17 [3991]E(f784(f313(a1,a859,a114),f784(f784(f110(f869(a1,a852)),f784(f313(a859,a1,f109(a1)),x39911)),f784(f313(a859,a1,f109(a1)),x39912))),f784(f784(f110(f869(a859,a852)),x39911),x39912))
% 11.41/11.17 [3992]E(f784(f313(a1,a859,a114),f784(f784(f111(f869(a1,a852)),f784(f313(a859,a1,f109(a1)),x39921)),f784(f313(a859,a1,f109(a1)),x39922))),f784(f784(f111(f869(a859,a852)),x39921),x39922))
% 11.41/11.17 [3996]E(f784(f266(x39961),f784(f784(f10(a852,a852,x39961),a341),f784(f784(f9(x39961,f869(x39961,a852),a852),f347(x39961)),x39962))),f784(f88(f869(x39961,a852)),x39962))
% 11.41/11.17 [4023]E(f784(f136(f860(x40231),f860(x40231),f130(x40231),f120(x40231)),f784(f784(f146(f860(x40231),f860(x40231)),f162(x40231)),f784(f162(f860(x40231)),x40232))),f784(f162(x40231),f784(f136(f860(x40231),f860(x40231),f130(x40231),f120(x40231)),x40232)))
% 11.41/11.17 [4050]E(f784(f784(f54(a859,f869(f868(x40501,x40501),a852)),f249(f869(a859,a852))),f784(f784(f9(a859,f869(f868(x40501,x40501),a852),f869(f868(x40501,x40501),a852)),f180(f868(x40501,x40501),a852)),x40502)),f310(x40501,x40502))
% 11.41/11.17 [4072]E(f94(x40721,f784(f784(f10(f869(x40721,a852),a852,x40721),f784(a343,x40722)),f784(f784(f9(x40721,f869(x40721,a852),f869(x40721,a852)),f312(x40721)),f187(f869(x40721,a852))))),f316(x40721,x40722))
% 11.41/11.17 [4095]E(f784(f784(f110(f869(f868(x40951,x40951),a852)),x40952),f784(f784(f291(x40951,x40951,x40951),f784(f784(f291(x40951,x40951,x40951),x40952),f310(x40951,x40952))),x40952)),f784(f784(f291(x40951,x40951,x40951),x40952),f310(x40951,x40952)))
% 11.41/11.17 [4117]P85(f784(f784(f242(f869(f868(x41171,x41171),a852)),f784(f784(f291(x41171,x41171,x41171),x41172),f310(x41171,x41172))),f784(f784(f258(x41171,x41171),f784(f286(x41171),x41172)),f784(f18(f869(x41171,a852),x41171),f784(f286(x41171),x41172)))))
% 11.41/11.17 [4162]E(f784(f266(f860(x41621)),f784(f784(f9(f860(x41621),f869(x41621,a852),a852),f784(f784(f10(f869(x41621,a852),f869(f869(x41621,a852),a852),f860(x41621)),f242(f869(x41621,a852))),f164(x41621))),x41622)),f152(x41621,x41622))
% 11.41/11.17 [4174]E(f784(f148(f860(x41741),x41741,f120(x41741),f784(f784(f10(f860(x41741),f869(f860(x41741),f860(x41741)),x41741),f784(f9(f860(x41741),f860(x41741),f860(x41741)),f130(x41741))),f784(f784(f9(x41741,f860(x41741),f860(x41741)),f144(x41741)),f120(x41741)))),x41742),f784(f161(x41741),x41742))
% 11.41/11.17 [4213]P26(f869(x42131,x42132),f869(f868(x42131,x42132),a852),f784(f784(f10(f869(f868(x42131,x42132),a852),f869(f868(x42131,x42132),a852),f869(x42131,x42132)),f266(f868(x42131,x42132))),f784(f784(f10(f869(x42131,f869(x42132,a852)),f869(f868(x42131,x42132),a852),f869(x42131,x42132)),f261(x42131,x42132,a852)),f784(f10(x42132,f869(x42132,a852),x42131),f784(f9(x42132,x42132,a852),a343)))),f249(f869(f869(x42131,x42132),a852)))
% 11.41/11.17 [4218]E(f60(a1,f784(f113(a1),f784(f784(f89(a1),x42181),x42181)),f784(f113(a1),f784(f784(f89(a1),x42182),x42182))),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f60(a1,f784(f113(a1),x42181),f784(f113(a1),x42182))))
% 11.41/11.17 [4259]E(f784(f784(f54(x42591,f869(f868(x42591,x42591),a852)),x42592),f784(f784(f9(x42591,f869(f868(x42591,x42591),a852),f869(f868(x42591,x42591),a852)),f784(f784(f10(f868(x42591,x42591),f869(f869(f868(x42591,x42591),a852),f869(f868(x42591,x42591),a852)),x42591),f312(f868(x42591,x42591))),f784(f784(f20(x42591,x42591,f868(x42591,x42591)),f251(x42591,x42591)),f7(x42591)))),f187(f869(f868(x42591,x42591),a852)))),f270(x42591,x42592))
% 11.41/11.17 [4267]E(f208(x42671,f784(f784(f251(a1,a1),f784(f88(a1),f784(f784(f82(f868(a1,a1),a1,x42671,f250(a1,a1)),f217(x42671)),x42672))),f784(f784(f82(f868(a1,a1),a1,x42671,f260(a1,a1)),f217(x42671)),x42672))),f231(x42671,x42672))
% 11.41/11.17 [4347]E(f784(f266(f869(x43471,a852)),f784(f784(f10(f869(f869(x43471,a852),a852),a852,f869(x43471,a852)),f96(f869(x43471,a852))),f784(f784(f9(f869(x43471,a852),f869(f869(x43471,a852),a852),f869(f869(x43471,a852),a852)),f784(f784(f10(f869(f869(x43471,a852),f869(a852,a852)),f869(f869(f869(x43471,a852),a852),f869(f869(x43471,a852),a852)),f869(x43471,a852)),f20(f869(x43471,a852),a852,a852)),f784(f784(f10(f869(f869(x43471,a852),a852),f869(f869(x43471,a852),f869(a852,a852)),f869(x43471,a852)),f784(f10(a852,f869(a852,a852),f869(x43471,a852)),a344)),f784(f784(f9(f869(x43471,a852),f869(f869(x43471,a852),f869(x43471,a852)),f869(f869(x43471,a852),a852)),f784(f784(f10(f869(f869(x43471,a852),a852),f869(f869(f869(x43471,a852),f869(x43471,a852)),f869(f869(x43471,a852),a852)),f869(x43471,a852)),f10(f869(x43471,a852),a852,f869(x43471,a852))),a343)),f88(f869(x43471,a852)))))),f784(f784(f10(f869(f869(x43471,a852),a852),a852,f869(x43471,a852)),f784(f347(f869(x43471,a852)),x43472)),f311(x43471))))),f784(f311(x43471),f784(f88(f869(x43471,a852)),x43472)))
% 11.41/11.17 [4492]~E(f784(f784(f89(a1),x44921),x44921),f784(f784(f3(a1),f784(f784(f89(a1),x44922),x44922)),a106))
% 11.41/11.17 [4493]~E(f784(f784(f89(a1),x44931),x44931),f784(f784(f3(a1),f784(f784(f89(a1),x44932),x44932)),a106))
% 11.41/11.17 [4498]~P85(f784(f784(f243(a859),f784(f784(f89(a859),x44981),x44982)),x44982))
% 11.41/11.17 [4499]~P85(f784(f784(f243(a859),f784(f784(f89(a859),x44991),x44992)),x44991))
% 11.41/11.17 [3689]E(f784(f784(f3(a859),x36891),f784(f784(f90(a859),f784(f784(f51(a859),x36891),x36892)),x36892)),f60(a859,x36891,x36892))
% 11.41/11.17 [3690]E(f784(f784(f3(a1),x36901),f784(f784(f90(a1),f784(f784(f51(a1),x36901),x36902)),x36902)),f60(a1,x36901,x36902))
% 11.41/11.17 [3725]E(f784(f784(f146(a859,x37251),f784(f155(x37251),x37252)),f134(a859,f784(f304(a859,f2(a859)),f784(f188(f860(x37251)),x37252)))),x37252)
% 11.41/11.17 [3784]E(f784(f287(x37841,x37841,f310(x37841,f187(f869(f868(x37841,x37841),a852)))),x37842),x37842)
% 11.41/11.17 [3905]E(f310(x39051,f784(f784(f3(f869(f868(x39051,x39051),a852)),x39052),f310(x39051,f187(f869(f868(x39051,x39051),a852))))),f310(x39051,x39052))
% 11.41/11.17 [3906]E(f310(x39061,f784(f784(f110(f869(f868(x39061,x39061),a852)),x39062),f310(x39061,f187(f869(f868(x39061,x39061),a852))))),f310(x39061,x39062))
% 11.41/11.17 [3960]E(f784(f784(f3(a1),f784(f784(f3(a1),f784(f784(f89(a1),x39601),x39601)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),x39602),x39602)),a106)),f784(f784(f89(a1),f784(f784(f3(a1),x39601),x39602)),f784(f784(f3(a1),x39601),x39602)))
% 11.41/11.17 [4001]E(f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f89(a1),x40011),x40012)),f784(f784(f89(a1),x40011),x40012))),a106),f784(f784(f89(a1),f784(f784(f89(a1),x40011),x40011)),f784(f784(f3(a1),f784(f784(f89(a1),x40012),x40012)),a106)))
% 11.41/11.17 [4027]E(f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),x40271),x40271)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),x40272),x40272)),a106)),f784(f784(f89(a1),f784(f784(f89(a1),x40271),f784(f784(f3(a1),x40272),a106))),f784(f784(f89(a1),x40271),f784(f784(f3(a1),x40272),a106))))
% 11.41/11.17 [4038]E(f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f89(a1),x40381),x40382)),f784(f784(f89(a1),x40381),x40382))),a106),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),x40381),x40381)),a106)),f784(f784(f89(a1),x40382),x40382)))
% 11.41/11.17 [4039]E(f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),x40391),x40392)),f784(f784(f3(a1),x40391),x40392))),a106),f784(f784(f3(a1),f784(f784(f3(a1),f784(f784(f89(a1),x40391),x40391)),a106)),f784(f784(f89(a1),x40392),x40392)))
% 11.41/11.17 [4092]E(f784(f109(a1),f784(f784(f51(a859),f784(f784(f90(a859),f784(a114,f784(f84(a1),x40921))),f784(a114,f784(f84(a1),x40922)))),f221(f784(a114,f784(f84(a1),x40921)),f784(a114,f784(f84(a1),x40922))))),f223(x40921,x40922))
% 11.41/11.17 [4137]E(f784(f784(f263(f868(a108,a108),a108,f868(a108,a108),f868(x41371,f868(a108,a108))),f274(f784(a5,f784(f188(f860(x41371)),x41372)))),f784(f784(f10(x41371,f869(f868(a108,a108),f868(x41371,f868(a108,a108))),a108),f251(x41371,f868(a108,a108))),f784(f784(f10(a859,x41371,a108),f784(f155(x41371),x41372)),a22))),f280(x41371,x41372))
% 11.41/11.17 [4219]E(f784(f136(a859,f860(x42191),f784(f9(f860(x42191),a859,a859),f784(f784(f10(a859,f869(a859,a859),f860(x42191)),f186(a859)),f188(f860(x42191)))),f2(a859)),f784(f162(f860(x42191)),f170(x42191,x42192))),f784(f188(f860(f860(x42191))),f784(f131(f860(x42191),f784(f784(f10(a852,a852,f860(x42191)),a341),f784(f784(f9(f860(x42191),f860(x42191),a852),a343),f120(x42191)))),x42192)))
% 11.41/11.17 [4225]E(f784(f784(f54(a859,f869(x42251,a852)),f249(f869(a859,a852))),f784(f784(f9(a859,f869(a859,f869(x42251,a852)),f869(x42251,a852)),f784(f784(f10(f869(a859,a852),f869(f869(a859,f869(x42251,a852)),f869(x42251,a852)),a859),f54(a859,f869(x42251,a852))),f304(a859,f2(a859)))),x42252)),f784(f784(f54(a859,f869(x42251,a852)),f249(f869(a859,a852))),x42252))
% 11.41/11.17 [4244]P85(f784(f71(a859),f784(f266(a859),f784(f784(f20(a859,a852,a852),f784(f784(f10(a852,f869(a852,a852),a859),a344),x42441)),f784(f784(f9(a859,a859,a852),f243(a859)),x42442)))))
% 11.41/11.17 [4356]E(f784(f266(f868(f860(x43561),f860(x43561))),f784(f261(f860(x43561),f860(x43561),a852),f784(f784(f20(f860(x43561),f869(f860(x43561),a852),f869(f860(x43561),a852)),f784(f784(f10(f869(f860(x43561),f869(a852,a852)),f869(f869(f860(x43561),a852),f869(f860(x43561),a852)),f860(x43561)),f20(f860(x43561),a852,a852)),f784(f784(f10(f869(f860(x43561),a852),f869(f860(x43561),f869(a852,a852)),f860(x43561)),f784(f10(a852,f869(a852,a852),f860(x43561)),a345)),f784(f784(f9(f860(x43561),f869(f860(x43561),a859),f869(f860(x43561),a852)),f784(f784(f10(f869(a859,a852),f869(f869(f860(x43561),a859),f869(f860(x43561),a852)),f860(x43561)),f10(a859,a852,f860(x43561))),f784(f784(f10(a859,f869(a859,a852),f860(x43561)),f243(a859)),f188(f860(x43561))))),f188(f860(x43561)))))),f784(f784(f20(f860(x43561),f869(f860(x43561),a852),f869(f860(x43561),a852)),f784(f784(f10(f869(f860(x43561),f869(a852,a852)),f869(f869(f860(x43561),a852),f869(f860(x43561),a852)),f860(x43561)),f20(f860(x43561),a852,a852)),f784(f784(f10(f869(f860(x43561),a852),f869(f860(x43561),f869(a852,a852)),f860(x43561)),f784(f10(a852,f869(a852,a852),f860(x43561)),a344)),f784(f784(f9(f860(x43561),f869(f860(x43561),a859),f869(f860(x43561),a852)),f784(f784(f10(f869(a859,a852),f869(f869(f860(x43561),a859),f869(f860(x43561),a852)),f860(x43561)),f10(a859,a852,f860(x43561))),f784(f784(f10(a859,f869(a859,a852),f860(x43561)),a343),f188(f860(x43561))))),f188(f860(x43561)))))),f784(f784(f9(f860(x43561),f869(f868(f860(x43561),f860(x43561)),a852),f869(f860(x43561),a852)),f784(f784(f10(f869(f860(x43561),f869(f869(f868(f860(x43561),f860(x43561)),a852),a852)),f869(f869(f868(f860(x43561),f860(x43561)),a852),f869(f860(x43561),a852)),f860(x43561)),f9(f860(x43561),f869(f868(f860(x43561),f860(x43561)),a852),a852)),f784(f784(f10(f869(f860(x43561),f868(f860(x43561),f860(x43561))),f869(f860(x43561),f869(f869(f868(f860(x43561),f860(x43561)),a852),a852)),f860(x43561)),f784(f10(f868(f860(x43561),f860(x43561)),f869(f869(f868(f860(x43561),f860(x43561)),a852),a852),f860(x43561)),f347(f868(f860(x43561),f860(x43561))))),f251(f860(x43561),f860(x43561))))),f139(x43561,x43562)))))),f140(x43561,x43562))
% 11.41/11.17 [4030]E(f784(f784(f89(a1),f784(f784(f89(a1),f784(f784(f90(a1),x40301),x40302)),f784(f784(f90(a1),x40301),x40302))),x40302),f784(f784(f90(a1),f784(f784(f3(a1),f784(f784(f89(a1),x40301),x40301)),a106)),x40302))
% 11.41/11.17 [4135]E(f784(a114,f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x41351),x41352)),f187(f869(f868(a859,a859),a852)))))),f784(f784(f3(a859),x41351),x41352))
% 11.41/11.17 [4140]E(f784(f784(f291(x41401,x41401,x41401),f784(f784(f110(f869(f868(x41401,x41401),a852)),x41402),f310(x41401,f187(f869(f868(x41401,x41401),a852))))),f310(x41401,f784(f784(f110(f869(f868(x41401,x41401),a852)),x41402),f310(x41401,f187(f869(f868(x41401,x41401),a852)))))),f310(x41401,x41402))
% 11.41/11.17 [4179]E(f275(x41791,f784(f131(f868(a108,x41791),f784(f261(a108,x41791,a852),f784(f784(f10(a852,f869(x41791,a852),a108),f18(a852,x41791)),f784(f243(a108),f2(a108))))),x41792)),f275(x41791,x41792))
% 11.41/11.17 [4180]E(f273(x41801,f784(f131(f868(a108,x41801),f784(f261(a108,x41801,a852),f784(f784(f10(a852,f869(x41801,a852),a108),f18(a852,x41801)),f784(f243(a108),f2(a108))))),x41802)),f273(x41801,x41802))
% 11.41/11.17 [4182]E(f784(f88(a1),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x41821),x41822)),f187(f869(f868(a859,a859),a852)))))),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x41822),x41821)),f187(f869(f868(a859,a859),a852))))))
% 11.41/11.17 [4256]E(f784(f784(f95(a1,a859),f784(f113(a1),f784(f784(f89(a1),x42561),a106))),f784(f784(f20(a1,a859,a859),f784(f784(f9(a1,a859,f869(a859,a859)),f784(f784(f10(a852,f869(a859,f869(a859,a859)),a1),f105(a859)),a193)),f2(a859))),f784(f784(f10(a859,a859,a1),a160),f784(f784(f10(a859,a859,a1),f784(f246(a859),x42562)),a114)))),f784(f784(f246(a859),f784(a160,x42562)),f784(f113(a859),x42561)))
% 11.41/11.17 [4257]E(f784(f784(f95(a1,a859),f784(f113(a1),f784(f784(f89(a1),x42571),a106))),f784(f784(f20(a1,a859,a859),f784(f784(f9(a1,a859,f869(a859,a859)),f784(f784(f10(a852,f869(a859,f869(a859,a859)),a1),f105(a859)),a193)),f784(a160,x42572))),f784(f784(f10(a859,a859,a1),a160),f784(f784(f10(a859,a859,a1),f784(f186(a859),x42572)),a114)))),f784(f784(f186(a859),f784(a160,x42572)),f784(f113(a859),x42571)))
% 11.41/11.17 [4277]E(f784(f136(f860(x42771),f860(x42771),f130(x42771),f120(x42771)),f784(f784(f146(f860(x42771),f860(x42771)),f148(f860(x42771),x42771,f120(x42771),f784(f784(f10(f860(x42771),f869(f860(x42771),f860(x42771)),x42771),f18(f860(x42771),f860(x42771))),f784(f784(f9(x42771,f860(x42771),f860(x42771)),f144(x42771)),f120(x42771))))),x42772)),f784(f784(f146(f860(x42771),x42771),f135(x42771)),f784(f131(f860(x42771),f784(f784(f10(a852,a852,f860(x42771)),a341),f784(f784(f9(f860(x42771),f860(x42771),a852),a343),f120(x42771)))),x42772)))
% 11.41/11.17 [4337]E(f784(f261(a1,a1,a852),f784(f784(f9(a1,f869(a1,a852),f869(a1,a852)),f784(f784(f10(f869(a1,f869(a852,a852)),f869(f869(a1,a852),f869(a1,a852)),a1),f20(a1,a852,a852)),f784(f784(f10(f869(a1,a852),f869(a1,f869(a852,a852)),a1),f784(f10(a852,f869(a852,a852),a1),a344)),f784(f784(f10(f869(a1,a1),f869(a1,a852),a1),f784(f10(a1,a852,a1),f784(a343,x43371))),f784(f784(f10(a1,f869(a1,a1),a1),f89(a1)),f784(f90(a1),x43372)))))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f784(f10(a852,a852,a1),f784(a348,f784(f784(f243(a1),f2(a1)),x43372))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),f2(a1)))),f784(f784(f9(a1,a1,a852),f243(a1)),x43372))))),f784(f784(f10(a852,a852,a1),f784(a348,f784(a341,f784(f784(f243(a1),f2(a1)),x43372)))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f243(a1),x43372))),f784(f784(f9(a1,a1,a852),f242(a1)),f2(a1))))))),f64(x43371,x43372))
% 11.41/11.17 [4339]E(f784(f266(x43391),f784(f784(f10(f869(a859,a852),a852,x43391),f96(a859)),f784(f784(f9(x43391,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),x43391),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),x43391),f784(f10(a852,f869(a852,a852),a859),a344)),f784(f784(f9(x43391,f869(a859,x43391),f869(a859,a852)),f784(f784(f10(f869(x43391,a852),f869(f869(a859,x43391),f869(a859,a852)),x43391),f10(x43391,a852,a859)),a343)),f784(f155(x43391),x43392))))),f784(f784(f9(a859,a859,a852),f243(a859)),f784(f188(f860(x43391)),x43392))))),f784(f164(x43391),x43392))
% 11.41/11.17 [4152]E(f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),x41521),a106)),x41522)),f784(f784(f3(a1),f784(f784(f89(a1),x41521),a106)),x41522))),a106),f784(f784(f3(a1),f784(f784(f89(a1),x41521),x41521)),f784(f784(f3(a1),f784(f784(f89(a1),x41522),x41522)),a106)))
% 11.41/11.17 [4272]E(f784(f136(f860(f860(x42721)),f860(f860(x42721)),f130(f860(x42721)),f120(f860(x42721))),f784(f784(f146(f860(x42721),f860(f860(x42721))),f148(f860(f860(x42721)),x42721,f120(f860(x42721)),f784(f18(f869(f860(x42721),f860(f860(x42721))),x42721),f784(f784(f9(f860(x42721),f860(f860(x42721)),f860(f860(x42721))),f144(f860(x42721))),f120(f860(x42721)))))),x42722)),f784(f784(f146(f860(x42721),f860(x42721)),f163(x42721)),f784(f131(f860(x42721),f784(f784(f10(a852,a852,f860(x42721)),a341),f784(f784(f9(f860(x42721),f860(x42721),a852),a343),f120(x42721)))),x42722)))
% 11.41/11.17 [4282]E(f784(f784(f95(a1,a859),f784(f113(a1),f784(f784(f89(a1),x42821),a106))),f784(f784(f20(a1,a859,a859),f784(f784(f9(a1,a859,f869(a859,a859)),f784(f784(f10(a852,f869(a859,f869(a859,a859)),a1),f105(a859)),a193)),f2(a859))),f784(f784(f10(a859,a859,a1),a160),f784(f784(f9(a1,a859,a859),f784(f784(f10(a859,f869(a859,a859),a1),f246(a859)),a114)),x42822)))),f784(f784(f246(a859),f784(f113(a859),x42821)),f784(a160,x42822)))
% 11.41/11.17 [4283]E(f784(f784(f95(a1,a859),f784(f113(a1),f784(f784(f89(a1),x42831),a106))),f784(f784(f20(a1,a859,a859),f784(f784(f9(a1,a859,f869(a859,a859)),f784(f784(f10(a852,f869(a859,f869(a859,a859)),a1),f105(a859)),a193)),f784(a160,x42832))),f784(f784(f10(a859,a859,a1),a160),f784(f784(f9(a1,a859,a859),f784(f784(f10(a859,f869(a859,a859),a1),f186(a859)),a114)),x42832)))),f784(f784(f186(a859),f784(f113(a859),x42831)),f784(a160,x42832)))
% 11.41/11.17 [4271]E(f784(f261(x42711,x42711,a852),f784(f784(f20(x42711,a852,f869(x42711,a852)),f784(f784(f10(f869(x42711,f869(a852,a852)),f869(a852,f869(x42711,a852)),x42711),f9(x42711,a852,a852)),f784(f784(f10(f869(x42711,a852),f869(x42711,f869(a852,a852)),x42711),f784(f10(a852,f869(a852,a852),x42711),a344)),a343))),x42712)),f270(x42711,x42712))
% 11.41/11.17 [4315]E(f784(f784(f51(a859),x43151),f784(f784(f89(a859),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),x43152)),f784(f784(f51(a859),x43151),f784(a160,f784(a160,f784(a160,x43152)))))
% 11.41/11.17 [4316]E(f60(a859,x43161,f784(f784(f89(a859),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),x43162)),f60(a859,x43161,f784(a160,f784(a160,f784(a160,x43162)))))
% 11.41/11.17 [4317]E(f60(a859,f784(f784(f89(a859),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),x43171),x43172),f60(a859,f784(a160,f784(a160,f784(a160,x43171))),x43172))
% 11.41/11.17 [4330]E(f128(f784(x43301,f784(f784(f90(a108),f784(f113(a108),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),x43302))),f784(f205(x43301),x43302))
% 11.41/11.17 [4331]E(f784(f784(f51(a859),f784(f784(f89(a859),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),x43311)),x43312),f784(f784(f51(a859),f784(a160,f784(a160,f784(a160,x43311)))),x43312))
% 11.41/11.17 [3511]P26(x35111,f870(x35112,x35111),f326(x35111,x35112),x35113)
% 11.41/11.17 [3512]P26(x35121,f870(x35121,x35122),f322(x35121,x35122),x35123)
% 11.41/11.17 [4401]~E(f30(x44011,x44012),f784(a29,x44013))
% 11.41/11.17 [4402]~E(f38(x44021,x44022),f784(a29,x44023))
% 11.41/11.17 [4403]~E(f37(x44031,x44032),f784(a29,x44033))
% 11.41/11.17 [4404]~E(f784(a29,x44041),f30(x44042,x44043))
% 11.41/11.17 [4405]~E(f784(a29,x44051),f38(x44052,x44053))
% 11.41/11.17 [4406]~E(f784(a29,x44061),f37(x44062,x44063))
% 11.41/11.17 [4422]~E(f33(x44221,x44222,x44223),a25)
% 11.41/11.17 [4423]~E(f35(x44231,x44232,x44233),a25)
% 11.41/11.17 [4424]~E(f34(x44241,x44242,x44243),a25)
% 11.41/11.17 [4425]~E(f33(x44251,x44252,x44253),a25)
% 11.41/11.17 [4426]~E(f35(x44261,x44262,x44263),a25)
% 11.41/11.17 [4427]~E(f34(x44271,x44272,x44273),a25)
% 11.41/11.17 [3121]E(f784(f204(x31211,x31212),x31213),f125(x31211,x31212))
% 11.41/11.17 [3122]E(f784(f192(x31221,x31222),x31223),f126(x31221,x31222))
% 11.41/11.17 [3214]E(f784(f784(f146(x32141,x32142),x32143),f120(x32141)),f120(x32142))
% 11.41/11.17 [3215]E(f784(f784(f206(x32151,x32152),x32153),f190(x32151)),f190(x32152))
% 11.41/11.17 [3235]E(f36(f33(x32351,x32352,x32353)),f2(a859))
% 11.41/11.17 [3254]E(f784(f181(x32541,x32542,x32543),f2(a859)),x32542)
% 11.41/11.17 [3255]E(f784(f188(a853),f33(x32551,x32552,x32553)),f2(a859))
% 11.41/11.17 [3256]E(f784(f784(f173(x32561,x32562),x32563),f120(x32562)),f120(f868(x32561,x32562)))
% 11.41/11.17 [3293]E(f94(x32931,f72(x32931,x32932,x32933)),f784(f73(x32931,x32932),x32933))
% 11.41/11.17 [3364]E(f784(f250(f860(x33641),f860(x33641)),f158(x33641,x33642,x33643)),f784(f131(x33641,x33642),x33643))
% 11.41/11.17 [3441]E(f19(x34411,x34412,x34413,f2(a108)),x34412)
% 11.41/11.17 [3442]E(f21(x34421,x34422,x34423,f2(a108)),x34422)
% 11.41/11.17 [3443]E(f182(x34431,x34432,x34433,f2(a859)),x34432)
% 11.41/11.17 [3450]E(f156(x34501,x34502,x34503,f120(x34501)),f120(x34502))
% 11.41/11.17 [3457]E(f784(f784(f155(x34571),f784(f784(f144(x34571),x34572),x34573)),f2(a859)),x34572)
% 11.41/11.17 [3510]P26(x35101,x35102,x35103,f187(f869(x35101,a852)))
% 11.41/11.17 [3605]E(f272(x36051,x36052,x36053),f784(f251(f869(a108,f869(a852,f864(f861(x36051)))),f868(a108,a108)),f56(x36051)))
% 11.41/11.17 [3664]E(f784(f82(x36641,x36642,x36641,x36643),f41(x36641)),x36643)
% 11.41/11.17 [3838]P85(f784(f784(f347(f868(x38381,x38381)),f784(f784(f251(x38381,x38381),x38382),x38382)),f310(x38381,x38383)))
% 11.41/11.17 [4502]~P85(f784(f784(f347(f868(f860(x45021),f860(x45021))),f784(f784(f251(f860(x45021),f860(x45021)),x45022),f120(x45021))),f139(x45021,x45023)))
% 11.41/11.17 [4503]~P85(f784(f784(f347(f868(f860(x45031),f860(x45031))),f784(f784(f251(f860(x45031),f860(x45031)),x45032),f120(x45031))),f141(x45031,x45033)))
% 11.41/11.17 [4504]~P85(f784(f784(f347(f868(f860(x45041),f860(x45041))),f784(f784(f251(f860(x45041),f860(x45041)),x45042),f120(x45041))),f149(x45041,x45043)))
% 11.41/11.17 [4505]~P85(f784(f784(f347(f868(f860(x45051),f860(x45051))),f784(f784(f251(f860(x45051),f860(x45051)),f120(x45051)),x45052)),f139(x45051,x45053)))
% 11.41/11.17 [4506]~P85(f784(f784(f347(f868(f860(x45061),f860(x45061))),f784(f784(f251(f860(x45061),f860(x45061)),f120(x45061)),x45062)),f149(x45061,x45063)))
% 11.41/11.17 [3190]E(f784(f784(f207(x31901),x31902),x31903),f208(x31901,f220(x31902,x31903)))
% 11.41/11.17 [3244]E(f784(f288(x32441,x32442),f784(f288(x32442,x32441),x32443)),x32443)
% 11.41/11.17 [3261]E(f325(x32611,x32612,f784(f322(x32611,x32612),x32613)),x32613)
% 11.41/11.17 [3262]E(f328(x32621,x32622,f784(f326(x32622,x32621),x32623)),x32623)
% 11.41/11.17 [3268]E(f784(f784(f173(x32681,x32682),f120(x32681)),x32683),f120(f868(x32681,x32682)))
% 11.41/11.17 [3271]E(f166(x32711,x32712,f784(f267(a859),x32713)),f784(f784(f165(x32711),x32713),x32712))
% 11.41/11.17 [3285]E(f784(f188(f870(x32851,x32852)),f784(f326(x32852,x32851),x32853)),f2(a859))
% 11.41/11.17 [3286]E(f784(f188(f870(x32861,x32862)),f784(f322(x32861,x32862),x32863)),f2(a859))
% 11.41/11.17 [3289]E(f784(f271(x32891,x32892),f784(f288(x32892,x32891),x32893)),f784(f269(x32892,x32891),x32893))
% 11.41/11.17 [3291]E(f784(f269(x32911,x32912),f784(f288(x32912,x32911),x32913)),f784(f271(x32912,x32911),x32913))
% 11.41/11.17 [3292]E(f784(f271(x32921,x32922),f784(f288(x32922,x32921),x32923)),f784(f269(x32922,x32921),x32923))
% 11.41/11.17 [3309]E(f784(f131(x33091,x33092),f784(f162(x33091),x33093)),f784(f162(x33091),f784(f131(x33091,x33092),x33093)))
% 11.41/11.17 [3322]E(f784(f784(f133(x33221),x33222),f784(f163(x33221),x33223)),f784(f784(f133(x33221),f784(a160,x33222)),x33223))
% 11.41/11.17 [3340]E(f36(f34(x33401,x33402,x33403)),f784(f784(f89(a859),f36(x33403)),f784(a160,f2(a859))))
% 11.41/11.17 [3341]E(f784(f313(x33411,x33412,x33413),f187(f869(x33411,a852))),f187(f869(x33412,a852)))
% 11.41/11.17 [3342]E(f784(f287(x33421,x33422,x33423),f187(f869(x33421,a852))),f187(f869(x33422,a852)))
% 11.41/11.17 [3343]E(f784(f315(x33431,x33432,x33433),f249(f869(x33432,a852))),f249(f869(x33431,a852)))
% 11.41/11.17 [3344]E(f784(f315(x33441,x33442,x33443),f187(f869(x33442,a852))),f187(f869(x33441,a852)))
% 11.41/11.17 [3381]E(f238(x33811,x33812,f784(f237(x33811),x33813)),f784(f784(f89(a859),f784(x33812,x33813)),f784(a160,f2(a859))))
% 11.41/11.17 [3461]E(f784(f188(a853),f34(x34611,x34612,x34613)),f784(f784(f89(a859),f784(f188(a853),x34613)),f784(a160,f2(a859))))
% 11.41/11.17 [3462]E(f784(f313(f868(x34621,x34622),x34622,f260(x34621,x34622)),x34623),f784(f269(x34621,x34622),x34623))
% 11.41/11.17 [3463]E(f784(f313(f868(x34631,x34632),x34631,f250(x34631,x34632)),x34633),f784(f271(x34631,x34632),x34633))
% 11.41/11.17 [3536]E(f784(f784(f251(x35361,x35362),f784(f250(x35361,x35362),x35363)),f784(f260(x35361,x35362),x35363)),x35363)
% 11.41/11.17 [3537]E(f784(f784(f251(x35371,x35372),f784(f250(x35371,x35372),x35373)),f784(f260(x35371,x35372),x35373)),x35373)
% 11.41/11.17 [3544]E(f784(f784(f261(x35441,x35442,x35441),f18(x35441,x35442)),x35443),f784(f250(x35441,x35442),x35443))
% 11.41/11.17 [3563]E(f176(x35631,x35632,x35633,f784(f18(f864(x35632),x35631),f190(x35632))),x35633)
% 11.41/11.17 [3564]E(f176(x35641,x35642,f784(f18(f864(x35642),x35641),f190(x35642)),x35643),x35643)
% 11.41/11.17 [3618]E(f36(f35(x36181,x36182,x36183)),f784(f784(f89(a859),f784(f784(f89(a859),f36(x36182)),f36(x36183))),f784(a160,f2(a859))))
% 11.41/11.17 [3668]E(f784(f82(x36681,x36681,x36682,f41(x36681)),x36683),x36683)
% 11.41/11.17 [3752]P85(f784(f71(x37521),f175(x37521,x37522,f172(x37521,x37522,x37523))))
% 11.41/11.17 [3774]P85(f784(f784(f194(f30(x37741,x37742)),x37743),f784(f784(f784(a196,x37743),x37741),f784(x37742,x37743))))
% 11.41/11.17 [3775]P85(f784(f784(f194(f30(x37751,x37752)),x37753),f784(f784(f784(a196,x37753),x37751),f784(x37752,x37753))))
% 11.41/11.17 [3777]E(f784(f188(a853),f35(x37771,x37772,x37773)),f784(f784(f89(a859),f784(f784(f89(a859),f784(f188(a853),x37772)),f784(f188(a853),x37773))),f784(a160,f2(a859))))
% 11.41/11.17 [3848]P85(f784(f784(f242(f869(x38481,a852)),f784(f164(x38481),f784(f131(x38481,x38482),x38483))),f784(f164(x38481),x38483)))
% 11.41/11.17 [3892]P85(f784(f784(f242(f869(x38921,a852)),f784(f164(x38921),f784(f784(f165(x38921),x38922),x38923))),f784(f164(x38921),x38923)))
% 11.41/11.17 [3893]P85(f784(f784(f242(f869(x38931,a852)),f784(f164(x38931),f784(f784(f133(x38931),x38932),x38933))),f784(f164(x38931),x38933)))
% 11.41/11.17 [3897]P85(f784(f784(f242(f869(x38971,a852)),f784(f164(x38971),f154(x38971,x38972,x38973))),f784(f164(x38971),x38973)))
% 11.41/11.17 [3898]P85(f784(f784(f242(f869(x38981,a852)),f784(f164(x38981),f166(x38981,x38982,x38983))),f784(f164(x38981),x38982)))
% 11.41/11.17 [3921]P26(f868(x39211,x39212),f868(x39212,x39211),f784(f261(x39211,x39212,f868(x39212,x39211)),f784(f9(x39212,x39211,f868(x39212,x39211)),f251(x39212,x39211))),x39213)
% 11.41/11.17 [3933]E(f784(f784(f784(f180(f860(x39331),f860(x39331)),f60(a859,x39332,f784(f188(f860(x39331)),x39333))),f161(x39331)),x39333),f784(f784(f784(f180(f860(x39331),f860(x39331)),x39332),f161(x39331)),x39333))
% 11.41/11.17 [3973]E(f784(f82(f860(x39731),f860(x39731),f860(x39731),f784(f784(f180(f860(x39731),f860(x39731)),x39732),f161(x39731))),f784(f784(f180(f860(x39731),f860(x39731)),x39733),f161(x39731))),f784(f784(f180(f860(x39731),f860(x39731)),f784(f784(f89(a859),x39732),x39733)),f161(x39731)))
% 11.41/11.17 [3976]P85(f784(f784(f347(f868(f860(x39761),f860(x39761))),f784(f784(f251(f860(x39761),f860(x39761)),x39762),x39762)),f150(x39761,f310(x39761,x39763))))
% 11.41/11.17 [4120]E(f94(f868(x41201,x41202),f784(f784(f20(f868(x41201,x41202),x41202,a852),f784(f784(f10(x41201,f869(x41202,a852),f868(x41201,x41202)),x41203),f250(x41201,x41202))),f260(x41201,x41202))),f94(f868(x41201,x41202),f784(f261(x41201,x41202,a852),x41203)))
% 11.41/11.17 [4121]E(f99(f868(x41211,x41212),f784(f784(f20(f868(x41211,x41212),x41212,a852),f784(f784(f10(x41211,f869(x41212,a852),f868(x41211,x41212)),x41213),f250(x41211,x41212))),f260(x41211,x41212))),f99(f868(x41211,x41212),f784(f261(x41211,x41212,a852),x41213)))
% 11.41/11.17 [4159]E(f784(f784(f290(f868(a859,x41591),x41591),f339(a859,x41591,a247,x41592)),f784(f784(f20(x41591,x41591,f868(a859,x41591)),f784(f784(f10(a859,f869(x41591,f868(a859,x41591)),x41591),f251(a859,x41591)),x41593)),f7(x41591))),f340(x41591,x41593,x41592))
% 11.41/11.17 [4221]E(f784(f262(x42211,x42211,x42212,x42212,f7(x42211),f7(x42212)),x42213),x42213)
% 11.41/11.17 [4355]E(f784(f784(f95(a1,x43551),f223(f784(f784(f82(f868(a1,a1),a1,x43551,f260(a1,a1)),f217(x43551)),x43552),f784(f784(f82(f868(a1,a1),a1,x43551,f260(a1,a1)),f217(x43551)),x43553))),f784(f784(f20(a1,a1,x43551),f784(f784(f10(a1,f869(a1,x43551),a1),f207(x43551)),f784(f784(f20(a1,a1,a1),f784(f784(f10(a1,f869(a1,a1),a1),f89(a1)),f784(f784(f10(a1,a1,a1),f784(f90(a1),f784(f784(f82(f868(a1,a1),a1,x43551,f250(a1,a1)),f217(x43551)),x43552))),f784(f784(f9(a1,a1,a1),f51(a1)),f784(f784(f82(f868(a1,a1),a1,x43551,f260(a1,a1)),f217(x43551)),x43552))))),f784(f784(f10(a1,a1,a1),f784(f90(a1),f784(f784(f82(f868(a1,a1),a1,x43551,f250(a1,a1)),f217(x43551)),x43553))),f784(f784(f9(a1,a1,a1),f51(a1)),f784(f784(f82(f868(a1,a1),a1,x43551,f260(a1,a1)),f217(x43551)),x43553)))))),f7(a1))),f234(x43551,x43552,x43553))
% 11.41/11.17 [4419]~E(f784(f784(f144(x44191),x44192),x44193),x44193)
% 11.41/11.17 [4420]~E(f784(f784(f144(x44201),x44202),x44203),x44203)
% 11.41/11.17 [4428]~E(f784(f784(f144(x44281),x44282),x44283),f120(x44281))
% 11.41/11.17 [4429]~E(f784(f784(f144(x44291),x44292),x44293),f120(x44291))
% 11.41/11.17 [4454]~E(f784(f784(f312(x44541),x44542),x44543),f187(f869(x44541,a852)))
% 11.41/11.17 [4455]~E(f784(f784(f312(x44551),x44552),x44553),f187(f869(x44551,a852)))
% 11.41/11.17 [4484]~E(f784(f313(x44841,f869(x44841,a852),x44842),x44843),f784(f311(x44841),x44843))
% 11.41/11.17 [3247]E(f784(f784(f151(x32471,f120(x32471)),x32472),x32473),f120(x32471))
% 11.41/11.17 [3248]E(f784(f784(f151(x32481,f120(x32481)),x32482),x32483),f120(x32481))
% 11.41/11.17 [3249]E(f784(f135(x32491),f784(f784(f144(x32491),x32492),x32493)),x32492)
% 11.41/11.17 [3250]E(f784(f163(x32501),f784(f784(f144(x32501),x32502),x32503)),x32503)
% 11.41/11.17 [3296]E(f784(f784(f133(x32961),f87(a859)),f784(f784(f144(x32961),x32962),x32963)),x32963)
% 11.41/11.17 [3328]E(f121(x33281,f784(f784(f133(x33281),x33282),x33283)),f784(f784(f133(x33281),x33282),f121(x33281,x33283)))
% 11.41/11.17 [3329]E(f121(x33291,f784(f784(f133(x33291),x33292),x33293)),f784(f784(f133(x33291),x33292),f121(x33291,x33293)))
% 11.41/11.17 [3331]E(f784(f784(f151(x33311,x33312),x33313),f784(f784(f155(x33311),x33312),x33313)),x33312)
% 11.41/11.17 [3354]E(f784(f784(f312(x33541),x33542),f784(f784(f312(x33541),x33542),x33543)),f784(f784(f312(x33541),x33542),x33543))
% 11.41/11.17 [3367]E(f784(f784(f312(x33671),x33672),f784(f164(x33671),x33673)),f784(f164(x33671),f784(f784(f144(x33671),x33672),x33673)))
% 11.41/11.17 [3368]E(f784(f784(f133(x33681),x33682),f784(f163(x33681),x33683)),f784(f163(x33681),f784(f784(f133(x33681),x33682),x33683)))
% 11.41/11.17 [3369]E(f784(f784(f133(x33691),x33692),f784(f163(x33691),x33693)),f784(f163(x33691),f784(f784(f133(x33691),x33692),x33693)))
% 11.41/11.17 [3378]E(f784(f784(f165(x33781),f87(a859)),f784(f784(f144(x33781),x33782),x33783)),f784(f784(f144(x33781),x33782),f120(x33781)))
% 11.41/11.17 [3410]E(f784(f172(x34101,x34102,f120(f868(x34101,x34102))),x34103),f190(x34102))
% 11.41/11.17 [3411]E(f784(f172(x34111,x34112,f120(f868(x34111,x34112))),x34113),f190(x34112))
% 11.41/11.17 [3426]E(f784(f73(x34261,x34262),f784(f784(f312(x34261),x34263),f187(f869(x34261,a852)))),x34263)
% 11.41/11.17 [3474]E(f784(f784(f89(a859),x34741),f784(f784(f89(a859),x34742),x34743)),f784(f784(f89(a859),x34742),f784(f784(f89(a859),x34741),x34743)))
% 11.41/11.17 [3475]E(f784(f784(f89(a1),x34751),f784(f784(f89(a1),x34752),x34753)),f784(f784(f89(a1),x34752),f784(f784(f89(a1),x34751),x34753)))
% 11.41/11.17 [3480]E(f784(f784(f258(x34801,x34802),f187(f869(x34801,a852))),x34803),f187(f869(f868(x34801,x34802),a852)))
% 11.41/11.17 [3502]E(f784(f784(f110(f869(x35021,a852)),x35022),x35023),f784(f784(f110(f869(x35021,a852)),x35023),x35022))
% 11.41/11.17 [3503]E(f784(f784(f111(f869(x35031,a852)),x35032),x35033),f784(f784(f111(f869(x35031,a852)),x35033),x35032))
% 11.41/11.17 [3505]E(f784(f784(f130(x35051),x35052),f784(f784(f144(x35051),x35053),f120(x35051))),f784(f161(x35051),f784(f784(f144(x35051),x35053),x35052)))
% 11.41/11.17 [3506]E(f784(f784(f130(x35061),f784(f162(x35061),x35062)),f784(f162(x35061),x35063)),f784(f162(x35061),f784(f784(f130(x35061),x35063),x35062)))
% 11.41/11.17 [3516]E(f784(f163(x35161),f784(f784(f165(x35161),f784(a160,x35162)),x35163)),f784(f784(f165(x35161),x35162),f784(f163(x35161),x35163)))
% 11.41/11.17 [3523]P85(f784(f784(f347(x35231),x35232),f784(f784(f312(x35231),x35232),x35233)))
% 11.41/11.17 [3527]E(f784(f784(f55(x35271,f869(x35272,a852)),f187(f869(x35271,a852))),x35273),f249(f869(x35272,a852)))
% 11.41/11.17 [3530]E(f784(f287(x35301,x35301,f270(x35301,x35302)),x35303),f784(f784(f111(f869(x35301,a852)),x35302),x35303))
% 11.41/11.17 [3542]E(f784(f188(f860(x35421)),f784(f784(f144(x35421),x35422),x35423)),f784(f784(f89(a859),f784(f188(f860(x35421)),x35423)),f784(a160,f2(a859))))
% 11.41/11.17 [3546]E(f138(x35461,f784(f784(f130(x35461),x35462),f784(f784(f144(x35461),x35463),f120(x35461)))),x35463)
% 11.41/11.17 [3547]E(f121(x35471,f784(f784(f130(x35471),x35472),f784(f784(f144(x35471),x35473),f120(x35471)))),x35472)
% 11.41/11.17 [3552]E(f784(f784(f130(x35521),f784(f784(f165(x35521),x35522),x35523)),f784(f784(f133(x35521),x35522),x35523)),x35523)
% 11.41/11.17 [3561]E(f784(f784(f3(a859),f784(f784(f89(a859),x35611),x35612)),f784(f784(f89(a859),x35613),x35612)),f784(f784(f3(a859),x35611),x35613))
% 11.41/11.17 [3562]E(f784(f784(f3(a859),f784(f784(f89(a859),x35621),x35622)),f784(f784(f89(a859),x35621),x35623)),f784(f784(f3(a859),x35622),x35623))
% 11.41/11.17 [3568]E(f784(f784(f130(x35681),f784(f162(x35681),x35682)),f784(f784(f144(x35681),x35683),f120(x35681))),f784(f162(x35681),f784(f784(f144(x35681),x35683),x35682)))
% 11.41/11.17 [3570]E(f784(f784(f89(a859),f784(f188(f860(x35701)),x35702)),f784(f188(f860(x35701)),x35703)),f784(f188(f860(x35701)),f784(f784(f130(x35701),x35702),x35703)))
% 11.41/11.17 [3579]E(f784(f784(f110(f869(x35791,a852)),f784(f164(x35791),x35792)),f784(f164(x35791),x35793)),f784(f164(x35791),f784(f784(f130(x35791),x35792),x35793)))
% 11.41/11.17 [3580]E(f60(a859,f784(f784(f90(a859),x35801),x35802),f784(f784(f90(a859),x35801),x35803)),f784(f784(f90(a859),x35801),f60(a859,x35802,x35803)))
% 11.41/11.17 [3593]E(f784(f784(f165(x35931),f784(f784(f3(a859),x35932),f87(a859))),f784(f163(x35931),x35933)),f784(f163(x35931),f784(f784(f165(x35931),x35932),x35933)))
% 11.41/11.17 [3598]E(f784(f784(f111(f869(x35981,a852)),x35982),f784(f88(f869(x35981,a852)),x35983)),f784(f784(f3(f869(x35981,a852)),x35982),x35983))
% 11.41/11.17 [3599]E(f784(f784(f3(f869(x35991,a852)),x35992),f784(f88(f869(x35991,a852)),x35993)),f784(f784(f111(f869(x35991,a852)),x35992),x35993))
% 11.41/11.17 [3621]E(f784(f784(f258(x36211,x36212),x36213),f784(f18(f869(x36212,a852),x36211),f187(f869(x36212,a852)))),f187(f869(f868(x36211,x36212),a852)))
% 11.41/11.17 [3623]E(f784(f784(f89(a859),f784(f784(f90(a859),x36231),x36232)),f784(f784(f90(a859),x36231),x36233)),f784(f784(f90(a859),x36231),f784(f784(f89(a859),x36232),x36233)))
% 11.41/11.17 [3624]E(f784(f784(f3(a859),f784(f784(f90(a859),x36241),x36242)),f784(f784(f90(a859),x36241),x36243)),f784(f784(f90(a859),x36241),f784(f784(f3(a859),x36242),x36243)))
% 11.41/11.17 [3625]E(f784(f784(f89(a1),f784(f784(f90(a1),x36251),x36252)),f784(f784(f90(a1),x36251),x36253)),f784(f784(f90(a1),x36251),f784(f784(f89(a1),x36252),x36253)))
% 11.41/11.17 [3626]E(f784(f784(f3(a1),f784(f784(f90(a1),x36261),x36262)),f784(f784(f90(a1),x36261),x36263)),f784(f784(f90(a1),x36261),f784(f784(f3(a1),x36262),x36263)))
% 11.41/11.17 [3627]E(f784(f784(f90(a1),f784(f784(f252(a1),x36271),x36272)),f784(f784(f252(a1),x36271),x36273)),f784(f784(f252(a1),x36271),f784(f784(f89(a859),x36272),x36273)))
% 11.41/11.17 [3640]E(f784(f784(f54(x36401,f869(x36402,a852)),x36403),f784(f18(f869(x36402,a852),x36401),f187(f869(x36402,a852)))),f187(f869(x36402,a852)))
% 11.41/11.17 [3642]E(f60(a859,f784(f784(f90(a859),x36421),x36422),f784(f784(f90(a859),x36423),x36422)),f784(f784(f90(a859),f60(a859,x36421,x36423)),x36422))
% 11.41/11.17 [3646]E(f60(a1,f784(f784(f90(a1),x36461),f60(a1,x36462,x36463)),x36463),f60(a1,f784(f784(f90(a1),x36461),x36462),x36463))
% 11.41/11.17 [3647]E(f60(a1,f784(f784(f90(a1),x36471),f60(a1,x36472,x36473)),x36473),f60(a1,f784(f784(f90(a1),x36471),x36472),x36473))
% 11.41/11.17 [3648]E(f60(a1,f784(f784(f3(a1),x36481),f60(a1,x36482,x36483)),x36483),f60(a1,f784(f784(f3(a1),x36481),x36482),x36483))
% 11.41/11.17 [3649]P85(f784(f784(f242(f869(x36491,a852)),x36492),f784(f784(f312(x36491),x36493),x36492)))
% 11.41/11.17 [3673]E(f784(f313(f868(x36731,x36732),x36731,f250(x36731,x36732)),f784(f164(f868(x36731,x36732)),x36733)),f175(x36731,x36732,f172(x36731,x36732,x36733)))
% 11.41/11.17 [3730]E(f784(f784(f55(f869(x37301,a852),f869(x37301,a852)),x37302),f784(f110(f869(x37301,a852)),x37303)),f784(f784(f110(f869(x37301,a852)),x37303),f53(f869(x37301,a852),x37302)))
% 11.41/11.17 [3731]E(f784(f784(f54(f869(x37311,a852),f869(x37311,a852)),x37312),f784(f111(f869(x37311,a852)),x37313)),f784(f784(f111(f869(x37311,a852)),x37313),f52(f869(x37311,a852),x37312)))
% 11.41/11.17 [3741]E(f784(f164(x37411),f784(f784(f784(f180(f860(x37411),f860(x37411)),x37412),f161(x37411)),x37413)),f784(f164(x37411),x37413))
% 11.41/11.17 [3745]E(f175(x37451,x37452,f784(f784(f10(x37452,f864(x37452),x37451),f237(x37452)),x37453)),f249(f869(x37451,a852)))
% 11.41/11.17 [3748]E(f784(f188(f860(x37481)),f784(f784(f784(f180(f860(x37481),f860(x37481)),x37482),f161(x37481)),x37483)),f784(f188(f860(x37481)),x37483))
% 11.41/11.17 [3750]E(f784(f784(f261(x37501,x37502,x37502),f784(f18(f869(x37502,x37502),x37501),f7(x37502))),x37503),f784(f260(x37501,x37502),x37503))
% 11.41/11.17 [3757]E(f60(a1,f784(f784(f3(a1),f60(a1,x37571,x37572)),x37573),x37572),f60(a1,f784(f784(f3(a1),x37571),x37573),x37572))
% 11.41/11.17 [3758]E(f60(a1,f784(f784(f252(a1),f60(a1,x37581,x37582)),x37583),x37582),f60(a1,f784(f784(f252(a1),x37581),x37583),x37582))
% 11.41/11.17 [3761]E(f784(f784(f54(f869(f868(x37611,x37612),a852),f869(x37612,a852)),x37613),f269(x37611,x37612)),f784(f269(x37611,x37612),f52(f869(f868(x37611,x37612),a852),x37613)))
% 11.41/11.17 [3762]E(f784(f784(f54(f869(f868(x37621,x37622),a852),f869(x37621,a852)),x37623),f271(x37621,x37622)),f784(f271(x37621,x37622),f52(f869(f868(x37621,x37622),a852),x37623)))
% 11.41/11.17 [3790]E(f784(f82(x37901,x37901,x37901,x37902),f784(f784(f180(x37901,x37901),x37903),x37902)),f784(f784(f180(x37901,x37901),f784(a160,x37903)),x37902))
% 11.41/11.17 [3800]E(f239(f864(x38001),x38002,f190(x38001),f784(f784(f10(x38001,f864(x38001),x38002),f237(x38001)),x38003)),f784(f206(x38002,x38001),x38003))
% 11.41/11.17 [3807]E(f784(f784(f133(x38071),f784(f784(f3(a859),f784(f188(f860(x38071)),x38072)),x38073)),f784(f162(x38071),x38072)),f784(f162(x38071),f784(f784(f165(x38071),x38073),x38072)))
% 11.41/11.17 [3808]E(f784(f784(f165(x38081),f784(f784(f3(a859),f784(f188(f860(x38081)),x38082)),x38083)),f784(f162(x38081),x38082)),f784(f162(x38081),f784(f784(f133(x38081),x38083),x38082)))
% 11.41/11.17 [3811]E(f784(f784(f89(a859),f784(f157(a859),f784(f784(f146(x38111,a859),x38112),x38113))),f784(f188(f860(x38111)),x38113)),f147(x38111,x38112,x38113))
% 11.41/11.17 [3820]E(f784(f784(f784(f180(f860(x38201),f860(x38201)),x38202),f161(x38201)),f784(f161(x38201),x38203)),f784(f161(x38201),f784(f784(f784(f180(f860(x38201),f860(x38201)),x38202),f161(x38201)),x38203)))
% 11.41/11.17 [3827]E(f784(f161(x38271),f784(f784(f784(f180(f860(x38271),f860(x38271)),x38272),f161(x38271)),x38273)),f784(f784(f784(f180(f860(x38271),f860(x38271)),f784(a160,x38272)),f161(x38271)),x38273))
% 11.41/11.17 [3839]P85(f784(f784(f242(a859),f784(f188(f860(x38391)),f784(f131(x38391,x38392),x38393))),f784(f188(f860(x38391)),x38393)))
% 11.41/11.17 [3856]E(f784(f784(f110(f869(f869(x38561,a852),a852)),f784(f311(x38561),x38562)),f784(f313(f869(x38561,a852),f869(x38561,a852),f784(f312(x38561),x38563)),f784(f311(x38561),x38562))),f784(f311(x38561),f784(f784(f312(x38561),x38563),x38562)))
% 11.41/11.17 [3873]P25(x38731,x38732,f784(f784(f312(f858(x38731)),f784(f784(f784(f100(x38731),x38733),a25),x38733)),f187(f869(f858(x38731),a852))))
% 11.41/11.17 [3874]P25(x38741,x38742,f784(f784(f312(f858(x38741)),f784(f784(f784(f100(x38741),x38743),a25),x38743)),f187(f869(f858(x38741),a852))))
% 11.41/11.17 [3896]E(f784(f271(x38961,x38962),f784(f266(f868(x38961,x38962)),f784(f261(x38961,x38962,a852),x38963))),f784(f266(x38961),f784(f784(f10(f869(x38962,a852),a852,x38961),f96(x38962)),x38963)))
% 11.41/11.17 [3909]E(f784(f313(a859,a859,f784(f784(f9(a859,a859,a859),f89(a859)),x39091)),f305(a859,x39092,x39093)),f305(a859,f784(f784(f89(a859),x39092),x39091),f784(f784(f89(a859),x39093),x39091)))
% 11.41/11.17 [3925]E(f784(f313(a859,a859,f784(f784(f9(a859,a859,a859),f89(a859)),x39251)),f784(f304(a859,x39252),x39253)),f784(f304(a859,f784(f784(f89(a859),x39252),x39251)),f784(f784(f89(a859),x39253),x39251)))
% 11.41/11.17 [3942]E(f784(f784(f173(x39421,x39422),f784(f784(f146(f868(x39421,x39422),x39421),f250(x39421,x39422)),x39423)),f784(f784(f146(f868(x39421,x39422),x39422),f260(x39421,x39422)),x39423)),x39423)
% 11.41/11.17 [3947]E(f784(f784(f89(a859),f784(f784(f90(a859),x39471),f60(a859,f784(f784(f51(a859),x39472),x39471),x39473))),f60(a859,x39472,x39471)),f60(a859,x39472,f784(f784(f90(a859),x39471),x39473)))
% 11.41/11.17 [3957]P85(f784(f71(f864(x39571)),f784(f313(x39572,f864(x39571),f172(x39572,x39571,x39573)),f249(f869(x39572,a852)))))
% 11.41/11.17 [3961]E(f784(f784(f130(x39611),x39612),f784(f136(f860(x39611),f860(x39611),f130(x39611),f120(x39611)),x39613)),f784(f136(f860(x39611),f860(x39611),f130(x39611),x39612),x39613))
% 11.41/11.17 [3980]P85(f784(f784(f347(f868(x39801,x39801)),f784(f784(f251(x39801,x39801),x39802),x39802)),f784(f784(f180(f868(x39801,x39801),a852),f2(a859)),x39803)))
% 11.41/11.17 [3986]E(f784(f266(x39861),f784(f784(f10(f869(x39862,a852),a852,x39861),f96(x39862)),f784(f9(x39862,x39861,a852),x39863))),f784(f269(x39862,x39861),f784(f266(f868(x39862,x39861)),f784(f261(x39862,x39861,a852),x39863))))
% 11.41/11.17 [4005]E(f784(f784(f110(f869(x40051,a852)),f784(f784(f54(a859,f869(x40051,a852)),f305(a859,f87(a859),x40052)),x40053)),f784(x40053,f2(a859))),f784(f784(f54(a859,f869(x40051,a852)),f784(f303(a859),x40052)),x40053))
% 11.41/11.17 [4020]E(f784(f136(f860(x40201),f860(x40201),f130(x40201),f120(x40201)),f784(f784(f146(f860(x40201),f860(x40201)),f131(x40201,x40202)),x40203)),f784(f131(x40201,x40202),f784(f136(f860(x40201),f860(x40201),f130(x40201),f120(x40201)),x40203)))
% 11.41/11.17 [4025]E(f784(f260(f860(x40251),f860(x40251)),f158(x40251,x40252,x40253)),f784(f131(x40251,f784(f82(a852,a852,x40251,a341),x40252)),x40253))
% 11.41/11.17 [4074]E(f784(f784(f89(a1),f784(f784(f89(a1),f784(f784(f90(a1),x40741),f784(f784(f51(a1),x40742),x40741))),f60(a1,x40742,x40741))),x40743),f784(f784(f89(a1),x40742),x40743))
% 11.41/11.17 [4109]E(f784(f784(f89(a1),f784(f784(f89(a1),f784(f784(f90(a1),f784(f784(f51(a1),x41091),x41092)),x41092)),f60(a1,x41091,x41092))),x41093),f784(f784(f89(a1),x41091),x41093))
% 11.41/11.17 [4138]E(f94(f868(x41381,x41382),f784(f261(x41381,x41382,a852),f784(f784(f10(f869(x41382,f868(x41381,x41382)),f869(x41382,a852),x41381),f784(f10(f868(x41381,x41382),a852,x41382),x41383)),f251(x41381,x41382)))),f94(f868(x41381,x41382),x41383))
% 11.41/11.17 [4139]E(f99(f868(x41391,x41392),f784(f261(x41391,x41392,a852),f784(f784(f10(f869(x41392,f868(x41391,x41392)),f869(x41392,a852),x41391),f784(f10(f868(x41391,x41392),a852,x41392),x41393)),f251(x41391,x41392)))),f99(f868(x41391,x41392),x41393))
% 11.41/11.17 [4170]P85(f784(f784(f242(f869(x41701,a852)),f52(f869(x41701,a852),f784(f784(f111(f869(f869(x41701,a852),a852)),x41702),x41703))),f784(f784(f111(f869(x41701,a852)),f52(f869(x41701,a852),x41702)),f52(f869(x41701,a852),x41703))))
% 11.41/11.17 [4171]E(f784(f162(x41711),f784(f784(f784(f180(f860(x41711),f860(x41711)),f784(f784(f3(a859),f784(f188(f860(x41711)),x41712)),f60(a859,x41713,f784(f188(f860(x41711)),x41712)))),f161(x41711)),x41712)),f784(f784(f784(f180(f860(x41711),f860(x41711)),x41713),f161(x41711)),f784(f162(x41711),x41712)))
% 11.41/11.17 [4183]E(f784(f266(x41831),f784(f784(f10(a852,a852,x41831),a341),f784(f784(f9(x41831,f864(x41832),a852),f784(f784(f10(f864(x41832),f869(f864(x41832),a852),x41831),a343),x41833)),f190(x41832)))),f175(x41831,x41832,x41833))
% 11.41/11.17 [4246]E(f784(f266(x42461),f784(f784(f10(f869(x42462,a852),a852,x42461),f96(x42462)),f784(f784(f10(f864(x42461),f869(x42462,a852),x42461),f784(f9(x42462,f864(x42461),a852),f784(f784(f10(f864(x42461),f869(f864(x42461),a852),x42462),a343),x42463))),f237(x42461)))),f177(x42462,x42461,x42463))
% 11.41/11.17 [4497]~P85(f784(f72(x44971,x44972,f187(f869(x44971,a852))),x44973))
% 11.41/11.17 [3517]E(f784(f188(f860(x35171)),f784(f784(f165(x35171),x35172),x35173)),f784(f784(f246(a859),f784(f188(f860(x35171)),x35173)),x35172))
% 11.41/11.17 [3518]E(f784(f188(f860(x35181)),f784(f784(f133(x35181),x35182),x35183)),f784(f784(f3(a859),f784(f188(f860(x35181)),x35183)),x35182))
% 11.41/11.17 [3554]E(f784(f784(f51(a859),f784(f784(f51(a859),x35541),x35542)),x35543),f784(f784(f51(a859),x35541),f784(f784(f90(a859),x35542),x35543)))
% 11.41/11.17 [3555]E(f784(f784(f89(a859),f784(f784(f89(a859),x35551),x35552)),x35553),f784(f784(f89(a859),x35551),f784(f784(f89(a859),x35552),x35553)))
% 11.41/11.17 [3556]E(f784(f784(f89(a1),f784(f784(f89(a1),x35561),x35562)),x35563),f784(f784(f89(a1),x35561),f784(f784(f89(a1),x35562),x35563)))
% 11.41/11.17 [3557]E(f784(f784(f90(a859),f784(f784(f90(a859),x35571),x35572)),x35573),f784(f784(f90(a859),x35571),f784(f784(f90(a859),x35572),x35573)))
% 11.41/11.17 [3558]E(f784(f784(f90(a1),f784(f784(f90(a1),x35581),x35582)),x35583),f784(f784(f90(a1),x35581),f784(f784(f90(a1),x35582),x35583)))
% 11.41/11.17 [3559]E(f784(f784(f3(a859),f784(f784(f3(a859),x35591),x35592)),x35593),f784(f784(f3(a859),x35591),f784(f784(f89(a859),x35592),x35593)))
% 11.41/11.17 [3560]E(f784(f784(f252(a1),f784(f784(f252(a1),x35601),x35602)),x35603),f784(f784(f252(a1),x35601),f784(f784(f90(a859),x35602),x35603)))
% 11.41/11.17 [3578]E(f153(x35781,f784(f784(f144(f869(x35781,a852)),x35782),x35783)),f167(x35781,x35782,f153(x35781,x35783)))
% 11.41/11.17 [3622]E(f784(f784(f3(a859),f784(f784(f3(a859),x36221),x36222)),x36223),f784(f784(f3(a859),f784(f784(f3(a859),x36221),x36223)),x36222))
% 11.41/11.17 [3630]E(f784(f784(f111(f869(x36301,a852)),x36302),f784(f784(f3(f869(x36301,a852)),x36303),x36302)),f187(f869(x36301,a852)))
% 11.41/11.17 [3675]E(f53(f869(x36751,a852),f784(f784(f312(f869(x36751,a852)),x36752),x36753)),f784(f784(f111(f869(x36751,a852)),x36752),f53(f869(x36751,a852),x36753)))
% 11.41/11.17 [3676]E(f52(f869(x36761,a852),f784(f784(f312(f869(x36761,a852)),x36762),x36763)),f784(f784(f110(f869(x36761,a852)),x36762),f52(f869(x36761,a852),x36763)))
% 11.41/11.17 [3678]E(f784(f784(f89(a859),f784(f784(f90(a859),x36781),x36782)),f784(f784(f90(a859),x36783),x36782)),f784(f784(f90(a859),f784(f784(f89(a859),x36781),x36783)),x36782))
% 11.41/11.17 [3679]E(f784(f784(f3(a859),f784(f784(f90(a859),x36791),x36792)),f784(f784(f90(a859),x36793),x36792)),f784(f784(f90(a859),f784(f784(f3(a859),x36791),x36793)),x36792))
% 11.41/11.17 [3680]E(f784(f784(f89(a1),f784(f784(f90(a1),x36801),x36802)),f784(f784(f90(a1),x36803),x36802)),f784(f784(f90(a1),f784(f784(f89(a1),x36801),x36803)),x36802))
% 11.41/11.17 [3682]E(f784(f784(f3(a1),f784(f784(f90(a1),x36821),x36822)),f784(f784(f90(a1),x36823),x36822)),f784(f784(f90(a1),f784(f784(f3(a1),x36821),x36823)),x36822))
% 11.41/11.17 [3683]E(f784(f784(f246(a859),f784(f784(f3(a859),x36831),x36832)),f784(f784(f3(a859),x36833),x36832)),f784(f784(f3(a859),f784(f784(f246(a859),x36831),x36833)),x36832))
% 11.41/11.17 [3707]E(f784(f784(f110(f869(x37071,a852)),x37072),f784(f784(f3(f869(x37071,a852)),x37073),x37072)),f784(f784(f110(f869(x37071,a852)),x37072),x37073))
% 11.41/11.17 [3708]E(f784(f784(f110(f869(x37081,a852)),x37082),f784(f784(f110(f869(x37081,a852)),x37082),x37083)),f784(f784(f110(f869(x37081,a852)),x37082),x37083))
% 11.41/11.17 [3709]E(f784(f784(f111(f869(x37091,a852)),x37092),f784(f784(f111(f869(x37091,a852)),x37092),x37093)),f784(f784(f111(f869(x37091,a852)),x37092),x37093))
% 11.41/11.17 [3721]E(f784(f784(f291(x37211,x37212,x37212),x37213),f310(x37212,f187(f869(f868(x37212,x37212),a852)))),x37213)
% 11.41/11.17 [3726]E(f784(f784(f110(f869(x37261,a852)),f784(f784(f312(x37261),x37262),f187(f869(x37261,a852)))),x37263),f784(f784(f312(x37261),x37262),x37263))
% 11.41/11.17 [3744]E(f784(f784(f3(a859),f784(f784(f3(a859),f784(a160,x37441)),x37442)),f784(a160,x37443)),f784(f784(f3(a859),f784(f784(f3(a859),x37441),x37442)),x37443))
% 11.41/11.17 [3770]E(f784(f784(f111(f869(f869(x37701,a852),a852)),f784(f311(x37701),x37702)),f784(f311(x37701),x37703)),f784(f311(x37701),f784(f784(f111(f869(x37701,a852)),x37702),x37703)))
% 11.41/11.17 [3773]E(f784(f784(f110(f869(x37731,a852)),f784(f88(f869(x37731,a852)),x37732)),x37733),f784(f88(f869(x37731,a852)),f784(f784(f3(f869(x37731,a852)),x37732),x37733)))
% 11.41/11.17 [3786]E(f784(f784(f312(x37861),x37862),f784(f784(f3(f869(x37861,a852)),x37863),f784(f784(f312(x37861),x37862),f187(f869(x37861,a852))))),f784(f784(f312(x37861),x37862),x37863))
% 11.41/11.17 [3797]P85(f784(f784(f242(f869(x37971,a852)),x37972),f784(f784(f110(f869(x37971,a852)),x37973),x37972)))
% 11.41/11.17 [3798]P85(f784(f784(f242(f869(x37981,a852)),x37982),f784(f784(f110(f869(x37981,a852)),x37982),x37983)))
% 11.41/11.17 [3801]E(f784(f784(f111(f869(x38011,a852)),f784(f88(f869(x38011,a852)),x38012)),f784(f88(f869(x38011,a852)),x38013)),f784(f88(f869(x38011,a852)),f784(f784(f110(f869(x38011,a852)),x38012),x38013)))
% 11.41/11.17 [3802]E(f784(f784(f110(f869(x38021,a852)),f784(f88(f869(x38021,a852)),x38022)),f784(f88(f869(x38021,a852)),x38023)),f784(f88(f869(x38021,a852)),f784(f784(f111(f869(x38021,a852)),x38022),x38023)))
% 11.41/11.17 [3815]P85(f784(f784(f242(f869(x38151,a852)),f784(f164(x38151),x38152)),f784(f164(x38151),f784(f784(f144(x38151),x38153),x38152))))
% 11.41/11.17 [3824]E(f784(f784(f110(f869(x38241,a852)),f784(f784(f3(f869(x38241,a852)),x38242),x38243)),f784(f784(f111(f869(x38241,a852)),x38242),x38243)),x38242)
% 11.41/11.17 [3876]E(f784(f784(f8(x38761,a1),f784(f784(f10(a859,a1,x38761),f109(a1)),x38762)),x38763),f784(f109(a1),f784(f784(f8(x38761,a859),x38762),x38763)))
% 11.41/11.17 [3877]E(f784(f784(f11(x38771,a1),f784(f784(f10(a859,a1,x38771),f109(a1)),x38772)),x38773),f784(f109(a1),f784(f784(f11(x38771,a859),x38772),x38773)))
% 11.41/11.17 [3931]E(f784(f88(f869(f868(x39311,x39312),a852)),f784(f784(f258(x39311,x39312),x39313),f784(f18(f869(x39312,a852),x39311),f249(f869(x39312,a852))))),f784(f784(f258(x39311,x39312),f784(f88(f869(x39311,a852)),x39313)),f784(f18(f869(x39312,a852),x39311),f249(f869(x39312,a852)))))
% 11.41/11.17 [3932]E(f784(f88(f869(f868(x39321,x39322),a852)),f784(f784(f258(x39321,x39322),f249(f869(x39321,a852))),f784(f18(f869(x39322,a852),x39321),x39323))),f784(f784(f258(x39321,x39322),f249(f869(x39321,a852))),f784(f18(f869(x39322,a852),x39321),f784(f88(f869(x39322,a852)),x39323))))
% 11.41/11.17 [3981]E(f784(f784(f54(f869(x39811,a852),f869(x39811,a852)),x39812),f784(f784(f9(f869(x39811,a852),f869(x39811,a852),f869(x39811,a852)),f111(f869(x39811,a852))),x39813)),f784(f784(f111(f869(x39811,a852)),f52(f869(x39811,a852),x39812)),x39813))
% 11.41/11.17 [3988]E(f784(f136(f860(x39881),f860(x39881),f130(x39881),f120(x39881)),f784(f784(f144(f860(x39881)),x39882),x39883)),f784(f784(f130(x39881),x39882),f784(f136(f860(x39881),f860(x39881),f130(x39881),f120(x39881)),x39883)))
% 11.41/11.17 [4011]E(f784(f784(f312(f869(x40111,a852)),f784(f287(x40111,x40111,x40112),f784(f784(f312(x40111),x40113),f187(f869(x40111,a852))))),f187(f869(f869(x40111,a852),a852))),f784(f784(f69(x40111),f784(f784(f312(x40111),x40113),f187(f869(x40111,a852)))),x40112))
% 11.41/11.17 [4021]E(f784(f784(f89(a859),f784(f784(f90(a859),x40211),f784(f784(f51(a859),x40212),x40213))),f784(f784(f51(a859),f784(f784(f90(a859),x40211),f60(a859,x40212,x40213))),x40213)),f784(f784(f51(a859),f784(f784(f90(a859),x40211),x40212)),x40213))
% 11.41/11.17 [4022]E(f784(f784(f89(a1),f784(f784(f90(a1),x40221),f784(f784(f51(a1),x40222),x40223))),f784(f784(f51(a1),f784(f784(f90(a1),x40221),f60(a1,x40222,x40223))),x40223)),f784(f784(f51(a1),f784(f784(f90(a1),x40221),x40222)),x40223))
% 11.41/11.17 [4106]E(f784(f784(f130(x41061),f784(f136(f860(x41061),f860(x41061),f130(x41061),f120(x41061)),x41062)),f784(f136(f860(x41061),f860(x41061),f130(x41061),f120(x41061)),x41063)),f784(f136(f860(x41061),f860(x41061),f130(x41061),f120(x41061)),f784(f784(f130(f860(x41061)),x41062),x41063)))
% 11.41/11.17 [4111]E(f784(f784(f251(f860(x41111),f860(x41111)),f784(f131(x41111,x41112),x41113)),f784(f131(x41111,f784(f82(a852,a852,x41111,a341),x41112)),x41113)),f158(x41111,x41112,x41113))
% 11.41/11.17 [4114]E(f784(f784(f89(a859),f784(f784(f89(a859),f784(f784(f51(a859),x41141),x41142)),f784(f784(f51(a859),x41143),x41142))),f784(f784(f51(a859),f784(f784(f89(a859),f60(a859,x41141,x41142)),f60(a859,x41143,x41142))),x41142)),f784(f784(f51(a859),f784(f784(f89(a859),x41141),x41143)),x41142))
% 11.41/11.17 [4115]E(f784(f784(f89(a1),f784(f784(f89(a1),f784(f784(f51(a1),x41151),x41152)),f784(f784(f51(a1),x41153),x41152))),f784(f784(f51(a1),f784(f784(f89(a1),f60(a1,x41151,x41152)),f60(a1,x41153,x41152))),x41152)),f784(f784(f51(a1),f784(f784(f89(a1),x41151),x41153)),x41152))
% 11.41/11.17 [4184]E(f784(f266(x41841),f784(f784(f20(x41841,a852,a852),f784(f784(f10(a852,f869(a852,a852),x41841),a345),f784(f784(f9(x41841,x41841,a852),a343),x41842))),f784(f784(f9(x41841,f869(x41841,a852),a852),f347(x41841)),x41843))),f784(f784(f312(x41841),x41842),x41843))
% 11.41/11.17 [4185]E(f784(f266(x41851),f784(f784(f20(x41851,a852,a852),f784(f784(f10(a852,f869(a852,a852),x41851),a345),f784(f784(f9(x41851,x41851,a852),a343),x41852))),f784(f784(f9(x41851,f869(x41851,a852),a852),f347(x41851)),x41853))),f784(f784(f312(x41851),x41852),x41853))
% 11.41/11.17 [4207]E(f784(f266(x42071),f784(f784(f20(x42071,a852,a852),f784(f784(f10(a852,f869(a852,a852),x42071),a345),f784(f784(f9(x42071,f869(x42071,a852),a852),f347(x42071)),x42072))),f784(f784(f9(x42071,f869(x42071,a852),a852),f347(x42071)),x42073))),f784(f784(f110(f869(x42071,a852)),x42072),x42073))
% 11.41/11.17 [4208]E(f784(f266(x42081),f784(f784(f20(x42081,a852,a852),f784(f784(f10(a852,f869(a852,a852),x42081),a344),f784(f784(f9(x42081,f869(x42081,a852),a852),f347(x42081)),x42082))),f784(f784(f9(x42081,f869(x42081,a852),a852),f347(x42081)),x42083))),f784(f784(f111(f869(x42081,a852)),x42082),x42083))
% 11.41/11.17 [4295]E(f784(f784(f54(x42951,f869(f869(x42951,a852),a852)),x42952),f784(f784(f9(x42951,f869(f869(x42951,a852),a852),f869(f869(x42951,a852),a852)),f784(f784(f10(f869(x42951,a852),f869(f869(f869(x42951,a852),a852),f869(f869(x42951,a852),a852)),x42951),f312(f869(x42951,a852))),f784(f784(f10(f869(x42951,a852),f869(x42951,a852),x42951),f287(x42951,x42951,x42953)),f784(f784(f9(x42951,f869(x42951,a852),f869(x42951,a852)),f312(x42951)),f187(f869(x42951,a852)))))),f187(f869(f869(x42951,a852),a852)))),f784(f784(f69(x42951),x42952),x42953))
% 11.41/11.17 [4297]E(f784(f784(f207(x42971),f784(f784(f90(a1),f784(f784(f82(f868(a1,a1),a1,x42971,f250(a1,a1)),f217(x42971)),x42972)),f784(f784(f82(f868(a1,a1),a1,x42971,f250(a1,a1)),f217(x42971)),x42973))),f784(f784(f90(a1),f784(f784(f82(f868(a1,a1),a1,x42971,f260(a1,a1)),f217(x42971)),x42972)),f784(f784(f82(f868(a1,a1),a1,x42971,f260(a1,a1)),f217(x42971)),x42973))),f232(x42971,x42972,x42973))
% 11.41/11.17 [3696]E(f60(a859,f784(f784(f89(a859),f784(f784(f90(a859),x36961),x36962)),x36963),x36962),f60(a859,x36963,x36962))
% 11.41/11.17 [3743]E(f134(a859,f784(f304(a859,f784(f784(f89(a859),x37431),x37432)),x37433)),f784(f784(f133(a859),x37432),f134(a859,f784(f304(a859,x37431),x37433))))
% 11.41/11.17 [3785]E(f784(f784(f89(a1),f784(f109(a1),x37851)),f784(f784(f89(a1),f784(f109(a1),x37852)),x37853)),f784(f784(f89(a1),f784(f109(a1),f784(f784(f89(a859),x37851),x37852))),x37853))
% 11.41/11.17 [3793]E(f784(f784(f3(f869(x37931,a852)),f784(f784(f3(f869(x37931,a852)),x37932),x37933)),x37933),f784(f784(f3(f869(x37931,a852)),x37932),x37933))
% 11.41/11.17 [3794]E(f784(f784(f110(f869(x37941,a852)),f784(f784(f3(f869(x37941,a852)),x37942),x37943)),x37943),f784(f784(f110(f869(x37941,a852)),x37942),x37943))
% 11.41/11.17 [3816]E(f784(f784(f291(x38161,x38161,x38162),f310(x38161,f187(f869(f868(x38161,x38161),a852)))),x38163),x38163)
% 11.41/11.17 [3821]E(f784(f784(f110(f869(x38211,a852)),f784(f286(x38211),x38212)),f784(f286(x38211),x38213)),f784(f286(x38211),f784(f784(f110(f869(f868(x38211,x38211),a852)),x38212),x38213)))
% 11.41/11.17 [3830]E(f273(x38301,f784(f784(f144(f868(a108,x38301)),f784(f784(f251(a108,x38301),f2(a108)),x38302)),x38303)),f273(x38301,x38303))
% 11.41/11.17 [3833]E(f784(f784(f111(f869(x38331,a852)),f53(f869(x38331,a852),x38332)),f53(f869(x38331,a852),x38333)),f53(f869(x38331,a852),f784(f784(f110(f869(f869(x38331,a852),a852)),x38332),x38333)))
% 11.41/11.17 [3834]E(f784(f784(f110(f869(x38341,a852)),f52(f869(x38341,a852),x38342)),f52(f869(x38341,a852),x38343)),f52(f869(x38341,a852),f784(f784(f110(f869(f869(x38341,a852),a852)),x38342),x38343)))
% 11.41/11.17 [3869]E(f784(f784(f291(x38691,x38691,x38691),f784(f784(f180(f868(x38691,x38691),a852),x38692),x38693)),x38693),f784(f784(f180(f868(x38691,x38691),a852),f784(a160,x38692)),x38693))
% 11.41/11.17 [3917]P85(f784(f784(f242(f869(x39171,a852)),f784(f784(f3(f869(x39171,a852)),x39172),x39173)),x39172))
% 11.41/11.17 [3918]P85(f784(f784(f242(f869(x39181,a852)),f784(f784(f111(f869(x39181,a852)),x39182),x39183)),x39183))
% 11.41/11.17 [3919]P85(f784(f784(f242(f869(x39191,a852)),f784(f784(f111(f869(x39191,a852)),x39192),x39193)),x39192))
% 11.41/11.17 [3944]E(f310(x39441,f784(f784(f110(f869(f868(x39441,x39441),a852)),f310(x39441,x39442)),f310(x39441,x39443))),f310(x39441,f784(f784(f110(f869(f868(x39441,x39441),a852)),x39442),x39443)))
% 11.41/11.17 [3948]E(f52(f869(x39481,a852),f784(f784(f312(f869(x39481,a852)),x39482),f784(f784(f312(f869(x39481,a852)),x39483),f187(f869(f869(x39481,a852),a852))))),f784(f784(f110(f869(x39481,a852)),x39482),x39483))
% 11.41/11.17 [3949]E(f53(f869(x39491,a852),f784(f784(f312(f869(x39491,a852)),x39492),f784(f784(f312(f869(x39491,a852)),x39493),f187(f869(f869(x39491,a852),a852))))),f784(f784(f111(f869(x39491,a852)),x39492),x39493))
% 11.41/11.17 [3954]E(f784(f784(f291(x39541,x39541,x39541),f784(f784(f180(f868(x39541,x39541),a852),x39542),x39543)),x39543),f784(f784(f291(x39541,x39541,x39541),x39543),f784(f784(f180(f868(x39541,x39541),a852),x39542),x39543)))
% 11.41/11.17 [4026]E(f784(f784(f110(f869(x40261,a852)),f784(f266(x40261),f784(f784(f9(x40261,x40261,a852),a343),x40262))),x40263),f784(f784(f312(x40261),x40262),x40263))
% 11.41/11.17 [4028]E(f784(a114,f784(f784(f8(x40281,a1),f784(f784(f10(a859,a1,x40281),f109(a1)),x40282)),x40283)),f784(f784(f8(x40281,a859),x40282),x40283))
% 11.41/11.17 [4029]E(f784(a114,f784(f784(f11(x40291,a1),f784(f784(f10(a859,a1,x40291),f109(a1)),x40292)),x40293)),f784(f784(f11(x40291,a859),x40292),x40293))
% 11.41/11.17 [4103]E(f784(f148(f860(x41031),x41031,f784(f163(x41031),x41032),f784(f18(f869(f860(x41031),f860(x41031)),x41031),f784(f784(f9(f860(x41031),f860(x41031),f860(x41031)),f130(x41031)),x41032))),x41033),f784(f163(x41031),f784(f784(f130(x41031),x41033),x41032)))
% 11.41/11.17 [4134]P85(f784(f784(f242(f869(f869(x41341,a852),a852)),f784(f784(f110(f869(f869(x41341,a852),a852)),f784(f311(x41341),x41342)),f784(f311(x41341),x41343))),f784(f311(x41341),f784(f784(f110(f869(x41341,a852)),x41342),x41343))))
% 11.41/11.17 [4226]E(f784(f266(x42261),f784(f784(f20(x42261,a852,a852),f784(f784(f10(a852,f869(a852,a852),x42261),a344),f784(f784(f9(x42261,f869(x42261,a852),a852),f347(x42261)),x42262))),f784(f784(f10(a852,a852,x42261),a341),f784(f784(f9(x42261,f869(x42261,a852),a852),f347(x42261)),x42263)))),f784(f784(f3(f869(x42261,a852)),x42262),x42263))
% 11.41/11.17 [4247]E(f784(f50(a859),f784(f266(a859),f784(f784(f20(a859,a852,a852),f784(f784(f10(a852,f869(a852,a852),a859),a344),f784(f784(f9(a859,a859,a852),f243(a859)),f784(f188(f860(x42471)),x42472)))),f784(f784(f10(x42471,a852,a859),x42473),f784(f155(x42471),x42472))))),f784(f188(f860(x42471)),f784(f131(x42471,x42473),x42472)))
% 11.41/11.17 [4249]E(f784(f188(f860(x42491)),f166(x42491,x42492,x42493)),f784(f50(a859),f784(f266(a859),f784(f784(f20(a859,a852,a852),f784(f784(f10(a852,f869(a852,a852),a859),a344),f784(f784(f9(a859,a859,a852),f243(a859)),f784(f188(f860(x42491)),x42492)))),f784(f784(f9(a859,f869(a859,a852),a852),f347(a859)),x42493)))))
% 11.41/11.17 [4342]E(f784(f784(f111(f869(f868(f860(x43421),f860(x43421)),a852)),f784(f313(f868(f868(x43421,f860(x43421)),f868(x43421,f860(x43421))),f868(f860(x43421),f860(x43421)),f262(f868(x43421,f860(x43421)),f860(x43421),f868(x43421,f860(x43421)),f860(x43421),f784(f261(x43421,f860(x43421),f860(x43421)),f144(x43421)),f784(f261(x43421,f860(x43421),f860(x43421)),f144(x43421)))),f339(x43421,f860(x43421),x43422,f784(f137(x43421,x43422),x43423)))),f784(f266(f868(f860(x43421),f860(x43421))),f784(f261(f860(x43421),f860(x43421),a852),f784(f784(f9(f860(x43421),f869(f860(x43421),a852),f869(f860(x43421),a852)),f784(f784(f10(f869(a852,a852),f869(f869(f860(x43421),a852),f869(f860(x43421),a852)),f860(x43421)),f10(a852,a852,f860(x43421))),f784(f784(f10(a852,f869(a852,a852),f860(x43421)),a344),f784(f784(f9(f860(x43421),a859,a852),f784(f784(f10(a859,f869(a859,a852),f860(x43421)),a343),f188(f860(x43421)))),f784(a160,x43423))))),f784(f784(f9(f860(x43421),a859,a852),f784(f784(f10(a859,f869(a859,a852),f860(x43421)),a343),f188(f860(x43421)))),f784(a160,x43423)))))),f784(f137(x43421,x43422),f784(a160,x43423)))
% 11.41/11.17 [3835]E(f60(a859,f784(a160,f784(f784(f89(a859),f784(f784(f90(a859),x38351),x38352)),x38353)),x38352),f60(a859,f784(a160,x38353),x38352))
% 11.41/11.17 [4093]E(f784(f266(x40931),f784(f784(f20(x40931,a852,a852),f784(f784(f10(a852,f869(a852,a852),x40931),a344),x40932)),x40933)),f784(f784(f111(f869(x40931,a852)),f784(f266(x40931),x40932)),f784(f266(x40931),x40933)))
% 11.41/11.17 [4094]E(f784(f266(x40941),f784(f784(f20(x40941,a852,a852),f784(f784(f10(a852,f869(a852,a852),x40941),a345),x40942)),x40943)),f784(f784(f110(f869(x40941,a852)),f784(f266(x40941),x40942)),f784(f266(x40941),x40943)))
% 11.41/11.17 [4096]E(f784(f784(f130(x40961),f784(f784(f133(x40961),f60(a859,x40962,f784(f188(f860(x40961)),x40963))),x40963)),f784(f784(f165(x40961),f60(a859,x40962,f784(f188(f860(x40961)),x40963))),x40963)),f784(f784(f784(f180(f860(x40961),f860(x40961)),x40962),f161(x40961)),x40963))
% 11.41/11.17 [4101]E(f784(f266(x41011),f784(f784(f20(x41011,a852,a852),f784(f784(f10(a852,f869(a852,a852),x41011),a348),x41012)),x41013)),f784(f784(f110(f869(x41011,a852)),f784(f88(f869(x41011,a852)),f784(f266(x41011),x41012))),f784(f266(x41011),x41013)))
% 11.41/11.17 [4116]E(f784(f784(f89(a859),f784(f188(f860(x41161)),f784(f131(x41161,x41162),x41163))),f784(f188(f860(x41161)),f784(f131(x41161,f784(f784(f10(a852,a852,x41161),a341),x41162)),x41163))),f784(f188(f860(x41161)),x41163))
% 11.41/11.17 [4141]P85(f784(f784(f242(f869(x41411,a852)),f784(f784(f110(f869(x41411,a852)),f53(f869(x41411,a852),x41412)),f53(f869(x41411,a852),x41413))),f53(f869(x41411,a852),f784(f784(f111(f869(f869(x41411,a852),a852)),x41412),x41413))))
% 11.41/11.17 [4157]E(f784(f164(x41571),f784(f131(x41571,f784(f784(f10(a852,a852,x41571),a341),f784(f784(f9(x41571,x41571,a852),a343),x41572))),x41573)),f784(f784(f3(f869(x41571,a852)),f784(f164(x41571),x41573)),f784(f784(f312(x41571),x41572),f187(f869(x41571,a852)))))
% 11.41/11.17 [4166]P85(f784(f784(f242(f869(f868(x41661,x41661),a852)),f784(f784(f110(f869(f868(x41661,x41661),a852)),f310(x41661,x41662)),f310(x41661,x41663))),f310(x41661,f784(f784(f110(f869(f868(x41661,x41661),a852)),x41662),x41663))))
% 11.41/11.17 [4190]E(f784(f784(f90(a859),f784(a160,f784(a160,f2(a859)))),f784(f784(f8(a859,a859),f784(f784(f10(a859,a859,a859),f784(f89(a859),x41901)),f784(f784(f9(a859,a859,a859),f90(a859)),x41902))),f784(f267(a859),x41903))),f784(f784(f90(a859),x41903),f784(f784(f89(a859),x41901),f784(f784(f89(a859),x41901),f784(f784(f90(a859),f784(f784(f3(a859),x41903),f87(a859))),x41902)))))
% 11.41/11.17 [4200]E(f784(f266(x42001),f784(f784(f20(x42001,a852,a852),f784(f784(f10(a852,f869(a852,a852),x42001),a344),f784(f784(f9(x42001,f869(x42001,a852),a852),f347(x42001)),f784(f164(x42001),x42002)))),x42003)),f784(f164(x42001),f784(f131(x42001,x42003),x42002)))
% 11.41/11.17 [4341]E(f784(f266(x43411),f784(f784(f10(f869(a859,a852),a852,x43411),f96(a859)),f784(f784(f9(x43411,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),x43411),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),x43411),f784(f10(a852,f869(a852,a852),a859),a344)),f784(f784(f9(x43411,f869(a859,x43411),f869(a859,a852)),f784(f784(f10(f869(x43411,a852),f869(f869(a859,x43411),f869(a859,a852)),x43411),f10(x43411,a852,a859)),a343)),f784(f155(x43411),x43412))))),f784(f784(f20(a859,a852,a852),f784(f784(f10(a852,f869(a852,a852),a859),a344),f784(f784(f9(a859,a859,a852),f243(a859)),f784(f188(f860(x43411)),x43412)))),f784(f784(f9(a859,f869(a859,a852),a852),f347(a859)),x43413))))),f784(f164(x43411),f166(x43411,x43412,x43413)))
% 11.41/11.17 [4237]E(f784(f266(x42371),f784(f784(f20(x42371,a852,a852),f784(f784(f10(a852,f869(a852,a852),x42371),a348),f784(f784(f10(a852,a852,x42371),a341),f784(f784(f9(x42371,x42371,a852),a343),x42372)))),x42373)),f784(f784(f312(x42371),x42372),f784(f266(x42371),x42373)))
% 11.41/11.17 [4268]E(f784(f784(f146(f868(x42681,a859),x42681),f250(x42681,a859)),f784(f131(f868(x42681,a859),f784(f784(f9(f868(x42681,a859),f869(a859,a852),a852),f784(f784(f10(a859,f869(f869(a859,a852),a852),f868(x42681,a859)),f347(a859)),f260(x42681,a859))),x42682)),f784(f784(f173(x42681,a859),x42683),f134(a859,f784(f304(a859,f2(a859)),f784(f188(f860(x42681)),x42683)))))),f166(x42681,x42683,x42682))
% 11.41/11.17 [4296]E(f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f784(f8(a859,a1),f784(f784(f10(a1,a1,a859),f784(f89(a1),x42961)),f784(f784(f9(a859,a1,a1),f784(f784(f10(a1,f869(a1,a1),a859),f90(a1)),f109(a1))),x42962))),f784(f267(a859),x42963))),f784(f784(f90(a1),f784(f109(a1),x42963)),f784(f784(f89(a1),x42961),f784(f784(f89(a1),x42961),f784(f784(f90(a1),f784(f109(a1),f784(f784(f3(a859),x42963),f87(a859)))),x42962)))))
% 11.41/11.17 [4335]E(f784(f266(f868(x43351,x43352)),f784(f261(x43351,x43352,a852),f784(f784(f9(x43351,f869(f868(x43352,x43351),a852),f869(x43352,a852)),f784(f784(f10(f869(x43352,f869(f869(f868(x43352,x43351),a852),a852)),f869(f869(f868(x43352,x43351),a852),f869(x43352,a852)),x43351),f9(x43352,f869(f868(x43352,x43351),a852),a852)),f784(f784(f10(f869(x43352,f868(x43352,x43351)),f869(x43352,f869(f869(f868(x43352,x43351),a852),a852)),x43351),f784(f10(f868(x43352,x43351),f869(f869(f868(x43352,x43351),a852),a852),x43352),f347(f868(x43352,x43351)))),f784(f9(x43352,x43351,f868(x43352,x43351)),f251(x43352,x43351))))),x43353))),f784(f288(x43352,x43351),x43353))
% 11.41/11.17 [4369]E(f784(f266(f860(x43691)),f784(f784(f10(f869(x43691,a852),a852,f860(x43691)),f96(x43691)),f784(f784(f10(f869(x43691,f869(f860(x43691),a852)),f869(x43691,a852),f860(x43691)),f784(f10(f869(f860(x43691),a852),a852,x43691),f96(f860(x43691)))),f784(f784(f9(f860(x43691),f869(x43691,f869(f860(x43691),a852)),f869(x43691,f869(f860(x43691),a852))),f784(f784(f10(f869(x43691,f869(f869(f860(x43691),a852),f869(f860(x43691),a852))),f869(f869(x43691,f869(f860(x43691),a852)),f869(x43691,f869(f860(x43691),a852))),f860(x43691)),f20(x43691,f869(f860(x43691),a852),f869(f860(x43691),a852))),f784(f784(f10(f869(x43691,f869(f860(x43691),f869(a852,a852))),f869(x43691,f869(f869(f860(x43691),a852),f869(f860(x43691),a852))),f860(x43691)),f784(f10(f869(f860(x43691),f869(a852,a852)),f869(f869(f860(x43691),a852),f869(f860(x43691),a852)),x43691),f20(f860(x43691),a852,a852))),f784(f784(f10(f869(x43691,f869(f860(x43691),a852)),f869(x43691,f869(f860(x43691),f869(a852,a852))),f860(x43691)),f784(f10(f869(f860(x43691),a852),f869(f860(x43691),f869(a852,a852)),x43691),f784(f10(a852,f869(a852,a852),f860(x43691)),a344))),f784(f784(f9(f860(x43691),f869(x43691,f869(f860(x43691),f860(x43691))),f869(x43691,f869(f860(x43691),a852))),f784(f784(f10(f869(f869(f860(x43691),f860(x43691)),f869(f860(x43691),a852)),f869(f869(x43691,f869(f860(x43691),f860(x43691))),f869(x43691,f869(f860(x43691),a852))),f860(x43691)),f10(f869(f860(x43691),f860(x43691)),f869(f860(x43691),a852),x43691)),f784(f784(f10(f869(f860(x43691),a852),f869(f869(f860(x43691),f860(x43691)),f869(f860(x43691),a852)),f860(x43691)),f10(f860(x43691),a852,f860(x43691))),a343))),f144(x43691)))))),f784(f784(f9(x43691,f869(f860(x43691),a852),f869(f860(x43691),a852)),f784(f784(f10(f869(a852,a852),f869(f869(f860(x43691),a852),f869(f860(x43691),a852)),x43691),f10(a852,a852,f860(x43691))),f784(f784(f10(a852,f869(a852,a852),x43691),a344),f784(f784(f9(x43691,f869(x43691,a852),a852),f347(x43691)),x43692)))),f784(f784(f9(f860(x43691),f869(f860(x43691),a852),a852),f347(f860(x43691))),x43693)))))),f167(x43691,x43692,x43693))
% 11.41/11.17 [4354]E(f784(f784(f95(a1,f868(a1,a1)),f784(f784(f3(a1),x43541),x43542)),f784(f784(f9(a1,f868(a1,a1),f868(a1,a1)),f784(f784(f20(a1,f868(a1,a1),f869(f868(a1,a1),f868(a1,a1))),f784(f784(f10(a852,f869(f868(a1,a1),f869(f868(a1,a1),f868(a1,a1))),a1),f105(f868(a1,a1))),f784(f242(a1),f2(a1)))),f784(f251(a1,a1),f784(f784(f89(a1),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x43543)),f87(a1))))),f784(f784(f251(a1,a1),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x43543)),x43541))),f784(f58(x43542),f784(f784(f251(a1,a1),x43543),x43541)))
% 11.41/11.17 [4407]~E(f38(x44071,x44072),f30(x44073,x44074))
% 11.41/11.17 [4408]~E(f38(x44081,x44082),f30(x44083,x44084))
% 11.41/11.17 [4409]~E(f37(x44091,x44092),f30(x44093,x44094))
% 11.41/11.17 [4410]~E(f37(x44101,x44102),f38(x44103,x44104))
% 11.41/11.17 [4411]~E(f37(x44111,x44112),f30(x44113,x44114))
% 11.41/11.17 [4412]~E(f37(x44121,x44122),f38(x44123,x44124))
% 11.41/11.17 [4430]~E(f784(a29,x44301),f33(x44302,x44303,x44304))
% 11.41/11.17 [4431]~E(f784(a29,x44311),f35(x44312,x44313,x44314))
% 11.41/11.17 [4432]~E(f784(a29,x44321),f34(x44322,x44323,x44324))
% 11.41/11.17 [4433]~E(f33(x44331,x44332,x44333),f784(a29,x44334))
% 11.41/11.17 [4434]~E(f35(x44341,x44342,x44343),f784(a29,x44344))
% 11.41/11.17 [4435]~E(f34(x44351,x44352,x44353),f784(a29,x44354))
% 11.41/11.17 [3388]E(f784(f784(f784(f81(x33881,x33882),x33883),x33884),f784(x33883,x33884)),x33883)
% 11.41/11.17 [3451]E(f784(f784(f253(x34511,x34512,x34513),x34514),f2(a859)),x34512)
% 11.41/11.17 [3466]E(f45(x34661,x34662,x34663,f42(x34664)),f784(x34663,x34664))
% 11.41/11.17 [3467]E(f45(x34671,x34672,x34673,f43(x34674)),f784(x34672,x34674))
% 11.41/11.17 [3468]E(f46(x34681,x34682,x34683,f42(x34684)),f784(x34683,x34684))
% 11.41/11.17 [3469]E(f46(x34691,x34692,x34693,f43(x34694)),f784(x34692,x34694))
% 11.41/11.17 [3494]E(f182(x34941,x34942,x34943,f784(a160,x34944)),f784(x34943,x34944))
% 11.41/11.17 [3535]E(f154(x35351,x35352,f154(x35351,x35353,x35354)),f154(x35351,x35353,f154(x35351,x35352,x35354)))
% 11.41/11.17 [3650]P38(f30(x36501,x36502),x36503,x36504,f784(f784(f784(a196,x36503),x36501),f784(x36502,x36503)))
% 11.41/11.17 [3651]P38(f30(x36511,x36512),x36513,x36514,f784(f784(f784(a196,x36513),x36511),f784(x36512,x36513)))
% 11.41/11.17 [3663]E(f784(f239(x36631,x36632,x36633,x36634),f190(x36632)),x36633)
% 11.41/11.17 [3665]E(f784(f148(x36651,x36652,x36653,x36654),f120(x36652)),x36653)
% 11.41/11.17 [3666]E(f784(f136(x36661,x36662,x36663,x36664),f120(x36662)),x36664)
% 11.41/11.17 [3703]E(f784(f188(f865(x37031,x37032)),f225(x37031,x37032,x37033,x37034)),f2(a859))
% 11.41/11.17 [3728]E(f784(f261(x37281,x37282,x37283),f259(x37281,x37282,x37283,x37284)),x37284)
% 11.41/11.17 [3782]E(f784(f239(f864(x37821),x37822,f190(x37821),f784(f18(f864(x37821),x37822),f190(x37821))),f784(x37823,x37824)),f190(x37821))
% 11.41/11.17 [3825]E(f784(f784(f110(f869(x38251,a852)),f175(x38251,x38252,x38253)),f175(x38251,x38252,x38254)),f175(x38251,x38252,f176(x38251,x38252,x38254,x38253)))
% 11.41/11.17 [3854]E(f784(f784(f263(x38541,x38542,x38543,f868(x38542,x38543)),x38544),f251(x38542,x38543)),x38544)
% 11.41/11.17 [3863]E(f240(x38631,x38632,x38633,x38634,f190(x38632)),x38633)
% 11.41/11.17 [3864]E(f178(x38641,x38642,x38643,x38644,f120(x38642)),x38643)
% 11.41/11.17 [3865]E(f178(x38651,x38652,x38653,f120(x38651),x38654),x38653)
% 11.41/11.17 [4147]P40(x41471,x41472,x41473,x41474,f187(f869(x41471,a852)),x41474)
% 11.41/11.17 [4148]P40(x41481,x41482,x41483,x41484,f187(f869(x41481,a852)),x41484)
% 11.41/11.17 [4456]~E(f784(f322(x44561,x44562),x44563),f784(f326(x44562,x44561),x44564))
% 11.41/11.17 [4457]~E(f784(f322(x44571,x44572),x44573),f784(f326(x44572,x44571),x44574))
% 11.41/11.17 [4458]~E(f784(f322(x44581,x44582),x44583),f784(f326(x44582,x44581),x44584))
% 11.41/11.17 [4459]~E(f784(f322(x44591,x44592),x44593),f784(f326(x44592,x44591),x44594))
% 11.41/11.17 [3196]E(f784(f784(f18(x31961,x31962),x31963),x31964),x31963)
% 11.41/11.17 [3300]E(f323(x33001,x33002,f784(f784(a314,x33003),x33004)),f784(f784(x33002,x33003),x33004))
% 11.41/11.17 [3301]E(f324(x33011,x33012,f784(f784(a314,x33013),x33014)),f784(f784(x33012,x33013),x33014))
% 11.41/11.17 [3310]E(f784(f784(f206(x33101,x33102),x33103),f784(f237(x33101),x33104)),f784(f237(x33102),f784(x33103,x33104)))
% 11.41/11.17 [3486]E(f154(x34861,x34862,f784(f131(x34861,x34863),x34864)),f784(f131(x34861,x34863),f154(x34861,x34862,x34864)))
% 11.41/11.17 [3519]E(f784(f784(f74(x35191,x35192,x35193),x35194),f187(f869(x35191,a852))),x35194)
% 11.41/11.17 [3541]E(f784(f784(f155(x35411),f784(f784(f144(x35411),x35412),x35413)),f784(a160,x35414)),f784(f784(f155(x35411),x35413),x35414))
% 11.41/11.17 [3603]E(f784(f784(x36031,x36032),f784(f181(x36033,x36034,x36031),x36032)),f784(f181(x36033,x36034,x36031),f784(a160,x36032)))
% 11.41/11.17 [3643]E(f259(x36431,x36432,x36433,f784(f261(x36431,x36432,x36433),x36434)),x36434)
% 11.41/11.17 [3701]E(f784(f784(f151(x37011,f784(f784(f144(x37011),x37012),x37013)),f2(a859)),x37014),f784(f784(f144(x37011),x37014),x37013))
% 11.41/11.17 [3711]E(f784(f784(f54(f869(x37111,a852),f869(x37112,a852)),x37113),f313(x37111,x37112,x37114)),f784(f313(x37111,x37112,x37114),f52(f869(x37111,a852),x37113)))
% 11.41/11.17 [3712]E(f784(f784(f54(f869(x37121,a852),f869(x37122,a852)),x37123),f315(x37122,x37121,x37124)),f784(f315(x37122,x37121,x37124),f52(f869(x37121,a852),x37123)))
% 11.41/11.17 [3810]E(f175(x38101,x38102,f179(x38101,x38102,x38103,x38104)),f784(f784(f111(f869(x38101,a852)),f175(x38101,x38102,x38103)),x38104))
% 11.41/11.17 [3829]E(f784(f136(x38291,x38292,f784(f9(x38292,x38291,x38291),x38293),x38294),f784(f162(x38292),f120(x38292))),x38294)
% 11.41/11.17 [3875]E(f85(x38751,x38752,x38753,x38754,f187(f869(x38751,a852))),x38753)
% 11.41/11.17 [3920]E(f784(f784(f784(f784(f81(x39201,f864(x39202)),f784(f18(f864(x39202),x39201),f190(x39202))),x39203),f190(x39202)),x39204),f190(x39202))
% 11.41/11.17 [4067]E(f332(x40671,x40672,x40673,f784(f784(f10(f870(x40671,x40673),x40672,x40671),x40674),f322(x40671,x40673)),f784(f784(f10(f870(x40671,x40673),x40672,x40673),x40674),f326(x40673,x40671))),x40674)
% 11.41/11.17 [4077]E(f784(f261(x40771,x40772,x40773),f784(f784(f10(f869(x40772,f868(x40771,x40772)),f869(x40772,x40773),x40771),f784(f10(f868(x40771,x40772),x40773,x40772),x40774)),f251(x40771,x40772))),x40774)
% 11.41/11.17 [3386]E(f784(f260(x33861,x33862),f784(f784(f251(x33861,x33862),x33863),x33864)),x33864)
% 11.41/11.17 [3387]E(f784(f250(x33871,x33872),f784(f784(f251(x33871,x33872),x33873),x33874)),x33873)
% 11.41/11.17 [3424]E(f784(f188(f860(x34241)),f784(f784(f146(x34242,x34241),x34243),x34244)),f784(f188(f860(x34242)),x34244))
% 11.41/11.17 [3425]E(f784(f188(f860(x34251)),f784(f784(f151(x34251,x34252),x34253),x34254)),f784(f188(f860(x34251)),x34252))
% 11.41/11.17 [3446]E(f784(f784(f133(x34461),f784(a160,x34462)),f784(f784(f144(x34461),x34463),x34464)),f784(f784(f133(x34461),x34462),x34464))
% 11.41/11.17 [3521]E(f784(f784(f312(x35211),x35212),f784(f784(f312(x35211),x35213),x35214)),f784(f784(f312(x35211),x35213),f784(f784(f312(x35211),x35212),x35214)))
% 11.41/11.17 [3524]E(f784(f784(f146(x35241,x35242),x35243),f121(x35241,x35244)),f121(x35242,f784(f784(f146(x35241,x35242),x35243),x35244)))
% 11.41/11.17 [3539]E(f784(f162(x35391),f784(f784(f146(x35392,x35391),x35393),x35394)),f784(f784(f146(x35392,x35391),x35393),f784(f162(x35392),x35394)))
% 11.41/11.17 [3540]E(f784(f784(f146(x35401,x35402),x35403),f784(f163(x35401),x35404)),f784(f163(x35402),f784(f784(f146(x35401,x35402),x35403),x35404)))
% 11.41/11.17 [3549]E(f784(f784(f165(x35491),f784(a160,x35492)),f784(f784(f144(x35491),x35493),x35494)),f784(f784(f144(x35491),x35493),f784(f784(f165(x35491),x35492),x35494)))
% 11.41/11.17 [3553]E(f784(f164(x35531),f784(f784(f146(x35532,x35531),x35533),x35534)),f784(f313(x35532,x35531,x35533),f784(f164(x35532),x35534)))
% 11.41/11.17 [3602]E(f19(x36021,x36022,x36023,f784(a5,f784(a160,f784(a22,x36024)))),f784(x36023,x36024))
% 11.41/11.17 [3606]E(f784(f784(f130(x36061),f784(f131(x36061,x36062),x36063)),f784(f131(x36061,x36062),x36064)),f784(f131(x36061,x36062),f784(f784(f130(x36061),x36063),x36064)))
% 11.41/11.17 [3633]E(f784(f288(x36331,x36331),f784(f784(f290(x36332,x36331),x36333),x36334)),f784(f784(f290(x36332,x36331),f784(f288(x36332,x36332),x36333)),x36334))
% 11.41/11.17 [3644]E(f784(f784(f291(x36441,x36442,x36443),x36444),f187(f869(f868(x36442,x36443),a852))),f187(f869(f868(x36441,x36443),a852)))
% 11.41/11.17 [3645]E(f784(f784(f165(x36451),f784(f784(f3(a859),x36452),x36453)),f784(f784(f133(x36451),x36453),x36454)),f784(f784(f133(x36451),x36453),f784(f784(f165(x36451),x36452),x36454)))
% 11.41/11.17 [3667]E(f784(f784(f784(f283(x36671),x36672),x36673),x36674),f784(f251(f869(a108,f869(a852,f864(f861(x36671)))),f868(a108,a108)),f784(f57(x36671),x36672)))
% 11.41/11.17 [3691]E(f52(f869(x36911,a852),f784(f313(x36912,f869(x36911,a852),x36913),x36914)),f784(f784(f54(x36912,f869(x36911,a852)),x36914),x36913))
% 11.41/11.17 [3692]E(f53(f869(x36921,a852),f784(f313(x36922,f869(x36921,a852),x36923),x36924)),f784(f784(f55(x36922,f869(x36921,a852)),x36924),x36923))
% 11.41/11.17 [3693]E(f53(f869(x36931,a852),f784(f313(x36932,f869(x36931,a852),x36933),x36934)),f784(f784(f55(x36932,f869(x36931,a852)),x36934),x36933))
% 11.41/11.17 [3694]E(f52(f869(x36941,a852),f784(f313(x36942,f869(x36941,a852),x36943),x36944)),f784(f784(f54(x36942,f869(x36941,a852)),x36944),x36943))
% 11.41/11.17 [3695]E(f784(f188(f860(f868(x36951,x36952))),f784(f784(f173(x36951,x36952),x36953),x36954)),f784(f784(f246(a859),f784(f188(f860(x36951)),x36953)),f784(f188(f860(x36952)),x36954)))
% 11.41/11.17 [3697]E(f784(f315(x36971,x36972,x36973),f784(f88(f869(x36972,a852)),x36974)),f784(f88(f869(x36971,a852)),f784(f315(x36971,x36972,x36973),x36974)))
% 11.41/11.17 [3729]E(f784(f179(x37291,x37292,x37293,f187(f869(x37291,a852))),x37294),f190(x37292))
% 11.41/11.17 [3747]E(f784(f315(x37471,x37472,x37473),f784(f266(x37472),x37474)),f784(f266(x37471),f784(f784(f10(x37472,a852,x37471),x37474),x37473)))
% 11.41/11.17 [3764]E(f784(f784(f155(x37641),f784(f784(f130(x37641),x37642),f784(f784(f144(x37641),x37643),x37644))),f784(f188(f860(x37641)),x37642)),x37643)
% 11.41/11.17 [3769]E(f784(f179(x37691,x37692,f784(f18(f864(x37692),x37691),f190(x37692)),x37693),x37694),f190(x37692))
% 11.41/11.17 [3791]E(f784(f313(x37911,x37912,x37913),f784(f315(x37911,x37912,x37913),x37914)),f784(f784(f111(f869(x37912,a852)),x37914),f784(f313(x37911,x37912,x37913),f249(f869(x37911,a852)))))
% 11.41/11.17 [3809]P85(f784(f784(f347(x38091),f784(x38092,x38093)),f784(f313(x38094,x38091,x38092),f249(f869(x38094,a852)))))
% 11.41/11.17 [3817]E(f21(x38171,x38172,x38173,f784(a5,f784(a160,f784(a22,x38174)))),f784(f784(x38173,x38174),f21(x38171,x38172,x38173,x38174)))
% 11.41/11.17 [3832]E(f147(x38321,x38322,f784(f784(f144(x38321),x38323),x38324)),f784(f784(f89(a859),f784(f784(f89(a859),f784(x38322,x38323)),f147(x38321,x38322,x38324))),f784(a160,f2(a859))))
% 11.41/11.17 [3845]E(f182(f860(x38451),f784(f784(f144(x38451),x38452),x38453),f784(f784(f9(a859,f860(x38451),f860(x38451)),f133(x38451)),x38453),x38454),f784(f784(f133(x38451),x38454),f784(f784(f144(x38451),x38452),x38453)))
% 11.41/11.17 [3846]P26(x38461,f868(x38462,x38461),f349(x38463,x38464,x38462,x38461),f784(f784(f54(x38462,f869(x38461,a852)),x38464),x38463))
% 11.41/11.17 [3855]E(f784(f784(f3(f869(x38551,a852)),f784(f784(f3(f869(x38551,a852)),x38552),x38553)),f784(f784(f312(x38551),x38554),f187(f869(x38551,a852)))),f784(f784(f3(f869(x38551,a852)),x38552),f784(f784(f312(x38551),x38554),x38553)))
% 11.41/11.17 [3868]E(f784(f784(f180(f869(x38681,x38682),f869(x38681,x38682)),x38683),f82(x38682,x38682,x38681,x38684)),f82(x38682,x38682,x38681,f784(f784(f180(x38682,x38682),x38683),x38684)))
% 11.41/11.17 [3943]E(f784(f784(f784(f180(f860(x39431),f860(x39431)),x39432),f161(x39431)),f784(f784(f784(f180(f860(x39431),f860(x39431)),x39433),f161(x39431)),x39434)),f784(f784(f784(f180(f860(x39431),f860(x39431)),f784(f784(f89(a859),x39432),x39433)),f161(x39431)),x39434))
% 11.41/11.17 [3990]E(f784(f784(f110(f869(f870(x39901,x39902),a852)),f784(f313(x39901,f870(x39901,x39902),f322(x39901,x39902)),x39903)),f784(f313(x39902,f870(x39901,x39902),f326(x39902,x39901)),x39904)),f327(x39901,x39902,x39903,x39904))
% 11.41/11.17 [4031]P85(f784(f784(f242(f869(x40311,a852)),f784(f164(x40311),f784(f784(f151(x40311,x40312),x40313),x40314))),f784(f784(f312(x40311),x40314),f784(f164(x40311),x40312))))
% 11.41/11.17 [4065]E(f784(f784(f54(f869(x40651,a852),f869(f868(x40651,x40652),a852)),x40653),f784(f784(f9(f869(x40651,a852),f869(x40651,f869(x40652,a852)),f869(f868(x40651,x40652),a852)),f258(x40651,x40652)),x40654)),f784(f784(f258(x40651,x40652),f52(f869(x40651,a852),x40653)),x40654))
% 11.41/11.17 [4102]E(f214(x41021,x41022,x41023,f784(f82(x41022,f869(a108,f869(a108,f869(f868(a108,a108),f869(a108,f861(x41022))))),x41021,f209(x41022)),x41024)),f215(x41021,x41022,x41024,x41023))
% 11.41/11.17 [4119]E(f211(x41191,x41192,x41193,f784(f82(x41192,f869(a108,f869(a108,f869(f868(a108,a108),f869(a108,f861(f864(x41192)))))),x41191,f210(x41192)),x41194)),f212(x41191,x41192,x41194,x41193))
% 11.41/11.17 [4122]P85(f784(f76(x41221,x41222,x41223,x41224,f187(f869(x41221,a852))),x41224))
% 11.41/11.17 [4123]P85(f784(f76(x41231,x41232,x41233,x41234,f187(f869(x41231,a852))),x41234))
% 11.41/11.17 [4169]E(f784(f784(f54(x41691,f869(x41692,a852)),x41693),f784(f784(f9(x41691,f869(x41692,a852),f869(x41692,a852)),f784(f784(f10(x41692,f869(f869(x41692,a852),f869(x41692,a852)),x41691),f312(x41692)),x41694)),f187(f869(x41692,a852)))),f784(f313(x41691,x41692,x41694),x41693))
% 11.41/11.17 [4175]P85(f784(f784(f242(f869(x41751,a852)),f784(f269(x41752,x41751),f784(f784(f111(f869(f868(x41752,x41751),a852)),x41753),x41754))),f784(f784(f111(f869(x41751,a852)),f784(f269(x41752,x41751),x41753)),f784(f269(x41752,x41751),x41754))))
% 11.41/11.17 [4176]P85(f784(f784(f242(f869(x41761,a852)),f784(f271(x41761,x41762),f784(f784(f111(f869(f868(x41761,x41762),a852)),x41763),x41764))),f784(f784(f111(f869(x41761,a852)),f784(f271(x41761,x41762),x41763)),f784(f271(x41761,x41762),x41764))))
% 11.41/11.17 [4235]P85(f784(f784(f242(f869(f868(x42351,x42352),a852)),f784(f313(x42352,f868(x42351,x42352),f349(x42353,x42354,x42351,x42352)),f784(f784(f54(x42351,f869(x42352,a852)),x42354),x42353))),f784(f784(f258(x42351,x42352),x42354),x42353)))
% 11.41/11.17 [4236]E(f281(x42361,x42362,x42363,f784(f82(x42362,f869(a108,f869(a108,f869(f868(a108,a108),f868(f869(a108,f869(a852,f864(f861(x42362)))),f868(a108,a108))))),x42361,f283(x42362)),x42364)),f284(x42361,x42362,x42364,x42363))
% 11.41/11.17 [4274]E(f94(f868(x42741,x42742),f784(f261(x42741,x42742,a852),f784(f784(f9(x42741,f869(x42742,a852),f869(x42742,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x42742,a852),f869(x42742,a852)),x42741),f10(a852,a852,x42742)),f784(f784(f10(a852,f869(a852,a852),x42741),a344),f784(a343,x42743)))),f784(a343,x42744)))),f784(f784(f251(x42741,x42742),x42743),x42744))
% 11.41/11.17 [4275]E(f99(f868(x42751,x42752),f784(f261(x42751,x42752,a852),f784(f784(f9(x42751,f869(x42752,a852),f869(x42752,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x42752,a852),f869(x42752,a852)),x42751),f10(a852,a852,x42752)),f784(f784(f10(a852,f869(a852,a852),x42751),a344),f784(a343,x42753)))),f784(a343,x42754)))),f784(f784(f251(x42751,x42752),x42753),x42754))
% 11.41/11.17 [4345]E(f784(f784(f261(f860(x43451),f860(x43451),f868(f860(x43451),f860(x43451))),f784(f784(f20(f860(x43451),f869(f860(x43451),f868(f860(x43451),f860(x43451))),f869(f860(x43451),f868(f860(x43451),f860(x43451)))),f784(f784(f10(f869(f860(x43451),f869(f868(f860(x43451),f860(x43451)),f868(f860(x43451),f860(x43451)))),f869(f869(f860(x43451),f868(f860(x43451),f860(x43451))),f869(f860(x43451),f868(f860(x43451),f860(x43451)))),f860(x43451)),f20(f860(x43451),f868(f860(x43451),f860(x43451)),f868(f860(x43451),f860(x43451)))),f784(f784(f10(f869(f860(x43451),f868(f860(x43451),f860(x43451))),f869(f860(x43451),f869(f868(f860(x43451),f860(x43451)),f868(f860(x43451),f860(x43451)))),f860(x43451)),f784(f10(f868(f860(x43451),f860(x43451)),f869(f868(f860(x43451),f860(x43451)),f868(f860(x43451),f860(x43451))),f860(x43451)),f784(f105(f868(f860(x43451),f860(x43451))),f784(x43452,x43453)))),f784(f784(f10(f860(x43451),f869(f860(x43451),f868(f860(x43451),f860(x43451))),f860(x43451)),f251(f860(x43451),f860(x43451))),f784(f144(x43451),x43453))))),f784(f784(f9(f860(x43451),f869(f860(x43451),f860(x43451)),f869(f860(x43451),f868(f860(x43451),f860(x43451)))),f784(f784(f10(f869(f860(x43451),f868(f860(x43451),f860(x43451))),f869(f869(f860(x43451),f860(x43451)),f869(f860(x43451),f868(f860(x43451),f860(x43451)))),f860(x43451)),f10(f860(x43451),f868(f860(x43451),f860(x43451)),f860(x43451))),f251(f860(x43451),f860(x43451)))),f784(f144(x43451),x43453)))),f158(x43451,x43452,x43454)),f158(x43451,x43452,f784(f784(f144(x43451),x43453),x43454)))
% 11.41/11.17 [4350]E(f784(f136(f869(x43501,f864(x43502)),f868(x43501,x43502),f784(f9(f868(x43501,x43502),f869(x43501,f864(x43502)),f869(x43501,f864(x43502))),f784(f261(x43501,x43502,f869(f869(x43501,f864(x43502)),f869(x43501,f864(x43502)))),f784(f784(f9(x43501,f869(x43502,f864(x43502)),f869(x43502,f869(f869(x43501,f864(x43502)),f869(x43501,f864(x43502))))),f784(f784(f10(f869(f864(x43502),f869(f869(x43501,f864(x43502)),f869(x43501,f864(x43502)))),f869(f869(x43502,f864(x43502)),f869(x43502,f869(f869(x43501,f864(x43502)),f869(x43501,f864(x43502))))),x43501),f10(f864(x43502),f869(f869(x43501,f864(x43502)),f869(x43501,f864(x43502))),x43502)),f784(f784(f10(f869(f869(x43501,f864(x43502)),f869(f864(x43502),f869(x43501,f864(x43502)))),f869(f864(x43502),f869(f869(x43501,f864(x43502)),f869(x43501,f864(x43502)))),x43501),f9(f869(x43501,f864(x43502)),f864(x43502),f869(x43501,f864(x43502)))),f784(f9(f869(x43501,f864(x43502)),x43501,f869(f864(x43502),f869(x43501,f864(x43502)))),f81(x43501,f864(x43502)))))),f237(x43502)))),x43503),f784(f162(f868(x43501,x43502)),x43504)),f176(x43501,x43502,x43503,f172(x43501,x43502,x43504)))
% 11.41/11.17 [3464]E(f784(f188(f858(x34641)),f784(f784(f784(f100(x34641),x34642),x34643),x34644)),f2(a859))
% 11.41/11.17 [3581]E(f784(f784(f165(x35811),x35812),f784(f784(f165(x35811),x35813),x35814)),f784(f784(f165(x35811),f784(f784(f246(a859),x35812),x35813)),x35814))
% 11.41/11.17 [3582]E(f784(f784(f133(x35821),x35822),f784(f784(f133(x35821),x35823),x35824)),f784(f784(f133(x35821),f784(f784(f89(a859),x35822),x35823)),x35824))
% 11.41/11.17 [3594]E(f784(f784(f130(x35941),f784(f784(f144(x35941),x35942),x35943)),x35944),f784(f784(f144(x35941),x35942),f784(f784(f130(x35941),x35943),x35944)))
% 11.41/11.17 [3595]E(f784(f784(f130(x35951),f784(f784(f130(x35951),x35952),x35953)),x35954),f784(f784(f130(x35951),x35952),f784(f784(f130(x35951),x35953),x35954)))
% 11.41/11.17 [3677]E(f784(f784(f155(x36771),f784(f784(f144(x36771),x36772),x36773)),x36774),f182(x36771,x36772,f784(f155(x36771),x36773),x36774))
% 11.41/11.17 [3686]E(f784(f784(f180(x36861,x36861),x36862),f784(f784(f180(x36861,x36861),x36863),x36864)),f784(f784(f180(x36861,x36861),f784(f784(f90(a859),x36863),x36862)),x36864))
% 11.41/11.17 [3714]E(f784(f784(f110(f869(x37141,a852)),x37142),f784(f784(f312(x37141),x37143),x37144)),f784(f784(f312(x37141),x37143),f784(f784(f110(f869(x37141,a852)),x37142),x37144)))
% 11.41/11.17 [3732]E(f784(f784(f784(f180(x37321,x37321),x37322),x37323),f784(x37323,x37324)),f784(x37323,f784(f784(f784(f180(x37321,x37321),x37322),x37323),x37324)))
% 11.41/11.17 [3739]E(f784(f784(f291(x37391,x37392,x37393),f187(f869(f868(x37391,x37392),a852))),x37394),f187(f869(f868(x37391,x37393),a852)))
% 11.41/11.17 [3753]E(f784(f784(f110(f869(x37531,a852)),f784(f784(f312(x37531),x37532),x37533)),x37534),f784(f784(f312(x37531),x37532),f784(f784(f110(f869(x37531,a852)),x37533),x37534)))
% 11.41/11.17 [3771]E(f784(f50(f868(x37711,x37712)),f784(f784(f258(x37711,x37712),x37713),f784(f18(f869(x37712,a852),x37711),x37714))),f784(f784(f90(a859),f784(f50(x37711),x37713)),f784(f50(x37712),x37714)))
% 11.41/11.17 [3779]E(f784(f784(f111(f869(x37791,a852)),f784(f784(f312(x37791),x37792),x37793)),f784(f784(f312(x37791),x37792),x37794)),f784(f784(f312(x37791),x37792),f784(f784(f111(f869(x37791,a852)),x37793),x37794)))
% 11.41/11.17 [3789]E(f176(x37891,x37892,f172(x37891,x37892,x37893),f172(x37891,x37892,x37894)),f172(x37891,x37892,f784(f784(f130(f868(x37891,x37892)),x37894),x37893)))
% 11.41/11.17 [3795]E(f784(f784(f110(f869(x37951,a852)),x37952),f784(f784(f110(f869(x37951,a852)),x37953),x37954)),f784(f784(f110(f869(x37951,a852)),x37953),f784(f784(f110(f869(x37951,a852)),x37952),x37954)))
% 11.41/11.17 [3796]E(f784(f784(f111(f869(x37961,a852)),x37962),f784(f784(f111(f869(x37961,a852)),x37963),x37964)),f784(f784(f111(f869(x37961,a852)),x37963),f784(f784(f111(f869(x37961,a852)),x37962),x37964)))
% 11.41/11.17 [3805]E(f74(x38051,x38052,f784(f784(f10(x38052,f869(x38052,x38052),x38051),x38053),x38054)),f784(f75(x38052,x38051,x38053),x38054))
% 11.41/11.17 [3814]E(f170(x38141,f784(f784(f146(f860(x38142),f860(x38141)),f784(f146(x38142,x38141),x38143)),x38144)),f784(f784(f146(f860(x38142),f860(x38141)),f784(f146(x38142,x38141),x38143)),f170(x38142,x38144)))
% 11.41/11.17 [3831]E(f179(x38311,x38312,x38313,f784(f88(f869(x38311,a852)),f784(f784(f312(x38311),x38314),f187(f869(x38311,a852))))),f784(f784(f784(f81(x38311,f864(x38312)),x38313),x38314),f190(x38312)))
% 11.41/11.17 [3889]E(f784(f82(x38891,x38891,x38891,f784(f784(f180(x38891,x38891),x38892),x38893)),f784(f784(f180(x38891,x38891),x38894),x38893)),f784(f784(f180(x38891,x38891),f784(f784(f89(a859),x38892),x38894)),x38893))
% 11.41/11.17 [3903]E(f784(f784(f784(f81(x39031,f864(x39032)),f172(x39031,x39032,x39033)),f784(f250(x39031,x39032),x39034)),f784(f237(x39032),f784(f260(x39031,x39032),x39034))),f172(x39031,x39032,f784(f784(f144(f868(x39031,x39032)),x39034),x39033)))
% 11.41/11.17 [3912]E(f784(f784(f111(f869(x39121,a852)),f784(f784(f3(f869(x39121,a852)),x39122),x39123)),f784(f784(f3(f869(x39121,a852)),x39122),x39124)),f784(f784(f3(f869(x39121,a852)),x39122),f784(f784(f110(f869(x39121,a852)),x39123),x39124)))
% 11.41/11.17 [3913]E(f784(f784(f110(f869(x39131,a852)),f784(f784(f3(f869(x39131,a852)),x39132),x39133)),f784(f784(f3(f869(x39131,a852)),x39132),x39134)),f784(f784(f3(f869(x39131,a852)),x39132),f784(f784(f111(f869(x39131,a852)),x39133),x39134)))
% 11.41/11.17 [3914]E(f784(f784(f111(f869(x39141,a852)),f784(f784(f110(f869(x39141,a852)),x39142),x39143)),f784(f784(f110(f869(x39141,a852)),x39142),x39144)),f784(f784(f110(f869(x39141,a852)),x39142),f784(f784(f111(f869(x39141,a852)),x39143),x39144)))
% 11.41/11.17 [3915]E(f784(f784(f3(f869(x39151,a852)),f784(f784(f111(f869(x39151,a852)),x39152),x39153)),f784(f784(f111(f869(x39151,a852)),x39152),x39154)),f784(f784(f111(f869(x39151,a852)),x39152),f784(f784(f3(f869(x39151,a852)),x39153),x39154)))
% 11.41/11.17 [3916]E(f784(f784(f110(f869(x39161,a852)),f784(f784(f111(f869(x39161,a852)),x39162),x39163)),f784(f784(f111(f869(x39161,a852)),x39162),x39164)),f784(f784(f111(f869(x39161,a852)),x39162),f784(f784(f110(f869(x39161,a852)),x39163),x39164)))
% 11.41/11.17 [3922]E(f784(f50(f868(x39221,x39222)),f784(f784(f258(x39221,x39222),f784(f784(f312(x39221),x39223),f187(f869(x39221,a852)))),f784(f18(f869(x39222,a852),x39221),x39224))),f784(f50(x39222),x39224))
% 11.41/11.17 [3958]E(f784(f784(f55(x39581,f869(x39582,a852)),x39583),f784(f784(f10(f869(x39582,a852),f869(x39582,a852),x39581),f88(f869(x39582,a852))),x39584)),f784(f88(f869(x39582,a852)),f784(f784(f54(x39581,f869(x39582,a852)),x39583),x39584)))
% 11.41/11.17 [3959]E(f784(f784(f54(x39591,f869(x39592,a852)),x39593),f784(f784(f10(f869(x39592,a852),f869(x39592,a852),x39591),f88(f869(x39592,a852))),x39594)),f784(f88(f869(x39592,a852)),f784(f784(f55(x39591,f869(x39592,a852)),x39593),x39594)))
% 11.41/11.17 [3974]E(f784(f784(f291(x39741,x39741,x39741),f784(f784(f180(f868(x39741,x39741),a852),x39742),x39743)),f784(f784(f180(f868(x39741,x39741),a852),x39744),x39743)),f784(f784(f180(f868(x39741,x39741),a852),f784(f784(f89(a859),x39742),x39744)),x39743))
% 11.41/11.17 [4006]E(f784(f784(f55(x40061,f869(f869(x40062,a852),a852)),x40063),f784(f784(f10(f869(x40062,a852),f869(f869(x40062,a852),a852),x40061),f311(x40062)),x40064)),f784(f311(x40062),f784(f784(f55(x40061,f869(x40062,a852)),x40063),x40064)))
% 11.41/11.17 [4034]E(f784(f784(f54(f869(x40341,a852),f869(x40342,a852)),x40343),f784(f784(f9(f869(x40341,a852),f869(x40341,f869(x40342,a852)),f869(x40342,a852)),f54(x40341,f869(x40342,a852))),x40344)),f784(f784(f54(x40341,f869(x40342,a852)),f52(f869(x40341,a852),x40343)),x40344))
% 11.41/11.17 [4035]E(f784(f784(f55(f869(x40351,a852),f869(x40352,a852)),x40353),f784(f784(f9(f869(x40351,a852),f869(x40351,f869(x40352,a852)),f869(x40352,a852)),f55(x40351,f869(x40352,a852))),x40354)),f784(f784(f55(x40351,f869(x40352,a852)),f52(f869(x40351,a852),x40353)),x40354))
% 11.41/11.17 [4036]E(f784(f784(f54(f869(x40361,a852),f869(x40362,a852)),x40363),f784(f784(f9(f869(x40361,a852),f869(x40361,f869(x40362,a852)),f869(x40362,a852)),f54(x40361,f869(x40362,a852))),x40364)),f784(f784(f54(x40361,f869(x40362,a852)),f52(f869(x40361,a852),x40363)),x40364))
% 11.41/11.17 [4037]E(f784(f784(f55(f869(x40371,a852),f869(x40372,a852)),x40373),f784(f784(f9(f869(x40371,a852),f869(x40371,f869(x40372,a852)),f869(x40372,a852)),f55(x40371,f869(x40372,a852))),x40374)),f784(f784(f55(x40371,f869(x40372,a852)),f52(f869(x40371,a852),x40373)),x40374))
% 11.41/11.17 [4042]E(f784(f784(f146(x40421,x40422),x40423),f784(f136(f860(x40421),f860(x40421),f130(x40421),f120(x40421)),x40424)),f784(f136(f860(x40422),f860(x40422),f130(x40422),f120(x40422)),f784(f784(f146(f860(x40421),f860(x40422)),f784(f146(x40421,x40422),x40423)),x40424)))
% 11.41/11.17 [4044]E(f182(f860(x40441),f120(x40441),f784(f784(f10(f860(x40441),f860(x40441),a859),f784(f144(x40441),x40442)),f784(f784(f9(a859,f860(x40441),f860(x40441)),f165(x40441)),x40443)),x40444),f784(f784(f165(x40441),x40444),f784(f784(f144(x40441),x40442),x40443)))
% 11.41/11.17 [4086]P85(f784(f784(f242(f869(x40861,a852)),f784(f313(x40862,x40861,x40863),f784(f315(x40862,x40861,x40863),x40864))),x40864))
% 11.41/11.17 [4089]E(f784(f313(f868(x40891,x40892),f868(x40892,x40891),f784(f261(x40891,x40892,f868(x40892,x40891)),f784(f9(x40892,x40891,f868(x40892,x40891)),f251(x40892,x40891)))),f784(f784(f258(x40891,x40892),x40893),f784(f18(f869(x40892,a852),x40891),x40894))),f784(f784(f258(x40892,x40891),x40894),f784(f18(f869(x40891,a852),x40892),x40893)))
% 11.41/11.17 [4098]E(f784(f784(f54(x40981,f869(x40982,a852)),x40983),f784(f784(f10(f869(x40981,a852),f869(x40982,a852),x40981),f287(x40981,x40982,x40984)),f784(f784(f9(x40981,f869(x40981,a852),f869(x40981,a852)),f312(x40981)),f187(f869(x40981,a852))))),f784(f287(x40981,x40982,x40984),x40983))
% 11.41/11.17 [4099]E(f784(f784(f54(x40991,f869(x40992,a852)),x40993),f784(f784(f10(f869(x40991,a852),f869(x40992,a852),x40991),f315(x40992,x40991,x40994)),f784(f784(f9(x40991,f869(x40991,a852),f869(x40991,a852)),f312(x40991)),f187(f869(x40991,a852))))),f784(f315(x40992,x40991,x40994),x40993))
% 11.41/11.17 [4189]E(f784(f784(f111(f869(x41891,a852)),f784(f784(f111(f869(x41891,a852)),f784(f784(f110(f869(x41891,a852)),x41892),x41893)),f784(f784(f110(f869(x41891,a852)),x41893),x41894))),f784(f784(f110(f869(x41891,a852)),x41894),x41892)),f784(f784(f110(f869(x41891,a852)),f784(f784(f110(f869(x41891,a852)),f784(f784(f111(f869(x41891,a852)),x41892),x41893)),f784(f784(f111(f869(x41891,a852)),x41893),x41894))),f784(f784(f111(f869(x41891,a852)),x41894),x41892)))
% 11.41/11.17 [4248]E(f784(f136(f860(x42481),f860(x42481),f130(x42481),f120(x42481)),f784(f784(f146(x42482,f860(x42481)),f784(f784(f9(x42482,f860(x42481),f860(x42481)),f784(f784(f10(x42481,f869(f860(x42481),f860(x42481)),x42482),f144(x42481)),x42483)),f120(x42481))),x42484)),f784(f784(f146(x42482,x42481),x42483),x42484))
% 11.41/11.17 [4258]E(f784(f784(f95(a1,x42581),f784(f113(a1),f784(f784(f89(a1),x42582),a106))),f784(f784(f20(a1,x42581,x42581),f784(f784(f9(a1,x42581,f869(x42581,x42581)),f784(f784(f10(a852,f869(x42581,f869(x42581,x42581)),a1),f105(x42581)),a193)),x42583)),f784(f784(f10(a859,x42581,a1),x42584),a114))),f182(x42581,x42583,x42584,f784(f113(a859),x42582)))
% 11.41/11.17 [4501]~P85(f784(f784(f187(f869(x45011,f869(x45012,a852))),x45013),x45014))
% 11.41/11.17 [3742]E(f784(f784(f155(x37421),f784(f784(f130(x37421),x37422),x37423)),f784(f784(f89(a859),f784(f188(f860(x37421)),x37422)),x37424)),f784(f784(f155(x37421),x37423),x37424))
% 11.41/11.17 [3746]E(f784(f784(f133(x37461),x37462),f784(f784(f165(x37461),f784(f784(f89(a859),x37463),x37462)),x37464)),f784(f784(f165(x37461),x37463),f784(f784(f133(x37461),x37462),x37464)))
% 11.41/11.17 [3843]E(f784(f784(f110(f869(x38431,a852)),f784(f269(x38432,x38431),x38433)),f784(f269(x38432,x38431),x38434)),f784(f269(x38432,x38431),f784(f784(f110(f869(f868(x38432,x38431),a852)),x38433),x38434)))
% 11.41/11.17 [3844]E(f784(f784(f110(f869(x38441,a852)),f784(f271(x38441,x38442),x38443)),f784(f271(x38441,x38442),x38444)),f784(f271(x38441,x38442),f784(f784(f110(f869(f868(x38441,x38442),a852)),x38443),x38444)))
% 11.41/11.17 [3849]E(f784(f784(f3(f869(x38491,a852)),f784(f784(f111(f869(x38491,a852)),x38492),x38493)),x38494),f784(f784(f111(f869(x38491,a852)),x38492),f784(f784(f3(f869(x38491,a852)),x38493),x38494)))
% 11.41/11.17 [3850]E(f784(f784(f110(f869(x38501,a852)),f784(f784(f110(f869(x38501,a852)),x38502),x38503)),x38504),f784(f784(f110(f869(x38501,a852)),x38502),f784(f784(f110(f869(x38501,a852)),x38503),x38504)))
% 11.41/11.17 [3851]E(f784(f784(f111(f869(x38511,a852)),f784(f784(f111(f869(x38511,a852)),x38512),x38513)),x38514),f784(f784(f111(f869(x38511,a852)),x38512),f784(f784(f111(f869(x38511,a852)),x38513),x38514)))
% 11.41/11.17 [3890]E(f784(f784(f110(f869(f868(x38901,x38902),a852)),f784(f288(x38902,x38901),x38903)),f784(f288(x38902,x38901),x38904)),f784(f288(x38902,x38901),f784(f784(f110(f869(f868(x38902,x38901),a852)),x38903),x38904)))
% 11.41/11.17 [3891]E(f784(f784(f111(f869(f868(x38911,x38912),a852)),f784(f288(x38912,x38911),x38913)),f784(f288(x38912,x38911),x38914)),f784(f288(x38912,x38911),f784(f784(f111(f869(f868(x38912,x38911),a852)),x38913),x38914)))
% 11.41/11.17 [3962]E(f784(f784(f110(f869(x39621,a852)),f784(f784(f3(f869(x39621,a852)),x39622),x39623)),f784(f784(f3(f869(x39621,a852)),x39624),x39623)),f784(f784(f3(f869(x39621,a852)),f784(f784(f110(f869(x39621,a852)),x39622),x39624)),x39623))
% 11.41/11.17 [3963]E(f784(f784(f111(f869(x39631,a852)),f784(f784(f110(f869(x39631,a852)),x39632),x39633)),f784(f784(f110(f869(x39631,a852)),x39634),x39633)),f784(f784(f110(f869(x39631,a852)),f784(f784(f111(f869(x39631,a852)),x39632),x39634)),x39633))
% 11.41/11.17 [3964]E(f784(f784(f3(f869(x39641,a852)),f784(f784(f111(f869(x39641,a852)),x39642),x39643)),f784(f784(f111(f869(x39641,a852)),x39644),x39643)),f784(f784(f111(f869(x39641,a852)),f784(f784(f3(f869(x39641,a852)),x39642),x39644)),x39643))
% 11.41/11.17 [3965]E(f784(f784(f110(f869(x39651,a852)),f784(f784(f111(f869(x39651,a852)),x39652),x39653)),f784(f784(f111(f869(x39651,a852)),x39654),x39653)),f784(f784(f111(f869(x39651,a852)),f784(f784(f110(f869(x39651,a852)),x39652),x39654)),x39653))
% 11.41/11.17 [3966]E(f784(f784(f3(f869(x39661,a852)),f784(f784(f111(f869(x39661,a852)),x39662),x39663)),f784(f784(f111(f869(x39661,a852)),x39664),x39663)),f784(f784(f3(f869(x39661,a852)),f784(f784(f111(f869(x39661,a852)),x39662),x39663)),x39664))
% 11.41/11.17 [3977]E(f784(f784(f3(f869(x39771,a852)),f784(f784(f3(f869(x39771,a852)),x39772),f784(f784(f312(x39771),x39773),f187(f869(x39771,a852))))),x39774),f784(f784(f3(f869(x39771,a852)),x39772),f784(f784(f312(x39771),x39773),x39774)))
% 11.41/11.17 [4033]E(f784(f784(f110(f869(x40331,a852)),f784(f784(f312(x40331),x40332),f784(f784(f312(x40331),x40333),f187(f869(x40331,a852))))),f784(f286(x40331),x40334)),f784(f286(x40331),f784(f784(f312(f868(x40331,x40331)),f784(f784(f251(x40331,x40331),x40332),x40333)),x40334)))
% 11.41/11.17 [4060]E(f784(f784(f54(a859,f869(x40601,a852)),f784(f303(a859),x40602)),f784(f784(f10(a859,f869(x40601,a852),a859),x40603),f784(f784(f9(a859,a859,a859),f89(a859)),x40604))),f784(f784(f54(a859,f869(x40601,a852)),f305(a859,x40604,f784(f784(f89(a859),x40602),x40604))),x40603))
% 11.41/11.17 [4061]E(f167(x40611,f784(f287(x40611,x40611,x40612),f784(f784(f312(x40611),x40613),f187(f869(x40611,a852)))),f784(f287(f860(x40611),f860(x40611),f150(x40611,x40612)),f784(f784(f312(f860(x40611)),x40614),f187(f869(f860(x40611),a852))))),f784(f287(f860(x40611),f860(x40611),f150(x40611,x40612)),f784(f784(f312(f860(x40611)),f784(f784(f144(x40611),x40613),x40614)),f187(f869(f860(x40611),a852)))))
% 11.41/11.17 [4124]E(f172(x41241,x41242,f784(f784(f146(x41241,f868(x41241,x41242)),f784(f784(f20(x41241,x41242,f868(x41241,x41242)),f251(x41241,x41242)),x41243)),x41244)),f179(x41241,x41242,f784(f82(x41242,f864(x41242),x41241,f237(x41242)),x41243),f784(f164(x41241),x41244)))
% 11.41/11.17 [4127]E(f784(f266(x41271),f784(f784(f9(x41271,f869(x41272,a852),a852),f784(f784(f10(x41272,f869(f869(x41272,a852),a852),x41271),f347(x41272)),x41273)),x41274)),f784(f315(x41271,x41272,x41273),x41274))
% 11.41/11.17 [4220]E(f784(f266(x42201),f784(f784(f9(x42201,f869(f868(x42202,x42201),a852),a852),f784(f784(f10(f868(x42202,x42201),f869(f869(f868(x42202,x42201),a852),a852),x42201),f347(f868(x42202,x42201))),f784(f251(x42202,x42201),x42203))),x42204)),f784(f287(x42202,x42201,x42204),f784(f784(f312(x42202),x42203),f187(f869(x42202,a852)))))
% 11.41/11.17 [4234]E(f784(f784(f146(f868(x42341,a859),x42341),f250(x42341,a859)),f784(f131(f868(x42341,a859),f784(f784(f10(a859,a852,f868(x42341,a859)),x42342),f784(f784(f10(a859,a859,f868(x42341,a859)),a160),f260(x42341,a859)))),f784(f784(f173(x42341,a859),x42343),x42344))),f784(f784(f146(f868(x42341,a859),x42341),f250(x42341,a859)),f784(f131(f868(x42341,a859),f784(f784(f10(a859,a852,f868(x42341,a859)),x42342),f260(x42341,a859))),f784(f784(f173(x42341,a859),x42343),f784(f784(f146(a859,a859),a160),x42344)))))
% 11.41/11.17 [4241]P85(f784(f784(f242(f869(f869(x42411,a852),a852)),f784(f784(f54(x42412,f869(f869(x42411,a852),a852)),x42413),f784(f784(f10(f869(x42411,a852),f869(f869(x42411,a852),a852),x42412),f311(x42411)),x42414))),f784(f311(x42411),f784(f784(f54(x42412,f869(x42411,a852)),x42413),x42414))))
% 11.41/11.17 [4281]E(f784(f784(f95(a1,x42811),f784(f113(a1),f784(f784(f89(a1),x42812),a106))),f784(f784(f20(a1,x42811,x42811),f784(f784(f9(a1,x42811,f869(x42811,x42811)),f784(f784(f10(a852,f869(x42811,f869(x42811,x42811)),a1),f105(x42811)),a193)),x42813)),f784(f784(f20(a1,x42811,x42811),f784(f784(f10(a859,f869(x42811,x42811),a1),x42814),a114)),f784(f784(f10(a859,x42811,a1),f181(x42811,x42813,x42814)),a114)))),f784(f181(x42811,x42813,x42814),f784(f113(a859),x42812)))
% 11.41/11.17 [4284]E(f784(f784(f146(x42841,x42842),f784(f82(f864(x42842),x42842,x42841,f241(x42842)),x42843)),f784(f131(x42841,f784(f784(f10(a852,a852,x42841),a341),f784(f784(f9(x42841,f864(x42842),a852),f784(f784(f10(f864(x42842),f869(f864(x42842),a852),x42841),a343),x42843)),f190(x42842)))),x42844)),f156(x42841,x42842,x42843,x42844))
% 11.41/11.17 [4305]E(f784(f266(f868(x43051,x43052)),f784(f261(x43051,x43052,a852),f784(f784(f9(x43051,f869(x43052,a852),f869(x43052,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x43052,a852),f869(x43052,a852)),x43051),f10(a852,a852,x43052)),f784(f784(f10(a852,f869(a852,a852),x43051),a344),f784(f784(f9(x43051,f869(x43051,a852),a852),f347(x43051)),x43053)))),f784(f784(f9(x43052,f869(x43052,a852),a852),f347(x43052)),x43054)))),f233(x43051,x43052,x43053,x43054))
% 11.41/11.17 [4338]E(f784(f784(f54(x43381,f869(f868(x43381,x43382),a852)),x43383),f784(f784(f20(x43381,f869(x43382,f869(f868(x43381,x43382),a852)),f869(f868(x43381,x43382),a852)),f784(f784(f10(f869(x43382,a852),f869(f869(x43382,f869(f868(x43381,x43382),a852)),f869(f868(x43381,x43382),a852)),x43381),f54(x43382,f869(f868(x43381,x43382),a852))),x43384)),f784(f784(f9(x43381,f869(f868(x43381,x43382),a852),f869(x43382,f869(f868(x43381,x43382),a852))),f784(f784(f10(f869(x43382,f869(f869(f868(x43381,x43382),a852),f869(f868(x43381,x43382),a852))),f869(f869(f868(x43381,x43382),a852),f869(x43382,f869(f868(x43381,x43382),a852))),x43381),f9(x43382,f869(f868(x43381,x43382),a852),f869(f868(x43381,x43382),a852))),f784(f784(f10(f869(x43382,f868(x43381,x43382)),f869(x43382,f869(f869(f868(x43381,x43382),a852),f869(f868(x43381,x43382),a852))),x43381),f784(f10(f868(x43381,x43382),f869(f869(f868(x43381,x43382),a852),f869(f868(x43381,x43382),a852)),x43382),f312(f868(x43381,x43382)))),f251(x43381,x43382)))),f187(f869(f868(x43381,x43382),a852))))),f784(f784(f258(x43381,x43382),x43383),x43384))
% 11.41/11.17 [3899]E(f784(f784(f130(x38991),f784(f784(f165(x38991),x38992),x38993)),f784(f784(f165(x38991),f784(f784(f3(a859),x38992),f784(f188(f860(x38991)),x38993))),x38994)),f784(f784(f165(x38991),x38992),f784(f784(f130(x38991),x38993),x38994)))
% 11.41/11.17 [3900]E(f784(f784(f130(x39001),f784(f784(f133(x39001),x39002),x39003)),f784(f784(f133(x39001),f784(f784(f3(a859),x39002),f784(f188(f860(x39001)),x39003))),x39004)),f784(f784(f133(x39001),x39002),f784(f784(f130(x39001),x39003),x39004)))
% 11.41/11.17 [3951]E(f784(f784(f89(a859),f784(f784(f90(a859),x39511),x39512)),f784(f784(f89(a859),f784(f784(f90(a859),x39513),x39512)),x39514)),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f89(a859),x39511),x39513)),x39512)),x39514))
% 11.41/11.17 [4154]P85(f784(f784(f242(f869(x41541,a852)),f784(f784(f3(f869(x41541,a852)),f784(f269(x41542,x41541),x41543)),f784(f269(x41542,x41541),x41544))),f784(f269(x41542,x41541),f784(f784(f3(f869(f868(x41542,x41541),a852)),x41543),x41544))))
% 11.41/11.17 [4155]P85(f784(f784(f242(f869(x41551,a852)),f784(f784(f3(f869(x41551,a852)),f784(f271(x41551,x41552),x41553)),f784(f271(x41551,x41552),x41554))),f784(f271(x41551,x41552),f784(f784(f3(f869(f868(x41551,x41552),a852)),x41553),x41554))))
% 11.41/11.17 [4260]E(f784(f784(f89(a1),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x42601),x42602)),f187(f869(f868(a859,a859),a852)))))),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x42603),x42604)),f187(f869(f868(a859,a859),a852)))))),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),f784(f784(f89(a859),x42601),x42603)),f784(f784(f89(a859),x42602),x42604))),f187(f869(f868(a859,a859),a852))))))
% 11.41/11.17 [4300]E(f784(f784(f90(a1),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x43001),x43002)),f187(f869(f868(a859,a859),a852)))))),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x43003),x43004)),f187(f869(f868(a859,a859),a852)))))),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),f784(f784(f89(a859),f784(f784(f90(a859),x43001),x43003)),f784(f784(f90(a859),x43002),x43004))),f784(f784(f89(a859),f784(f784(f90(a859),x43001),x43004)),f784(f784(f90(a859),x43002),x43003)))),f187(f869(f868(a859,a859),a852))))))
% 11.41/11.17 [4320]E(f784(f266(x43201),f784(f784(f10(f869(x43202,a852),a852,x43201),f97(x43202)),f784(f784(f10(f869(x43202,a852),f869(x43202,a852),x43201),f784(f20(x43202,a852,a852),f784(f784(f10(a852,f869(a852,a852),x43202),a348),f784(f784(f9(x43202,f869(x43202,a852),a852),f347(x43202)),x43203)))),f784(f784(f9(x43201,f869(x43202,f869(x43201,a852)),f869(x43202,a852)),f784(f784(f10(f869(f869(x43201,a852),a852),f869(f869(x43202,f869(x43201,a852)),f869(x43202,a852)),x43201),f10(f869(x43201,a852),a852,x43202)),f347(x43201))),x43204)))),f784(f784(f55(x43202,f869(x43201,a852)),x43203),x43204))
% 11.41/11.17 [4353]E(f784(f784(f291(x43531,x43531,x43531),f784(f784(f312(f868(x43531,x43531)),f784(f784(f251(x43531,x43531),x43532),x43533)),x43534)),f310(x43531,f784(f784(f312(f868(x43531,x43531)),f784(f784(f251(x43531,x43531),x43532),x43533)),x43534))),f784(f784(f110(f869(f868(x43531,x43531),a852)),f784(f784(f291(x43531,x43531,x43531),x43534),f310(x43531,x43534))),f784(f266(f868(x43531,x43531)),f784(f261(x43531,x43531,a852),f784(f784(f9(x43531,f869(x43531,a852),f869(x43531,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x43531,a852),f869(x43531,a852)),x43531),f10(a852,a852,x43531)),f784(f784(f10(a852,f869(a852,a852),x43531),a344),f784(f784(f9(x43531,f869(f868(x43531,x43531),a852),a852),f784(f784(f10(f868(x43531,x43531),f869(f869(f868(x43531,x43531),a852),a852),x43531),f347(f868(x43531,x43531))),f784(f784(f9(x43531,x43531,f868(x43531,x43531)),f251(x43531,x43531)),x43532))),f310(x43531,x43534))))),f784(f784(f9(x43531,f869(f868(x43531,x43531),a852),a852),f784(f784(f10(f868(x43531,x43531),f869(f869(f868(x43531,x43531),a852),a852),x43531),f347(f868(x43531,x43531))),f784(f251(x43531,x43531),x43533))),f310(x43531,x43534)))))))
% 11.41/11.17 [4156]E(f784(f131(x41561,f784(f784(f20(x41561,a852,a852),f784(f784(f10(a852,f869(a852,a852),x41561),a344),x41562)),x41563)),x41564),f784(f131(x41561,x41563),f784(f131(x41561,x41562),x41564)))
% 11.41/11.17 [4254]E(f784(f784(f130(x42541),f784(f784(f784(f105(f860(x42541)),f784(f784(f347(a859),f2(a859)),x42542)),f784(f784(f144(x42541),x42543),f120(x42541))),f120(x42541))),f166(x42541,x42544,f784(f266(a859),f784(f784(f9(a859,f869(a859,a852),a852),f784(f784(f10(a859,f869(f869(a859,a852),a852),a859),f347(a859)),a160)),x42542)))),f166(x42541,f784(f784(f144(x42541),x42543),x42544),x42542))
% 11.41/11.17 [4348]E(f784(f266(f868(x43481,x43482)),f784(f784(f10(f869(a859,a852),a852,f868(x43481,x43482)),f96(a859)),f784(f784(f9(f868(x43481,x43482),f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),f868(x43481,x43482)),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),f868(x43481,x43482)),f784(f10(a852,f869(a852,a852),a859),a344)),f784(f784(f9(f868(x43481,x43482),f869(a859,f868(x43481,x43482)),f869(a859,a852)),f784(f784(f10(f869(f868(x43481,x43482),a852),f869(f869(a859,f868(x43481,x43482)),f869(a859,a852)),f868(x43481,x43482)),f10(f868(x43481,x43482),a852,a859)),a343)),f784(f784(f20(a859,x43482,f868(x43481,x43482)),f784(f784(f10(x43481,f869(x43482,f868(x43481,x43482)),a859),f251(x43481,x43482)),f784(f155(x43481),x43483))),f784(f155(x43482),x43484)))))),f784(f784(f9(a859,a859,a852),f243(a859)),f784(f784(f246(a859),f784(f188(f860(x43481)),x43483)),f784(f188(f860(x43482)),x43484)))))),f784(f164(f868(x43481,x43482)),f784(f784(f173(x43481,x43482),x43483),x43484)))
% 11.41/11.17 [4273]E(f784(f266(f868(x42731,x42732)),f784(f261(x42731,x42732,a852),f784(f784(f9(x42731,f869(x42732,a852),f869(x42732,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x42732,a852),f869(x42732,a852)),x42731),f10(a852,a852,x42732)),f784(f784(f10(a852,f869(a852,a852),x42731),a344),x42733))),x42734))),f784(f784(f258(x42731,x42732),f784(f266(x42731),x42733)),f784(f18(f869(x42732,a852),x42731),f784(f266(x42732),x42734))))
% 11.41/11.17 [4276]E(f784(f266(f868(x42761,x42762)),f784(f261(x42761,x42762,a852),f784(f784(f20(x42761,f869(x42762,a852),f869(x42762,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x42762,a852),f869(x42762,a852)),x42761),f10(a852,a852,x42762)),f784(f784(f10(a852,f869(a852,a852),x42761),a344),x42763))),x42764))),f784(f784(f258(x42761,x42762),f784(f266(x42761),x42763)),f784(f784(f10(f869(x42762,a852),f869(x42762,a852),x42761),f266(x42762)),x42764)))
% 11.41/11.17 [4291]E(f784(f266(x42911),f784(f784(f10(f869(x42912,a852),a852,x42911),f97(x42912)),f784(f784(f10(f869(x42912,a852),f869(x42912,a852),x42911),f784(f20(x42912,a852,a852),f784(f784(f10(a852,f869(a852,a852),x42912),a348),f784(f784(f9(x42912,f869(x42912,a852),a852),f347(x42912)),x42913)))),x42914))),f784(f784(f55(x42912,f869(x42911,a852)),x42913),f784(f784(f10(f869(x42911,a852),f869(x42911,a852),x42912),f266(x42911)),f784(f9(x42911,x42912,a852),x42914))))
% 11.41/11.17 [4333]E(f784(f784(f146(f868(x43331,a859),x43331),f250(x43331,a859)),f784(f131(f868(x43331,a859),f784(f784(f9(f868(x43331,a859),f869(a859,a852),a852),f784(f784(f10(a859,f869(f869(a859,a852),a852),f868(x43331,a859)),f347(a859)),f260(x43331,a859))),x43332)),f784(f784(f173(x43331,a859),x43333),f134(a859,f784(f304(a859,x43334),f784(f784(f89(a859),x43334),f784(f188(f860(x43331)),x43333))))))),f784(f784(f146(f868(x43331,a859),x43331),f250(x43331,a859)),f784(f131(f868(x43331,a859),f784(f784(f9(f868(x43331,a859),f869(a859,a852),a852),f784(f784(f10(a859,f869(f869(a859,a852),a852),f868(x43331,a859)),f347(a859)),f784(f784(f9(f868(x43331,a859),a859,a859),f784(f784(f10(a859,f869(a859,a859),f868(x43331,a859)),f89(a859)),f260(x43331,a859))),x43334))),x43332)),f784(f784(f173(x43331,a859),x43333),f134(a859,f784(f304(a859,f2(a859)),f784(f188(f860(x43331)),x43333)))))))
% 11.41/11.17 [4334]E(f784(a160,f784(f784(f186(a859),f784(f188(f860(x43341)),x43342)),f784(f136(a859,f860(x43343),f784(f9(f860(x43343),a859,a859),f784(f784(f10(a859,f869(a859,a859),f860(x43343)),f186(a859)),f784(f784(f9(f860(x43343),a859,a859),f784(f784(f10(a859,f869(a859,a859),f860(x43343)),f3(a859)),f188(f860(x43343)))),f784(a160,f2(a859))))),f2(a859)),f784(f162(f860(x43343)),f784(f131(f860(x43343),f784(f784(f10(a852,a852,f860(x43343)),a341),f784(f784(f9(f860(x43343),f860(x43343),a852),a343),f120(x43343)))),x43344))))),f784(f784(f186(a859),f784(a160,f784(f188(f860(x43341)),x43342))),f784(f136(a859,f860(x43343),f784(f9(f860(x43343),a859,a859),f784(f784(f10(a859,f869(a859,a859),f860(x43343)),f186(a859)),f188(f860(x43343)))),f2(a859)),f784(f162(f860(x43343)),x43344))))
% 11.41/11.17 [4290]E(f784(f784(f130(x42901),f166(x42901,x42902,x42903)),f166(x42901,x42904,f784(f266(a859),f784(f784(f9(a859,f869(a859,a852),a852),f784(f784(f10(a859,f869(f869(a859,a852),a852),a859),f347(a859)),f784(f784(f9(a859,a859,a859),f89(a859)),f784(f188(f860(x42901)),x42902)))),x42903)))),f166(x42901,f784(f784(f130(x42901),x42902),x42904),x42903))
% 11.41/11.17 [4340]E(f784(f784(f144(f860(x43401)),f784(f784(f144(x43401),x43402),f784(f136(f860(x43401),f860(x43401),f130(x43401),f120(x43401)),f784(f784(f146(f860(x43401),f860(x43401)),f148(f860(x43401),x43401,f120(x43401),f784(f784(f10(f860(x43401),f869(f860(x43401),f860(x43401)),x43401),f18(f860(x43401),f860(x43401))),f784(f784(f9(x43401,f860(x43401),f860(x43401)),f144(x43401)),f120(x43401))))),x43403)))),f170(x43401,f784(f784(f144(f860(x43401)),x43404),f784(f136(f860(f860(x43401)),f860(f860(x43401)),f130(f860(x43401)),f120(f860(x43401))),f784(f784(f146(f860(x43401),f860(f860(x43401))),f148(f860(f860(x43401)),x43401,f120(f860(x43401)),f784(f18(f869(f860(x43401),f860(f860(x43401))),x43401),f784(f784(f9(f860(x43401),f860(f860(x43401)),f860(f860(x43401))),f144(f860(x43401))),f120(f860(x43401)))))),x43403))))),f170(x43401,f784(f784(f144(f860(x43401)),f784(f784(f144(x43401),x43402),x43404)),x43403)))
% 11.41/11.17 [4349]E(f784(f266(f868(x43491,x43491)),f784(f261(x43491,x43491,a852),f784(f784(f9(x43491,f869(f868(x43492,x43492),a852),f869(x43491,a852)),f784(f784(f10(f869(x43491,f869(f869(f868(x43492,x43492),a852),a852)),f869(f869(f868(x43492,x43492),a852),f869(x43491,a852)),x43491),f9(x43491,f869(f868(x43492,x43492),a852),a852)),f784(f784(f10(f869(x43491,f868(x43492,x43492)),f869(x43491,f869(f869(f868(x43492,x43492),a852),a852)),x43491),f784(f10(f868(x43492,x43492),f869(f869(f868(x43492,x43492),a852),a852),x43491),f347(f868(x43492,x43492)))),f784(f784(f9(x43491,f869(x43491,x43492),f869(x43491,f868(x43492,x43492))),f784(f784(f10(f869(x43492,f868(x43492,x43492)),f869(f869(x43491,x43492),f869(x43491,f868(x43492,x43492))),x43491),f10(x43492,f868(x43492,x43492),x43491)),f784(f784(f10(x43492,f869(x43492,f868(x43492,x43492)),x43491),f251(x43492,x43492)),x43493))),x43493)))),x43494))),f784(f784(f290(x43492,x43491),x43494),x43493))
% 11.41/11.17 [4436]~E(f30(x44361,x44362),f33(x44363,x44364,x44365))
% 11.41/11.17 [4437]~E(f30(x44371,x44372),f35(x44373,x44374,x44375))
% 11.41/11.17 [4438]~E(f30(x44381,x44382),f34(x44383,x44384,x44385))
% 11.41/11.17 [4439]~E(f38(x44391,x44392),f33(x44393,x44394,x44395))
% 11.41/11.17 [4440]~E(f38(x44401,x44402),f35(x44403,x44404,x44405))
% 11.41/11.17 [4441]~E(f38(x44411,x44412),f34(x44413,x44414,x44415))
% 11.41/11.17 [4442]~E(f37(x44421,x44422),f33(x44423,x44424,x44425))
% 11.41/11.17 [4443]~E(f37(x44431,x44432),f35(x44433,x44434,x44435))
% 11.41/11.17 [4444]~E(f37(x44441,x44442),f34(x44443,x44444,x44445))
% 11.41/11.17 [4445]~E(f33(x44451,x44452,x44453),f30(x44454,x44455))
% 11.41/11.17 [4446]~E(f33(x44461,x44462,x44463),f38(x44464,x44465))
% 11.41/11.17 [4447]~E(f33(x44471,x44472,x44473),f37(x44474,x44475))
% 11.41/11.17 [4448]~E(f35(x44481,x44482,x44483),f30(x44484,x44485))
% 11.41/11.17 [4449]~E(f35(x44491,x44492,x44493),f38(x44494,x44495))
% 11.41/11.17 [4450]~E(f35(x44501,x44502,x44503),f37(x44504,x44505))
% 11.41/11.17 [4451]~E(f34(x44511,x44512,x44513),f30(x44514,x44515))
% 11.41/11.17 [4452]~E(f34(x44521,x44522,x44523),f38(x44524,x44525))
% 11.41/11.17 [4453]~E(f34(x44531,x44532,x44533),f37(x44534,x44535))
% 11.41/11.17 [3841]E(f784(f176(x38411,x38412,x38413,x38414),x38415),f784(f239(f864(x38412),x38412,f784(x38413,x38415),f237(x38412)),f784(x38414,x38415)))
% 11.41/11.17 [3927]E(f176(x39271,x39272,f176(x39271,x39272,x39273,x39274),x39275),f176(x39271,x39272,x39273,f176(x39271,x39272,x39274,x39275)))
% 11.41/11.17 [4108]E(f784(f784(f110(f869(x41081,a852)),f784(f164(x41081),f784(f784(f165(x41081),f784(f188(f860(x41082)),x41083)),x41084))),f175(x41081,x41082,x41085)),f175(x41081,x41082,f178(x41081,x41082,x41085,x41084,x41083)))
% 11.41/11.17 [3670]E(f784(f784(f261(x36701,x36702,x36703),x36704),x36705),f784(f784(x36704,f784(f250(x36701,x36702),x36705)),f784(f260(x36701,x36702),x36705)))
% 11.41/11.17 [3671]E(f784(f784(f261(x36711,x36712,x36713),x36714),x36715),f784(f784(x36714,f784(f250(x36711,x36712),x36715)),f784(f260(x36711,x36712),x36715)))
% 11.41/11.17 [3672]E(f784(f784(f261(x36721,x36722,x36723),x36724),x36725),f784(f784(x36724,f784(f250(x36721,x36722),x36725)),f784(f260(x36721,x36722),x36725)))
% 11.41/11.17 [3698]E(f784(f239(x36981,x36982,x36983,x36984),f784(f237(x36982),x36985)),f784(x36984,x36985))
% 11.41/11.17 [3706]E(f784(f784(f784(f75(x37061,x37062,x37063),x37064),x37065),f187(f869(x37062,a852))),x37065)
% 11.41/11.17 [3722]E(f784(f329(x37221,x37222,x37223,x37224),f784(f322(x37221,x37223),x37225)),f784(x37224,x37225))
% 11.41/11.17 [3723]E(f784(f330(x37231,x37232,x37233,x37234),f784(f326(x37231,x37233),x37235)),f784(x37234,x37235))
% 11.41/11.17 [3872]E(f240(x38721,x38722,x38723,x38724,f784(f237(x38722),x38725)),f784(x38724,x38725))
% 11.41/11.17 [3907]E(f331(x39071,x39072,x39073,x39074,f784(f326(x39072,x39071),x39075)),f784(f784(f89(a859),f784(x39074,x39075)),f784(a160,f2(a859))))
% 11.41/11.17 [3908]E(f331(x39081,x39082,x39083,x39084,f784(f322(x39081,x39082),x39085)),f784(f784(f89(a859),f784(x39083,x39085)),f784(a160,f2(a859))))
% 11.41/11.17 [3983]E(f784(f82(f864(x39831),f864(x39832),f864(x39833),f784(f206(x39831,x39832),x39834)),f784(f206(x39833,x39831),x39835)),f784(f206(x39833,x39832),f784(f82(x39831,x39832,x39833,x39834),x39835)))
% 11.41/11.17 [3984]E(f784(f82(f860(x39841),f860(x39842),f860(x39843),f784(f146(x39841,x39842),x39844)),f784(f146(x39843,x39841),x39845)),f784(f146(x39843,x39842),f784(f82(x39841,x39842,x39843,x39844),x39845)))
% 11.41/11.17 [3985]E(f784(f82(f860(x39851),f860(x39852),f860(x39853),f784(f146(x39851,x39852),x39854)),f784(f146(x39853,x39851),x39855)),f784(f146(x39853,x39852),f784(f82(x39851,x39852,x39853,x39854),x39855)))
% 11.41/11.17 [4064]E(f94(x40641,f76(x40642,x40641,x40643,x40644,x40645)),f784(f784(f74(x40642,x40641,x40643),x40644),x40645))
% 11.41/11.17 [4100]E(f784(f784(f89(a859),f784(f784(f89(a859),f784(x41001,f784(f250(x41002,x41003),x41004))),f784(x41005,f784(f260(x41002,x41003),x41004)))),f784(a160,f2(a859))),f265(x41002,x41003,x41001,x41005,x41004))
% 11.41/11.17 [4286]E(f156(x42861,x42862,f784(f784(f9(x42861,f864(x42862),f864(x42862)),f784(f784(f20(x42861,f864(x42862),f869(f864(x42862),f864(x42862))),f784(f784(f10(a852,f869(f864(x42862),f869(f864(x42862),f864(x42862))),x42861),f105(f864(x42862))),x42863)),f784(f784(f10(x42862,f864(x42862),x42861),f237(x42862)),x42864))),f190(x42862)),x42865),f784(f784(f146(x42861,x42862),x42864),f784(f131(x42861,x42863),x42865)))
% 11.41/11.17 [4494]~E(f784(f784(f784(f81(x44941,f864(x44942)),x44943),x44944),f784(f237(x44942),x44945)),f784(f18(f864(x44942),x44941),f190(x44942)))
% 11.41/11.17 [3607]E(f784(f784(f165(x36071),x36072),f784(f784(f146(x36073,x36071),x36074),x36075)),f784(f784(f146(x36073,x36071),x36074),f784(f784(f165(x36073),x36072),x36075)))
% 11.41/11.17 [3608]E(f784(f784(f133(x36081),x36082),f784(f784(f146(x36083,x36081),x36084),x36085)),f784(f784(f146(x36083,x36081),x36084),f784(f784(f133(x36083),x36082),x36085)))
% 11.41/11.17 [3638]E(f784(f784(f146(x36381,x36382),x36383),f784(f784(f144(x36381),x36384),x36385)),f784(f784(f144(x36382),f784(x36383,x36384)),f784(f784(f146(x36381,x36382),x36383),x36385)))
% 11.41/11.17 [3702]E(f784(f313(x37021,x37022,x37023),f784(f784(f312(x37021),x37024),x37025)),f784(f784(f312(x37022),f784(x37023,x37024)),f784(f313(x37021,x37022,x37023),x37025)))
% 11.41/11.17 [3766]E(f784(f784(f173(x37661,x37662),f784(f784(f165(x37661),x37663),x37664)),f784(f784(f165(x37662),x37663),x37665)),f784(f784(f165(f868(x37661,x37662)),x37663),f784(f784(f173(x37661,x37662),x37664),x37665)))
% 11.41/11.17 [3767]E(f784(f784(f173(x37671,x37672),f784(f784(f133(x37671),x37673),x37674)),f784(f784(f133(x37672),x37673),x37675)),f784(f784(f133(f868(x37671,x37672)),x37673),f784(f784(f173(x37671,x37672),x37674),x37675)))
% 11.41/11.17 [3778]E(f784(f784(f151(x37781,f784(f784(f144(x37781),x37782),x37783)),f784(a160,x37784)),x37785),f784(f784(f144(x37781),x37782),f784(f784(f151(x37781,x37783),x37784),x37785)))
% 11.41/11.17 [3781]E(f784(f239(f864(x37811),x37812,f190(x37811),x37813),f784(f784(f18(f864(x37812),x37814),f190(x37812)),x37815)),f190(x37811))
% 11.41/11.17 [3783]E(f784(f784(f130(x37831),f784(f784(f146(x37832,x37831),x37833),x37834)),f784(f784(f146(x37832,x37831),x37833),x37835)),f784(f784(f146(x37832,x37831),x37833),f784(f784(f130(x37832),x37834),x37835)))
% 11.41/11.17 [3787]E(f784(f784(x37871,x37872),f784(f784(f253(x37873,x37874,x37871),x37872),x37875)),f784(f784(f253(x37873,x37874,x37871),x37872),f784(a160,x37875)))
% 11.41/11.17 [3828]E(f784(f784(f291(x38281,x38282,x38283),f784(f288(x38282,x38281),x38284)),f784(f288(x38283,x38282),x38285)),f784(f288(x38283,x38281),f784(f784(f291(x38283,x38282,x38281),x38285),x38284)))
% 11.41/11.17 [3859]E(f784(f784(f784(f180(f860(x38591),f860(x38591)),x38592),f161(x38591)),f784(f784(f146(x38593,x38591),x38594),x38595)),f784(f784(f146(x38593,x38591),x38594),f784(f784(f784(f180(f860(x38593),f860(x38593)),x38592),f161(x38593)),x38595)))
% 11.41/11.17 [3860]E(f784(f784(f263(x38601,x38602,x38601,x38603),f784(f251(x38602,x38601),x38604)),x38605),f784(x38605,x38604))
% 11.41/11.17 [3886]E(f147(x38861,x38862,f784(f784(f146(x38863,x38861),x38864),x38865)),f147(x38863,f784(f82(x38861,a859,x38863,x38862),x38864),x38865))
% 11.41/11.17 [3950]E(f784(f784(f82(f864(x39501),f864(x39502),x39503,f784(f206(x39501,x39502),x39504)),f784(f18(f864(x39501),x39503),f190(x39501))),x39505),f190(x39502))
% 11.41/11.17 [3955]E(f784(f313(x39551,x39552,f784(f784(f10(x39553,x39552,x39551),x39554),x39555)),f249(f869(x39551,a852))),f784(f313(x39553,x39552,x39554),f784(f313(x39551,x39553,x39555),f249(f869(x39551,a852)))))
% 11.41/11.17 [3989]E(f784(f784(f110(f869(x39891,a852)),f784(f315(x39891,x39892,x39893),f784(f784(f312(x39892),x39894),f187(f869(x39892,a852))))),f784(f315(x39891,x39892,x39893),x39895)),f784(f315(x39891,x39892,x39893),f784(f784(f312(x39892),x39894),x39895)))
% 11.41/11.17 [4049]E(f784(f784(f146(x40491,x40492),x40493),f168(x40491,f784(f82(x40492,a852,x40491,x40494),x40493),x40495)),f168(x40492,x40494,f784(f784(f146(x40491,x40492),x40493),x40495)))
% 11.41/11.17 [4056]E(f784(f136(x40561,x40562,f784(f9(x40562,x40561,x40561),f784(f9(x40561,x40562,x40561),x40563)),x40564),f784(f162(x40562),f784(f162(x40562),x40565))),f784(f136(x40561,x40562,x40563,x40564),x40565))
% 11.41/11.17 [4057]E(f784(f784(f784(f81(x40571,f864(x40572)),f179(x40571,x40572,x40573,x40574)),x40575),f784(x40573,x40575)),f179(x40571,x40572,x40573,f784(f784(f312(x40571),x40575),x40574)))
% 11.41/11.17 [4066]E(f784(f332(x40661,x40662,x40663,f784(f18(x40662,x40661),x40664),f784(f18(x40662,x40663),x40664)),x40665),x40664)
% 11.41/11.17 [4125]E(f784(f239(f860(x41251),x41251,f156(x41252,x41251,x41253,x41254),f784(f784(f9(x41251,f860(x41251),f860(x41251)),f144(x41251)),f156(x41252,x41251,x41253,x41254))),f784(x41253,x41255)),f156(x41252,x41251,x41253,f784(f784(f144(x41252),x41255),x41254)))
% 11.41/11.17 [4164]P85(f784(f784(f242(f869(x41641,a852)),f784(f313(x41642,x41641,x41643),f784(f784(f111(f869(x41642,a852)),x41644),x41645))),f784(f784(f111(f869(x41641,a852)),f784(f313(x41642,x41641,x41643),x41644)),f784(f313(x41642,x41641,x41643),x41645))))
% 11.41/11.17 [4165]P85(f784(f784(f242(f869(x41651,a852)),f784(f287(x41652,x41651,x41653),f784(f784(f111(f869(x41652,a852)),x41654),x41655))),f784(f784(f111(f869(x41651,a852)),f784(f287(x41652,x41651,x41653),x41654)),f784(f287(x41652,x41651,x41653),x41655))))
% 11.41/11.17 [4261]E(f784(f260(x42611,x42612),f784(f262(x42613,x42611,x42612,x42612,x42614,f41(x42612)),x42615)),f784(f260(x42613,x42612),x42615))
% 11.41/11.17 [4262]E(f784(f250(x42621,x42622),f784(f262(x42621,x42621,x42623,x42622,f41(x42621),x42624),x42625)),f784(f250(x42621,x42623),x42625))
% 11.41/11.17 [4265]E(f784(f250(x42651,x42652),f784(f262(x42653,x42651,x42652,x42652,x42654,f41(x42652)),x42655)),f784(x42654,f784(f250(x42653,x42652),x42655)))
% 11.41/11.17 [4266]E(f784(f260(x42661,x42662),f784(f262(x42661,x42661,x42663,x42662,f41(x42661),x42664),x42665)),f784(x42664,f784(f260(x42661,x42663),x42665)))
% 11.41/11.17 [4343]P25(x43431,x43432,f784(f784(f312(f858(x43431)),f784(f784(f784(f100(x43431),f784(f784(f9(x43431,f869(a857,a857),f869(a857,a852)),f784(f784(f10(f869(a857,a852),f869(f869(a857,a857),f869(a857,a852)),x43431),f10(a857,a852,a857)),x43433)),f784(f784(f20(a857,a859,a857),f784(f784(f9(a857,a854,f869(a859,a857)),a196),x43434)),x43435))),f30(x43434,x43435)),x43433)),f187(f869(f858(x43431),a852))))
% 11.41/11.17 [4344]P25(x43441,x43442,f784(f784(f312(f858(x43441)),f784(f784(f784(f100(x43441),f784(f784(f9(x43441,f869(a857,a857),f869(a857,a852)),f784(f784(f10(f869(a857,a852),f869(f869(a857,a857),f869(a857,a852)),x43441),f10(a857,a852,a857)),x43443)),f784(f784(f20(a857,a859,a857),f784(f784(f9(a857,a854,f869(a859,a857)),a196),x43444)),x43445))),f30(x43444,x43445)),x43443)),f187(f869(f858(x43441),a852))))
% 11.41/11.17 [4346]E(f784(f136(f869(x43461,f864(x43462)),f868(x43461,x43462),f784(f784(f10(f869(x43461,f869(x43462,f869(x43461,f864(x43462)))),f869(f868(x43461,x43462),f869(x43461,f864(x43462))),f869(x43461,f864(x43462))),f261(x43461,x43462,f869(x43461,f864(x43462)))),f784(f784(f9(f869(x43461,f864(x43462)),f869(x43462,f864(x43462)),f869(x43461,f869(x43462,f869(x43461,f864(x43462))))),f784(f784(f10(f869(x43461,f869(f869(x43462,f864(x43462)),f869(x43462,f869(x43461,f864(x43462))))),f869(f869(x43462,f864(x43462)),f869(x43461,f869(x43462,f869(x43461,f864(x43462))))),f869(x43461,f864(x43462))),f9(x43461,f869(x43462,f864(x43462)),f869(x43462,f869(x43461,f864(x43462))))),f784(f784(f10(f869(x43461,f869(f864(x43462),f869(x43461,f864(x43462)))),f869(x43461,f869(f869(x43462,f864(x43462)),f869(x43462,f869(x43461,f864(x43462))))),f869(x43461,f864(x43462))),f784(f10(f869(f864(x43462),f869(x43461,f864(x43462))),f869(f869(x43462,f864(x43462)),f869(x43462,f869(x43461,f864(x43462)))),x43461),f10(f864(x43462),f869(x43461,f864(x43462)),x43462))),f81(x43461,f864(x43462))))),f237(x43462))),x43463),f784(f784(f173(x43461,x43462),x43464),x43465)),f178(x43461,x43462,x43463,x43464,x43465))
% 11.41/11.17 [3452]E(f784(f784(f784(f784(f209(x34521),x34522),x34523),x34524),x34525),f204(x34521,x34522))
% 11.41/11.17 [3453]E(f784(f784(f784(f784(f210(x34531),x34532),x34533),x34534),x34535),f192(x34531,x34532))
% 11.41/11.17 [3501]E(f102(x35011,x35012,f784(f784(f784(f100(x35011),x35013),x35014),x35015)),f2(a859))
% 11.41/11.17 [3590]E(f784(f784(f784(f784(f81(x35901,x35902),x35903),x35904),x35905),x35904),x35905)
% 11.41/11.17 [3818]E(f784(f784(f54(x38181,f869(x38182,a852)),f784(f784(f312(x38181),x38183),x38184)),x38185),f784(f784(f110(f869(x38182,a852)),f784(x38185,x38183)),f784(f784(f54(x38181,f869(x38182,a852)),x38184),x38185)))
% 11.41/11.17 [3819]E(f784(f784(f55(x38191,f869(x38192,a852)),f784(f784(f312(x38191),x38193),x38194)),x38195),f784(f784(f111(f869(x38192,a852)),f784(x38195,x38193)),f784(f784(f55(x38191,f869(x38192,a852)),x38194),x38195)))
% 11.41/11.17 [3879]E(f784(f784(f110(f869(x38791,a852)),f784(f313(x38792,x38791,x38793),x38794)),f784(f313(x38792,x38791,x38793),x38795)),f784(f313(x38792,x38791,x38793),f784(f784(f110(f869(x38792,a852)),x38794),x38795)))
% 11.41/11.17 [3880]E(f784(f784(f110(f869(x38801,a852)),f784(f287(x38802,x38801,x38803),x38804)),f784(f287(x38802,x38801,x38803),x38805)),f784(f287(x38802,x38801,x38803),f784(f784(f110(f869(x38802,a852)),x38804),x38805)))
% 11.41/11.17 [3881]E(f784(f784(f3(f869(x38811,a852)),f784(f315(x38811,x38812,x38813),x38814)),f784(f315(x38811,x38812,x38813),x38815)),f784(f315(x38811,x38812,x38813),f784(f784(f3(f869(x38812,a852)),x38814),x38815)))
% 11.41/11.17 [3882]E(f784(f784(f110(f869(x38821,a852)),f784(f315(x38821,x38822,x38823),x38824)),f784(f315(x38821,x38822,x38823),x38825)),f784(f315(x38821,x38822,x38823),f784(f784(f110(f869(x38822,a852)),x38824),x38825)))
% 11.41/11.17 [3883]E(f784(f784(f111(f869(x38831,a852)),f784(f315(x38831,x38832,x38833),x38834)),f784(f315(x38831,x38832,x38833),x38835)),f784(f315(x38831,x38832,x38833),f784(f784(f111(f869(x38832,a852)),x38834),x38835)))
% 11.41/11.17 [3885]E(f179(x38851,x38852,f179(x38851,x38852,x38853,x38854),x38855),f179(x38851,x38852,x38853,f784(f784(f111(f869(x38851,a852)),x38854),x38855)))
% 11.41/11.17 [3887]E(f123(x38871,x38872,f784(x38873,x38874),f784(f784(f9(x38871,a108,f861(x38872)),x38875),x38874)),f784(f202(x38871,x38872,x38873,x38875),x38874))
% 11.41/11.17 [3946]E(f784(f784(f151(x39461,f784(f784(f130(x39461),x39462),f784(f784(f144(x39461),x39463),x39464))),f784(f188(f860(x39461)),x39462)),x39465),f784(f784(f130(x39461),x39462),f784(f784(f144(x39461),x39465),x39464)))
% 11.41/11.17 [3952]E(f784(f784(f55(x39521,f869(x39522,a852)),x39523),f784(f784(f10(f869(x39522,a852),f869(x39522,a852),x39521),f784(f312(x39522),x39524)),x39525)),f784(f784(f312(x39522),x39524),f784(f784(f55(x39521,f869(x39522,a852)),x39523),x39525)))
% 11.41/11.17 [3953]E(f784(f784(f55(x39531,f869(x39532,a852)),x39533),f784(f784(f10(f869(x39532,a852),f869(x39532,a852),x39531),f784(f312(x39532),x39534)),x39535)),f784(f784(f312(x39532),x39534),f784(f784(f55(x39531,f869(x39532,a852)),x39533),x39535)))
% 11.41/11.17 [4024]E(f179(x40241,x40242,f784(f784(f784(f81(x40241,f864(x40242)),x40243),x40244),f784(f237(x40242),x40245)),f784(f88(f869(x40241,a852)),f784(f784(f312(x40241),x40244),f187(f869(x40241,a852))))),f179(x40241,x40242,x40243,f784(f88(f869(x40241,a852)),f784(f784(f312(x40241),x40244),f187(f869(x40241,a852))))))
% 11.41/11.17 [4068]E(f784(f784(f3(f869(f868(x40681,x40682),a852)),f784(f784(f258(x40681,x40682),x40683),f784(f18(f869(x40682,a852),x40681),x40684))),f784(f784(f258(x40681,x40682),x40685),f784(f18(f869(x40682,a852),x40681),x40684))),f784(f784(f258(x40681,x40682),f784(f784(f3(f869(x40681,a852)),x40683),x40685)),f784(f18(f869(x40682,a852),x40681),x40684)))
% 11.41/11.17 [4069]E(f784(f784(f110(f869(f868(x40691,x40692),a852)),f784(f784(f258(x40691,x40692),x40693),f784(f18(f869(x40692,a852),x40691),x40694))),f784(f784(f258(x40691,x40692),x40695),f784(f18(f869(x40692,a852),x40691),x40694))),f784(f784(f258(x40691,x40692),f784(f784(f110(f869(x40691,a852)),x40693),x40695)),f784(f18(f869(x40692,a852),x40691),x40694)))
% 11.41/11.17 [4070]E(f784(f784(f111(f869(f868(x40701,x40702),a852)),f784(f784(f258(x40701,x40702),x40703),f784(f18(f869(x40702,a852),x40701),x40704))),f784(f784(f258(x40701,x40702),x40705),f784(f18(f869(x40702,a852),x40701),x40704))),f784(f784(f258(x40701,x40702),f784(f784(f111(f869(x40701,a852)),x40703),x40705)),f784(f18(f869(x40702,a852),x40701),x40704)))
% 11.41/11.17 [4112]E(f784(f784(f146(x41121,x41122),x41123),f784(f131(x41121,f784(f82(x41122,a852,x41121,x41124),x41123)),x41125)),f784(f131(x41122,x41124),f784(f784(f146(x41121,x41122),x41123),x41125)))
% 11.41/11.17 [4118]E(f784(f188(f860(x41181)),f784(f131(x41181,x41182),f784(f784(f146(x41183,x41181),x41184),x41185))),f784(f188(f860(x41183)),f784(f131(x41183,f784(f82(x41181,a852,x41183,x41182),x41184)),x41185)))
% 11.41/11.17 [4253]E(f784(f784(f110(f869(x42531,a852)),f784(f784(f3(f869(x42531,a852)),f175(x42531,x42532,x42533)),f784(f266(x42531),f784(f784(f9(x42531,f869(x42531,a852),a852),f347(x42531)),f784(f784(f3(f869(x42531,a852)),x42534),f175(x42531,x42532,x42535)))))),f784(f266(x42531),f784(f784(f9(x42531,f869(x42531,a852),a852),f347(x42531)),f784(f784(f111(f869(x42531,a852)),x42534),f175(x42531,x42532,x42535))))),f175(x42531,x42532,f85(x42531,f864(x42532),x42533,x42535,x42534)))
% 11.41/11.17 [4325]E(f784(f148(f860(f868(x43251,x43252)),x43252,f120(f868(x43251,x43252)),f784(f784(f9(x43252,f869(f860(x43252),f860(f868(x43251,x43252))),f869(f860(x43252),f860(f868(x43251,x43252)))),f784(f784(f10(f869(f860(f868(x43251,x43252)),f860(f868(x43251,x43252))),f869(f869(f860(x43252),f860(f868(x43251,x43252))),f869(f860(x43252),f860(f868(x43251,x43252)))),x43252),f10(f860(f868(x43251,x43252)),f860(f868(x43251,x43252)),f860(x43252))),f784(f784(f10(f868(x43251,x43252),f869(f860(f868(x43251,x43252)),f860(f868(x43251,x43252))),x43252),f144(f868(x43251,x43252))),f784(f251(x43251,x43252),x43253)))),f784(f173(x43251,x43252),x43254))),x43255),f784(f784(f173(x43251,x43252),f784(f784(f144(x43251),x43253),x43254)),x43255))
% 11.41/11.17 [3813]E(f784(f784(f151(x38131,f784(f784(f151(x38131,x38132),x38133),x38134)),x38133),x38135),f784(f784(f151(x38131,x38132),x38133),x38135))
% 11.41/11.17 [3861]E(f784(f269(x38611,x38612),f784(f784(f312(f868(x38611,x38612)),f784(f784(f251(x38611,x38612),x38613),x38614)),x38615)),f784(f784(f312(x38612),x38614),f784(f269(x38611,x38612),x38615)))
% 11.41/11.17 [3862]E(f784(f271(x38621,x38622),f784(f784(f312(f868(x38621,x38622)),f784(f784(f251(x38621,x38622),x38623),x38624)),x38625)),f784(f784(f312(x38621),x38623),f784(f271(x38621,x38622),x38625)))
% 11.41/11.17 [3910]E(f127(x39101,x39102,f784(x39103,x39104),f784(f784(f9(x39101,a108,f861(f864(x39102))),x39105),x39104)),f784(f200(x39101,x39102,x39103,x39105),x39104))
% 11.41/11.17 [3939]E(f784(f784(f3(f869(f868(x39391,x39392),a852)),f784(f784(f258(x39391,x39392),x39393),x39394)),f784(f784(f258(x39391,x39392),x39395),x39394)),f784(f784(f258(x39391,x39392),f784(f784(f3(f869(x39391,a852)),x39393),x39395)),x39394))
% 11.41/11.17 [3940]E(f784(f784(f110(f869(f868(x39401,x39402),a852)),f784(f784(f258(x39401,x39402),x39403),x39404)),f784(f784(f258(x39401,x39402),x39405),x39404)),f784(f784(f258(x39401,x39402),f784(f784(f110(f869(x39401,a852)),x39403),x39405)),x39404))
% 11.41/11.17 [3941]E(f784(f784(f111(f869(f868(x39411,x39412),a852)),f784(f784(f258(x39411,x39412),x39413),x39414)),f784(f784(f258(x39411,x39412),x39415),x39414)),f784(f784(f258(x39411,x39412),f784(f784(f111(f869(x39411,a852)),x39413),x39415)),x39414))
% 11.41/11.17 [4002]E(f784(f784(f110(f869(x40021,a852)),f784(f784(f54(x40022,f869(x40021,a852)),x40023),x40024)),f784(f784(f54(x40022,f869(x40021,a852)),x40025),x40024)),f784(f784(f54(x40022,f869(x40021,a852)),f784(f784(f110(f869(x40022,a852)),x40023),x40025)),x40024))
% 11.41/11.17 [4003]E(f784(f784(f111(f869(x40031,a852)),f784(f784(f55(x40032,f869(x40031,a852)),x40033),x40034)),f784(f784(f55(x40032,f869(x40031,a852)),x40035),x40034)),f784(f784(f55(x40032,f869(x40031,a852)),f784(f784(f110(f869(x40032,a852)),x40033),x40035)),x40034))
% 11.41/11.17 [4012]E(f784(f784(f54(x40121,f869(x40122,a852)),x40123),f784(f784(f10(f869(x40122,a852),f869(x40122,a852),x40121),f784(f3(f869(x40122,a852)),x40124)),x40125)),f784(f784(f3(f869(x40122,a852)),x40124),f784(f784(f55(x40121,f869(x40122,a852)),x40123),x40125)))
% 11.41/11.17 [4013]E(f784(f784(f55(x40131,f869(x40132,a852)),x40133),f784(f784(f10(f869(x40132,a852),f869(x40132,a852),x40131),f784(f110(f869(x40132,a852)),x40134)),x40135)),f784(f784(f110(f869(x40132,a852)),x40134),f784(f784(f55(x40131,f869(x40132,a852)),x40133),x40135)))
% 11.41/11.17 [4014]E(f784(f784(f55(x40141,f869(x40142,a852)),x40143),f784(f784(f10(f869(x40142,a852),f869(x40142,a852),x40141),f784(f110(f869(x40142,a852)),x40144)),x40145)),f784(f784(f110(f869(x40142,a852)),x40144),f784(f784(f55(x40141,f869(x40142,a852)),x40143),x40145)))
% 11.41/11.17 [4015]E(f784(f784(f54(x40151,f869(x40152,a852)),x40153),f784(f784(f10(f869(x40152,a852),f869(x40152,a852),x40151),f784(f111(f869(x40152,a852)),x40154)),x40155)),f784(f784(f111(f869(x40152,a852)),x40154),f784(f784(f54(x40151,f869(x40152,a852)),x40153),x40155)))
% 11.41/11.17 [4016]E(f784(f784(f54(x40161,f869(x40162,a852)),x40163),f784(f784(f10(f869(x40162,a852),f869(x40162,a852),x40161),f784(f111(f869(x40162,a852)),x40164)),x40165)),f784(f784(f111(f869(x40162,a852)),x40164),f784(f784(f54(x40161,f869(x40162,a852)),x40163),x40165)))
% 11.41/11.17 [4017]E(f784(f784(f54(x40171,f869(x40172,a852)),x40173),f784(f784(f10(f869(x40172,a852),f869(x40172,a852),x40171),f784(f3(f869(x40172,a852)),x40174)),x40175)),f784(f784(f3(f869(x40172,a852)),x40174),f784(f784(f55(x40171,f869(x40172,a852)),x40173),x40175)))
% 11.41/11.17 [4018]E(f784(f784(f54(x40181,f869(x40182,a852)),x40183),f784(f784(f10(f869(x40182,a852),f869(x40182,a852),x40181),f784(f111(f869(x40182,a852)),x40184)),x40185)),f784(f784(f111(f869(x40182,a852)),x40184),f784(f784(f54(x40181,f869(x40182,a852)),x40183),x40185)))
% 11.41/11.17 [4019]E(f784(f784(f55(x40191,f869(x40192,a852)),x40193),f784(f784(f10(f869(x40192,a852),f869(x40192,a852),x40191),f784(f110(f869(x40192,a852)),x40194)),x40195)),f784(f784(f110(f869(x40192,a852)),x40194),f784(f784(f55(x40191,f869(x40192,a852)),x40193),x40195)))
% 11.41/11.17 [4078]E(f182(f860(x40781),f784(f784(f144(x40781),x40782),x40783),f784(f784(f10(f860(x40781),f860(x40781),a859),f784(f144(x40781),x40784)),f784(f784(f9(a859,x40781,f860(x40781)),f151(x40781,x40783)),x40782)),x40785),f784(f784(f151(x40781,f784(f784(f144(x40781),x40784),x40783)),x40785),x40782))
% 11.41/11.17 [4081]E(f784(f784(f54(x40811,f869(f868(x40812,x40813),a852)),x40814),f784(f784(f10(f869(f868(x40813,x40812),a852),f869(f868(x40812,x40813),a852),x40811),f288(x40813,x40812)),x40815)),f784(f288(x40813,x40812),f784(f784(f54(x40811,f869(f868(x40813,x40812),a852)),x40814),x40815)))
% 11.41/11.17 [4082]E(f784(f784(f55(x40821,f869(f868(x40822,x40823),a852)),x40824),f784(f784(f10(f869(f868(x40823,x40822),a852),f869(f868(x40822,x40823),a852),x40821),f288(x40823,x40822)),x40825)),f784(f288(x40823,x40822),f784(f784(f55(x40821,f869(f868(x40823,x40822),a852)),x40824),x40825)))
% 11.41/11.17 [4136]E(f175(x41361,x41362,f784(f784(f20(x41361,f864(x41363),f864(x41362)),f784(f784(f10(f869(x41363,x41362),f869(f864(x41363),f864(x41362)),x41361),f206(x41363,x41362)),x41364)),x41365)),f175(x41361,x41363,x41365))
% 11.41/11.17 [4188]P85(f784(f784(f242(f869(x41881,a852)),f784(f784(f3(f869(x41881,a852)),f784(f313(x41882,x41881,x41883),x41884)),f784(f313(x41882,x41881,x41883),x41885))),f784(f313(x41882,x41881,x41883),f784(f784(f3(f869(x41882,a852)),x41884),x41885))))
% 11.41/11.17 [4329]E(f784(f148(f860(f868(x43291,x43292)),x43291,f120(f868(x43291,x43292)),f784(f784(f9(x43291,f869(f860(x43291),f860(f868(x43291,x43292))),f869(f860(x43291),f860(f868(x43291,x43292)))),f784(f784(f10(f869(f860(f868(x43291,x43292)),f860(f868(x43291,x43292))),f869(f869(f860(x43291),f860(f868(x43291,x43292))),f869(f860(x43291),f860(f868(x43291,x43292)))),x43291),f10(f860(f868(x43291,x43292)),f860(f868(x43291,x43292)),f860(x43291))),f784(f784(f10(f868(x43291,x43292),f869(f860(f868(x43291,x43292)),f860(f868(x43291,x43292))),x43291),f144(f868(x43291,x43292))),f784(f784(f9(x43291,x43292,f868(x43291,x43292)),f251(x43291,x43292)),x43293)))),f784(f784(f9(f860(x43291),f860(x43292),f860(f868(x43291,x43292))),f173(x43291,x43292)),x43294))),x43295),f784(f784(f173(x43291,x43292),x43295),f784(f784(f144(x43292),x43293),x43294)))
% 11.41/11.17 [4043]E(f784(f784(f110(f869(x40431,a852)),f784(f287(x40432,x40431,x40433),x40434)),f784(f287(x40432,x40431,x40435),x40434)),f784(f287(x40432,x40431,f784(f784(f110(f869(f868(x40432,x40431),a852)),x40433),x40435)),x40434))
% 11.41/11.17 [4084]E(f784(f784(f130(f868(x40841,x40842)),f784(f784(f173(x40841,x40842),x40843),f784(f784(f165(x40842),f784(f188(f860(x40841)),x40843)),x40844))),f784(f784(f173(x40841,x40842),x40845),f784(f784(f133(x40842),f784(f188(f860(x40841)),x40843)),x40844))),f784(f784(f173(x40841,x40842),f784(f784(f130(x40841),x40843),x40845)),x40844))
% 11.41/11.17 [4191]E(f784(f784(f258(x41911,x41912),x41913),f784(f784(f20(x41911,f869(x41912,a852),f869(x41912,a852)),f784(f784(f10(f869(x41912,a852),f869(f869(x41912,a852),f869(x41912,a852)),x41911),f3(f869(x41912,a852))),x41914)),x41915)),f784(f784(f3(f869(f868(x41911,x41912),a852)),f784(f784(f258(x41911,x41912),x41913),x41914)),f784(f784(f258(x41911,x41912),x41913),x41915)))
% 11.41/11.17 [4192]E(f784(f784(f258(x41921,x41922),x41923),f784(f784(f20(x41921,f869(x41922,a852),f869(x41922,a852)),f784(f784(f10(f869(x41922,a852),f869(f869(x41922,a852),f869(x41922,a852)),x41921),f110(f869(x41922,a852))),x41924)),x41925)),f784(f784(f110(f869(f868(x41921,x41922),a852)),f784(f784(f258(x41921,x41922),x41923),x41924)),f784(f784(f258(x41921,x41922),x41923),x41925)))
% 11.41/11.17 [4193]E(f784(f784(f258(x41931,x41932),x41933),f784(f784(f20(x41931,f869(x41932,a852),f869(x41932,a852)),f784(f784(f10(f869(x41932,a852),f869(f869(x41932,a852),f869(x41932,a852)),x41931),f111(f869(x41932,a852))),x41934)),x41935)),f784(f784(f111(f869(f868(x41931,x41932),a852)),f784(f784(f258(x41931,x41932),x41933),x41934)),f784(f784(f258(x41931,x41932),x41933),x41935)))
% 11.41/11.17 [4194]E(f784(f784(f54(x41941,f869(x41942,a852)),x41943),f784(f784(f9(x41941,f869(x41942,a852),f869(x41942,a852)),f784(f784(f10(f869(x41942,a852),f869(f869(x41942,a852),f869(x41942,a852)),x41941),f3(f869(x41942,a852))),x41944)),x41945)),f784(f784(f3(f869(x41942,a852)),f784(f784(f54(x41941,f869(x41942,a852)),x41943),x41944)),x41945))
% 11.41/11.17 [4195]E(f784(f784(f55(x41951,f869(x41952,a852)),x41953),f784(f784(f9(x41951,f869(x41952,a852),f869(x41952,a852)),f784(f784(f10(f869(x41952,a852),f869(f869(x41952,a852),f869(x41952,a852)),x41951),f110(f869(x41952,a852))),x41954)),x41955)),f784(f784(f110(f869(x41952,a852)),f784(f784(f55(x41951,f869(x41952,a852)),x41953),x41954)),x41955))
% 11.41/11.17 [4196]E(f784(f784(f54(x41961,f869(x41962,a852)),x41963),f784(f784(f9(x41961,f869(x41962,a852),f869(x41962,a852)),f784(f784(f10(f869(x41962,a852),f869(f869(x41962,a852),f869(x41962,a852)),x41961),f111(f869(x41962,a852))),x41964)),x41965)),f784(f784(f111(f869(x41962,a852)),f784(f784(f54(x41961,f869(x41962,a852)),x41963),x41964)),x41965))
% 11.41/11.17 [4197]E(f784(f784(f54(x41971,f869(x41972,a852)),x41973),f784(f784(f9(x41971,f869(x41972,a852),f869(x41972,a852)),f784(f784(f10(f869(x41972,a852),f869(f869(x41972,a852),f869(x41972,a852)),x41971),f3(f869(x41972,a852))),x41974)),x41975)),f784(f784(f3(f869(x41972,a852)),f784(f784(f54(x41971,f869(x41972,a852)),x41973),x41974)),x41975))
% 11.41/11.17 [4198]E(f784(f784(f54(x41981,f869(x41982,a852)),x41983),f784(f784(f9(x41981,f869(x41982,a852),f869(x41982,a852)),f784(f784(f10(f869(x41982,a852),f869(f869(x41982,a852),f869(x41982,a852)),x41981),f111(f869(x41982,a852))),x41984)),x41985)),f784(f784(f111(f869(x41982,a852)),f784(f784(f54(x41981,f869(x41982,a852)),x41983),x41984)),x41985))
% 11.41/11.17 [4199]E(f784(f784(f55(x41991,f869(x41992,a852)),x41993),f784(f784(f9(x41991,f869(x41992,a852),f869(x41992,a852)),f784(f784(f10(f869(x41992,a852),f869(f869(x41992,a852),f869(x41992,a852)),x41991),f110(f869(x41992,a852))),x41994)),x41995)),f784(f784(f110(f869(x41992,a852)),f784(f784(f55(x41991,f869(x41992,a852)),x41993),x41994)),x41995))
% 11.41/11.17 [4203]E(f784(f784(f54(x42031,f869(x42032,a852)),x42033),f784(f784(f20(x42031,f869(x42032,a852),f869(x42032,a852)),f784(f784(f10(f869(x42032,a852),f869(f869(x42032,a852),f869(x42032,a852)),x42031),f110(f869(x42032,a852))),x42034)),x42035)),f784(f784(f110(f869(x42032,a852)),f784(f784(f54(x42031,f869(x42032,a852)),x42033),x42034)),f784(f784(f54(x42031,f869(x42032,a852)),x42033),x42035)))
% 11.41/11.17 [4204]E(f784(f784(f55(x42041,f869(x42042,a852)),x42043),f784(f784(f20(x42041,f869(x42042,a852),f869(x42042,a852)),f784(f784(f10(f869(x42042,a852),f869(f869(x42042,a852),f869(x42042,a852)),x42041),f111(f869(x42042,a852))),x42044)),x42045)),f784(f784(f111(f869(x42042,a852)),f784(f784(f55(x42041,f869(x42042,a852)),x42043),x42044)),f784(f784(f55(x42041,f869(x42042,a852)),x42043),x42045)))
% 11.41/11.17 [4216]E(f784(f784(f54(x42161,f869(x42162,a852)),x42163),f784(f784(f20(x42161,f869(x42162,a852),f869(x42162,a852)),f784(f784(f10(f869(x42162,a852),f869(f869(x42162,a852),f869(x42162,a852)),x42161),f110(f869(x42162,a852))),x42164)),x42165)),f784(f784(f110(f869(x42162,a852)),f52(f869(x42162,a852),f784(f313(x42161,f869(x42162,a852),x42164),x42163))),f52(f869(x42162,a852),f784(f313(x42161,f869(x42162,a852),x42165),x42163))))
% 11.41/11.17 [4217]E(f784(f784(f55(x42171,f869(x42172,a852)),x42173),f784(f784(f20(x42171,f869(x42172,a852),f869(x42172,a852)),f784(f784(f10(f869(x42172,a852),f869(f869(x42172,a852),f869(x42172,a852)),x42171),f111(f869(x42172,a852))),x42174)),x42175)),f784(f784(f111(f869(x42172,a852)),f53(f869(x42172,a852),f784(f313(x42171,f869(x42172,a852),x42174),x42173))),f53(f869(x42172,a852),f784(f313(x42171,f869(x42172,a852),x42175),x42173))))
% 11.41/11.17 [4126]E(f784(f784(f130(f868(x41261,x41262)),f784(f784(f173(x41261,x41262),f784(f784(f165(x41261),f784(f188(f860(x41262)),x41263)),x41264)),x41263)),f784(f784(f173(x41261,x41262),f784(f784(f133(x41261),f784(f188(f860(x41262)),x41263)),x41264)),x41265)),f784(f784(f173(x41261,x41262),x41264),f784(f784(f130(x41262),x41263),x41265)))
% 11.41/11.17 [4242]E(f94(x42421,f784(f784(f20(x42421,a852,a852),f784(f784(f10(a852,f869(a852,a852),x42421),a344),f784(f784(f9(x42421,f869(x42421,a852),a852),f347(x42421)),x42422))),f784(f784(f9(x42421,x42423,a852),f784(f784(f10(x42423,f869(x42423,a852),x42421),a343),x42424)),x42425))),f784(f86(x42421,x42423,x42422,x42424),x42425))
% 11.41/11.17 [4292]E(f784(f784(f95(a1,x42921),f784(f113(a1),f784(f784(f89(a1),x42922),a106))),f784(f784(f20(a1,x42921,x42921),f784(f784(f9(a1,x42921,f869(x42921,x42921)),f784(f784(f10(a852,f869(x42921,f869(x42921,x42921)),a1),f105(x42921)),a193)),f182(x42921,x42923,x42924,x42925))),f784(f784(f10(a859,x42921,a1),x42924),f784(f784(f9(a1,a859,a859),f784(f784(f10(a859,f869(a859,a859),a1),f89(a859)),a114)),x42925)))),f182(x42921,x42923,x42924,f784(f784(f89(a859),f784(f113(a859),x42922)),x42925)))
% 11.41/11.17 [4326]E(f172(x43261,x43262,f784(f784(f146(f868(x43261,x43263),f868(x43261,x43262)),f784(f261(x43261,x43263,f868(x43261,x43262)),f784(f784(f9(x43261,f869(x43263,x43262),f869(x43263,f868(x43261,x43262))),f784(f784(f10(f869(x43262,f868(x43261,x43262)),f869(f869(x43263,x43262),f869(x43263,f868(x43261,x43262))),x43261),f10(x43262,f868(x43261,x43262),x43263)),f251(x43261,x43262))),x43264))),x43265)),f784(f82(f864(x43263),f864(x43262),x43261,f784(f206(x43263,x43262),x43264)),f172(x43261,x43263,x43265)))
% 11.41/11.17 [4285]E(f175(x42851,x42852,f784(f784(f20(x42851,f864(x42852),f864(x42852)),f784(f784(f20(x42851,f864(x42852),f869(f864(x42852),f864(x42852))),f784(f784(f10(a852,f869(f864(x42852),f869(f864(x42852),f864(x42852))),x42851),f105(f864(x42852))),x42853)),x42854)),x42855)),f784(f784(f110(f869(x42851,a852)),f784(f784(f111(f869(x42851,a852)),f175(x42851,x42852,x42854)),f784(f266(x42851),x42853))),f784(f784(f111(f869(x42851,a852)),f175(x42851,x42852,x42855)),f784(f266(x42851),f784(f784(f10(a852,a852,x42851),a341),x42853)))))
% 11.41/11.17 [4324]E(f784(f784(f95(a1,x43241),f784(f113(a1),f784(f784(f89(a1),x43242),a106))),f784(f784(f20(a1,x43241,x43241),f784(f784(f9(a1,x43241,f869(x43241,x43241)),f784(f784(f10(a852,f869(x43241,f869(x43241,x43241)),a1),f105(x43241)),a193)),f784(f181(x43241,x43243,x43244),x43245))),f784(f784(f20(a1,x43241,x43241),f784(f784(f10(a859,f869(x43241,x43241),a1),x43244),f784(f784(f9(a1,a859,a859),f784(f784(f10(a859,f869(a859,a859),a1),f89(a859)),a114)),x43245))),f784(f784(f10(a859,x43241,a1),f181(x43241,x43243,x43244)),f784(f784(f9(a1,a859,a859),f784(f784(f10(a859,f869(a859,a859),a1),f89(a859)),a114)),x43245))))),f784(f181(x43241,x43243,x43244),f784(f784(f89(a859),f784(f113(a859),x43242)),x43245)))
% 11.41/11.17 [4372]E(f784(f266(f868(x43721,x43722)),f784(f261(x43721,x43722,a852),f784(f784(f10(f869(x43722,f869(x43723,a852)),f869(x43722,a852),x43721),f784(f10(f869(x43723,a852),a852,x43722),f96(x43723))),f784(f784(f9(x43721,f869(x43722,f869(x43723,a852)),f869(x43722,f869(x43723,a852))),f784(f784(f10(f869(f869(x43723,a852),f869(x43723,a852)),f869(f869(x43722,f869(x43723,a852)),f869(x43722,f869(x43723,a852))),x43721),f10(f869(x43723,a852),f869(x43723,a852),x43722)),f784(f784(f10(f869(x43723,f869(a852,a852)),f869(f869(x43723,a852),f869(x43723,a852)),x43721),f20(x43723,a852,a852)),f784(f784(f10(f869(x43723,a852),f869(x43723,f869(a852,a852)),x43721),f784(f10(a852,f869(a852,a852),x43723),a344)),f784(f784(f9(x43721,f869(f868(x43721,x43723),a852),f869(x43723,a852)),f784(f784(f10(f869(x43723,f869(f869(f868(x43721,x43723),a852),a852)),f869(f869(f868(x43721,x43723),a852),f869(x43723,a852)),x43721),f9(x43723,f869(f868(x43721,x43723),a852),a852)),f784(f784(f10(f869(x43723,f868(x43721,x43723)),f869(x43723,f869(f869(f868(x43721,x43723),a852),a852)),x43721),f784(f10(f868(x43721,x43723),f869(f869(f868(x43721,x43723),a852),a852),x43723),f347(f868(x43721,x43723)))),f251(x43721,x43723)))),x43724))))),f784(f784(f9(x43722,f869(f868(x43723,x43722),a852),f869(x43723,a852)),f784(f784(f10(f869(x43723,f869(f869(f868(x43723,x43722),a852),a852)),f869(f869(f868(x43723,x43722),a852),f869(x43723,a852)),x43722),f9(x43723,f869(f868(x43723,x43722),a852),a852)),f784(f784(f10(f869(x43723,f868(x43723,x43722)),f869(x43723,f869(f869(f868(x43723,x43722),a852),a852)),x43722),f784(f10(f868(x43723,x43722),f869(f869(f868(x43723,x43722),a852),a852),x43723),f347(f868(x43723,x43722)))),f784(f9(x43723,x43722,f868(x43723,x43722)),f251(x43723,x43722))))),x43725))))),f784(f784(f291(x43721,x43723,x43722),x43724),x43725))
% 11.41/11.17 [4475]~E(f35(x44751,x44752,x44753),f33(x44754,x44755,x44756))
% 11.41/11.17 [4476]~E(f35(x44761,x44762,x44763),f33(x44764,x44765,x44766))
% 11.41/11.17 [4477]~E(f34(x44771,x44772,x44773),f33(x44774,x44775,x44776))
% 11.41/11.17 [4478]~E(f34(x44781,x44782,x44783),f35(x44784,x44785,x44786))
% 11.41/11.17 [4479]~E(f34(x44791,x44792,x44793),f33(x44794,x44795,x44796))
% 11.41/11.17 [4480]~E(f34(x44801,x44802,x44803),f35(x44804,x44805,x44806))
% 11.41/11.17 [3969]E(f228(x39691,x39692,x39693,x39694,f225(x39691,x39692,x39695,x39696)),f784(f784(x39694,x39695),x39696))
% 11.41/11.17 [3970]E(f229(x39701,x39702,x39703,x39704,f225(x39701,x39702,x39705,x39706)),f784(f784(x39704,x39705),x39706))
% 11.41/11.17 [4110]E(f178(x41101,x41102,f176(x41101,x41102,x41103,x41104),x41105,x41106),f176(x41101,x41102,x41103,f178(x41101,x41102,x41104,x41105,x41106)))
% 11.41/11.17 [4232]E(f784(f82(f868(x42321,x42322),x42322,f868(x42323,x42324),f260(x42321,x42322)),f262(x42323,x42321,x42324,x42322,x42325,x42326)),f784(f82(x42324,x42322,f868(x42323,x42324),x42326),f260(x42323,x42324)))
% 11.41/11.17 [4233]E(f784(f82(f868(x42331,x42332),x42331,f868(x42333,x42334),f250(x42331,x42332)),f262(x42333,x42331,x42334,x42332,x42335,x42336)),f784(f82(x42333,x42331,f868(x42333,x42334),x42335),f250(x42333,x42334)))
% 11.41/11.17 [3836]E(f784(f784(f82(x38361,x38362,x38363,x38364),x38365),x38366),f784(x38364,f784(x38365,x38366)))
% 11.41/11.17 [3837]E(f784(f784(f82(x38371,x38372,x38373,x38374),x38375),x38376),f784(x38374,f784(x38375,x38376)))
% 11.41/11.17 [4032]E(f230(x40321,x40322,x40323,x40324,f225(x40321,x40322,x40325,x40326)),f784(f784(f89(a859),f784(f784(f89(a859),f784(x40323,x40325)),f784(x40324,x40326))),f784(a160,f2(a859))))
% 11.41/11.17 [4054]E(f784(f332(x40541,x40542,x40543,x40544,x40545),f784(f326(x40543,x40541),x40546)),f784(x40545,x40546))
% 11.41/11.17 [4055]E(f784(f332(x40551,x40552,x40553,x40554,x40555),f784(f322(x40551,x40553),x40556)),f784(x40554,x40556))
% 11.41/11.17 [4149]E(f333(x41491,x41492,x41493,x41494,x41495,f784(f326(x41493,x41491),x41496)),f784(x41495,x41496))
% 11.41/11.17 [4150]E(f333(x41501,x41502,x41503,x41504,x41505,f784(f322(x41501,x41503),x41506)),f784(x41504,x41506))
% 11.41/11.17 [3634]E(f784(f784(f261(x36341,x36342,x36343),x36344),f784(f784(f251(x36341,x36342),x36345),x36346)),f784(f784(x36344,x36345),x36346))
% 11.41/11.17 [3635]E(f784(f784(f261(x36351,x36352,x36353),x36354),f784(f784(f251(x36351,x36352),x36355),x36356)),f784(f784(x36354,x36355),x36356))
% 11.41/11.17 [3636]E(f784(f784(f261(x36361,x36362,x36363),x36364),f784(f784(f251(x36361,x36362),x36365),x36366)),f784(f784(x36364,x36365),x36366))
% 11.41/11.17 [3699]E(f784(f784(f784(f10(x36991,x36992,x36993),x36994),x36995),x36996),f784(x36994,f784(x36995,x36996)))
% 11.41/11.17 [3700]E(f784(f784(f784(f9(x37001,x37002,x37003),x37004),x37005),x37006),f784(f784(x37004,x37006),x37005))
% 11.41/11.17 [3716]E(f784(f784(f784(f20(x37161,x37162,x37163),x37164),x37165),x37166),f784(f784(x37164,x37166),f784(x37165,x37166)))
% 11.41/11.17 [3740]E(f784(f148(x37401,x37402,x37403,x37404),f784(f784(f144(x37402),x37405),x37406)),f784(f784(x37404,x37405),x37406))
% 11.41/11.17 [3840]E(f784(f784(f144(f868(x38401,x38402)),f784(f784(f251(x38401,x38402),x38403),x38404)),f784(f784(f173(x38401,x38402),x38405),x38406)),f784(f784(f173(x38401,x38402),f784(f784(f144(x38401),x38403),x38405)),f784(f784(f144(x38402),x38404),x38406)))
% 11.41/11.17 [3842]E(f784(f784(f146(x38421,x38422),x38423),f784(f784(f151(x38421,x38424),x38425),x38426)),f784(f784(f151(x38422,f784(f784(f146(x38421,x38422),x38423),x38424)),x38425),f784(x38423,x38426)))
% 11.41/11.17 [3866]E(f784(f784(f259(x38661,x38662,x38663,x38664),x38665),x38666),f784(x38664,f784(f784(f251(x38661,x38662),x38665),x38666)))
% 11.41/11.17 [3867]E(f784(f784(f259(x38671,x38672,x38673,x38674),x38675),x38676),f784(x38674,f784(f784(f251(x38671,x38672),x38675),x38676)))
% 11.41/11.17 [3884]E(f784(f136(x38841,x38842,x38843,x38844),f784(f784(f144(x38842),x38845),x38846)),f784(f136(x38841,x38842,x38843,f784(f784(x38843,x38844),x38845)),x38846))
% 11.41/11.17 [3911]E(f264(x39111,x39112,x39113,x39114,f784(f784(f251(x39111,x39112),x39115),x39116)),f784(f784(x39114,x39115),x39116))
% 11.41/11.17 [3995]E(f784(f784(f54(x39951,f869(x39952,a852)),x39953),f784(f82(x39954,f869(x39952,a852),x39951,x39955),x39956)),f784(f784(f54(x39954,f869(x39952,a852)),f784(f313(x39951,x39954,x39956),x39953)),x39955))
% 11.41/11.17 [4045]E(f784(f784(f146(x40451,x40452),x40453),f784(f784(f146(x40454,x40451),x40455),x40456)),f784(f784(f146(x40454,x40452),f784(f82(x40451,x40452,x40454,x40453),x40455)),x40456))
% 11.41/11.17 [4046]E(f784(f784(f146(x40461,x40462),x40463),f784(f784(f146(x40464,x40461),x40465),x40466)),f784(f784(f146(x40464,x40462),f784(f82(x40461,x40462,x40464,x40463),x40465)),x40466))
% 11.41/11.17 [4047]E(f784(f784(f206(x40471,x40472),x40473),f784(f784(f206(x40474,x40471),x40475),x40476)),f784(f784(f206(x40474,x40472),f784(f82(x40471,x40472,x40474,x40473),x40475)),x40476))
% 11.41/11.17 [4048]E(f784(f784(f206(x40481,x40482),x40483),f784(f784(f206(x40484,x40481),x40485),x40486)),f784(f784(f206(x40484,x40482),f784(f82(x40481,x40482,x40484,x40483),x40485)),x40486))
% 11.41/11.17 [4052]E(f784(f313(x40521,x40522,f784(f82(x40523,x40522,x40521,x40524),x40525)),x40526),f784(f313(x40523,x40522,x40524),f784(f313(x40521,x40523,x40525),x40526)))
% 11.41/11.17 [4053]E(f784(f315(x40531,x40532,f784(f82(x40533,x40532,x40531,x40534),x40535)),x40536),f784(f315(x40531,x40533,x40535),f784(f315(x40533,x40532,x40534),x40536)))
% 11.41/11.17 [4083]E(f176(x40831,x40832,x40833,f784(f784(f784(f81(x40831,f864(x40832)),x40834),x40835),f784(f237(x40832),x40836))),f784(f784(f784(f81(x40831,f864(x40832)),f176(x40831,x40832,x40833,x40834)),x40835),f784(f237(x40832),x40836)))
% 11.41/11.17 [4085]E(f784(f136(x40851,x40852,x40853,f784(f136(x40851,x40852,x40853,x40854),x40855)),x40856),f784(f136(x40851,x40852,x40853,x40854),f784(f784(f130(x40852),x40855),x40856)))
% 11.41/11.17 [4222]E(f784(f262(x42221,x42221,x42222,x42223,f41(x42221),x42224),f784(f784(f251(x42221,x42222),x42225),x42226)),f784(f784(f251(x42221,x42223),x42225),f784(x42224,x42226)))
% 11.41/11.17 [4223]E(f784(f262(x42231,x42232,x42233,x42233,x42234,f41(x42233)),f784(f784(f251(x42231,x42233),x42235),x42236)),f784(f784(f251(x42232,x42233),f784(x42234,x42235)),x42236))
% 11.41/11.17 [4308]E(f784(f784(f146(f868(x43081,x43082),f868(x43081,x43083)),f784(f261(x43081,x43082,f868(x43081,x43083)),f784(f784(f9(x43081,f869(x43082,x43083),f869(x43082,f868(x43081,x43083))),f784(f784(f10(f869(x43083,f868(x43081,x43083)),f869(f869(x43082,x43083),f869(x43082,f868(x43081,x43083))),x43081),f10(x43083,f868(x43081,x43083),x43082)),f251(x43081,x43083))),x43084))),f784(f784(f173(x43081,x43082),x43085),x43086)),f784(f784(f173(x43081,x43083),x43085),f784(f784(f146(x43082,x43083),x43084),x43086)))
% 11.41/11.17 [3704]E(f103(x37041,x37042,x37043,f784(f784(f784(f100(x37041),x37044),x37045),x37046)),f784(f784(f784(x37043,x37044),x37045),x37046))
% 11.41/11.17 [3705]E(f104(x37051,x37052,x37053,f784(f784(f784(f100(x37051),x37054),x37055),x37056)),f784(f784(f784(x37053,x37054),x37055),x37056))
% 11.41/11.17 [3894]E(f784(f784(f82(x38941,x38942,x38943,f784(f18(x38942,x38941),x38944)),x38945),x38946),x38944)
% 11.41/11.17 [3929]E(f784(f313(x39291,x39292,x39293),f784(f313(x39294,x39291,x39295),x39296)),f784(f313(x39294,x39292,f784(f784(f10(x39291,x39292,x39294),x39293),x39295)),x39296))
% 11.41/11.17 [3935]E(f784(f784(f54(x39351,f869(x39352,a852)),f784(f313(x39353,x39351,x39354),x39355)),x39356),f784(f784(f54(x39353,f869(x39352,a852)),x39355),f784(f784(f10(x39351,f869(x39352,a852),x39353),x39356),x39354)))
% 11.41/11.17 [3936]E(f784(f784(f55(x39361,f869(x39362,a852)),f784(f313(x39363,x39361,x39364),x39365)),x39366),f784(f784(f55(x39363,f869(x39362,a852)),x39365),f784(f784(f10(x39361,f869(x39362,a852),x39363),x39366),x39364)))
% 11.41/11.17 [3937]E(f784(f784(f54(x39371,f869(x39372,a852)),x39373),f784(f784(f10(x39374,f869(x39372,a852),x39371),x39375),x39376)),f784(f784(f54(x39374,f869(x39372,a852)),f784(f313(x39371,x39374,x39376),x39373)),x39375))
% 11.41/11.17 [3938]E(f784(f784(f55(x39381,f869(x39382,a852)),x39383),f784(f784(f10(x39384,f869(x39382,a852),x39381),x39385),x39386)),f784(f784(f55(x39384,f869(x39382,a852)),f784(f313(x39381,x39384,x39386),x39383)),x39385))
% 11.41/11.17 [3997]E(f784(f784(f54(x39971,f869(x39972,a852)),x39973),f784(f784(f10(f869(x39974,a852),f869(x39972,a852),x39971),f313(x39974,x39972,x39975)),x39976)),f784(f313(x39974,x39972,x39975),f784(f784(f54(x39971,f869(x39974,a852)),x39973),x39976)))
% 11.41/11.17 [3998]E(f784(f784(f54(x39981,f869(x39982,a852)),x39983),f784(f784(f10(f869(x39984,a852),f869(x39982,a852),x39981),f287(x39984,x39982,x39985)),x39986)),f784(f287(x39984,x39982,x39985),f784(f784(f54(x39981,f869(x39984,a852)),x39983),x39986)))
% 11.41/11.17 [3999]E(f784(f784(f54(x39991,f869(x39992,a852)),x39993),f784(f784(f10(f869(x39994,a852),f869(x39992,a852),x39991),f315(x39992,x39994,x39995)),x39996)),f784(f315(x39992,x39994,x39995),f784(f784(f54(x39991,f869(x39994,a852)),x39993),x39996)))
% 11.41/11.17 [4000]E(f784(f784(f55(x40001,f869(x40002,a852)),x40003),f784(f784(f10(f869(x40004,a852),f869(x40002,a852),x40001),f315(x40002,x40004,x40005)),x40006)),f784(f315(x40002,x40004,x40005),f784(f784(f55(x40001,f869(x40004,a852)),x40003),x40006)))
% 11.41/11.17 [4091]E(f784(f136(x40911,x40912,f784(f9(x40912,x40911,x40911),x40913),x40914),f784(f162(x40912),f784(f784(f144(x40912),x40915),x40916))),f784(f784(x40913,x40915),f784(f136(x40911,x40912,f784(f9(x40912,x40911,x40911),x40913),x40914),f784(f162(x40912),x40916))))
% 11.41/11.17 [4151]E(f784(f784(f20(f868(x41511,x41512),x41512,x41513),f784(f784(f10(x41514,f869(x41512,x41513),f868(x41511,x41512)),x41515),f784(f784(f10(x41511,x41514,f868(x41511,x41512)),x41516),f250(x41511,x41512)))),f260(x41511,x41512)),f784(f261(x41511,x41512,x41513),f784(f784(f10(x41514,f869(x41512,x41513),x41511),x41515),x41516)))
% 11.41/11.17 [4158]E(f784(f136(x41581,x41582,f784(f9(x41582,x41581,x41581),x41583),f784(f136(x41581,x41582,f784(f9(x41582,x41581,x41581),x41583),x41584),f784(f162(x41582),x41585))),f784(f162(x41582),x41586)),f784(f136(x41581,x41582,f784(f9(x41582,x41581,x41581),x41583),x41584),f784(f162(x41582),f784(f784(f130(x41582),x41586),x41585))))
% 11.41/11.17 [4160]E(f784(f784(f146(f868(x41601,x41602),f868(x41603,x41602)),f784(f261(x41601,x41602,f868(x41603,x41602)),f784(f784(f10(x41603,f869(x41602,f868(x41603,x41602)),x41601),f251(x41603,x41602)),x41604))),f784(f784(f173(x41601,x41602),x41605),x41606)),f784(f784(f173(x41603,x41602),f784(f784(f146(x41601,x41603),x41604),x41605)),x41606))
% 11.41/11.17 [4206]P85(f784(f784(f242(f869(x42061,a852)),f784(f287(x42062,x42061,x42063),f784(f784(f55(x42064,f869(x42062,a852)),x42065),x42066))),f784(f784(f55(x42064,f869(x42061,a852)),x42065),f784(f784(f10(f869(x42062,a852),f869(x42061,a852),x42064),f287(x42062,x42061,x42063)),x42066))))
% 11.41/11.17 [4010]E(f784(f784(f173(x40101,x40102),f784(f784(f151(x40101,x40103),x40104),f784(f250(x40101,x40102),x40105))),f784(f784(f151(x40102,x40106),x40104),f784(f260(x40101,x40102),x40105))),f784(f784(f151(f868(x40101,x40102),f784(f784(f173(x40101,x40102),x40103),x40106)),x40104),x40105))
% 11.41/11.17 [4073]E(f784(f784(f110(f869(f868(x40731,x40732),a852)),f784(f784(f291(x40731,x40733,x40732),x40734),x40735)),f784(f784(f291(x40731,x40733,x40732),x40734),x40736)),f784(f784(f291(x40731,x40733,x40732),x40734),f784(f784(f110(f869(f868(x40733,x40732),a852)),x40735),x40736)))
% 11.41/11.17 [4172]E(f784(f784(f312(f868(x41721,x41722)),f784(f784(f251(x41721,x41722),x41723),x41724)),f784(f784(f110(f869(f868(x41721,x41722),a852)),f784(f784(f258(x41721,x41722),x41725),f784(f18(f869(x41722,a852),x41721),f784(f784(f312(x41722),x41724),x41726)))),f784(f784(f258(x41721,x41722),f784(f784(f312(x41721),x41723),x41725)),f784(f18(f869(x41722,a852),x41721),x41726)))),f784(f784(f258(x41721,x41722),f784(f784(f312(x41721),x41723),x41725)),f784(f18(f869(x41722,a852),x41721),f784(f784(f312(x41722),x41724),x41726))))
% 11.41/11.17 [4245]E(f784(f784(f111(f869(x42451,a852)),f784(f315(x42451,x42452,f784(f82(f868(x42452,x42453),x42452,x42451,f250(x42452,x42453)),x42454)),x42455)),f784(f315(x42451,x42453,f784(f82(f868(x42452,x42453),x42453,x42451,f260(x42452,x42453)),x42454)),x42456)),f784(f315(x42451,f868(x42452,x42453),x42454),f784(f784(f258(x42452,x42453),x42455),f784(f18(f869(x42453,a852),x42452),x42456))))
% 11.41/11.17 [3994]E(f784(f784(f784(f81(x39941,x39942),f784(f784(f784(f81(x39941,x39942),x39943),x39944),x39945)),x39944),x39946),f784(f784(f784(f81(x39941,x39942),x39943),x39944),x39946))
% 11.41/11.17 [4097]E(f784(f784(f110(f869(f868(x40971,x40972),a852)),f784(f784(f291(x40971,x40973,x40972),x40974),x40975)),f784(f784(f291(x40971,x40973,x40972),x40976),x40975)),f784(f784(f291(x40971,x40973,x40972),f784(f784(f110(f869(f868(x40971,x40973),a852)),x40974),x40976)),x40975))
% 11.41/11.17 [4227]E(f784(f784(f54(x42271,f869(x42272,a852)),x42273),f784(f784(f9(x42271,f869(x42274,f869(x42272,a852)),f869(x42272,a852)),f784(f784(f10(f869(x42274,a852),f869(f869(x42274,f869(x42272,a852)),f869(x42272,a852)),x42271),f54(x42274,f869(x42272,a852))),x42275)),x42276)),f784(f784(f54(x42274,f869(x42272,a852)),f784(f784(f54(x42271,f869(x42274,a852)),x42273),x42275)),x42276))
% 11.41/11.17 [4228]E(f784(f784(f54(x42281,f869(x42282,a852)),x42283),f784(f784(f9(x42281,f869(x42284,f869(x42282,a852)),f869(x42282,a852)),f784(f784(f10(f869(x42284,a852),f869(f869(x42284,f869(x42282,a852)),f869(x42282,a852)),x42281),f54(x42284,f869(x42282,a852))),x42285)),x42286)),f784(f784(f54(x42284,f869(x42282,a852)),f784(f784(f54(x42281,f869(x42284,a852)),x42283),x42285)),x42286))
% 11.41/11.17 [4229]E(f784(f784(f55(x42291,f869(x42292,a852)),x42293),f784(f784(f9(x42291,f869(x42294,f869(x42292,a852)),f869(x42292,a852)),f784(f784(f10(f869(x42294,a852),f869(f869(x42294,f869(x42292,a852)),f869(x42292,a852)),x42291),f55(x42294,f869(x42292,a852))),x42295)),x42296)),f784(f784(f55(x42294,f869(x42292,a852)),f784(f784(f54(x42291,f869(x42294,a852)),x42293),x42295)),x42296))
% 11.41/11.17 [4230]E(f784(f784(f54(x42301,f869(x42302,a852)),x42303),f784(f784(f9(x42301,f869(x42304,f869(x42302,a852)),f869(x42302,a852)),f784(f784(f10(f869(x42304,a852),f869(f869(x42304,f869(x42302,a852)),f869(x42302,a852)),x42301),f54(x42304,f869(x42302,a852))),x42305)),x42306)),f784(f784(f54(x42304,f869(x42302,a852)),f784(f784(f54(x42301,f869(x42304,a852)),x42303),x42305)),x42306))
% 11.41/11.17 [4231]E(f784(f784(f55(x42311,f869(x42312,a852)),x42313),f784(f784(f9(x42311,f869(x42314,f869(x42312,a852)),f869(x42312,a852)),f784(f784(f10(f869(x42314,a852),f869(f869(x42314,f869(x42312,a852)),f869(x42312,a852)),x42311),f55(x42314,f869(x42312,a852))),x42315)),x42316)),f784(f784(f55(x42314,f869(x42312,a852)),f784(f784(f54(x42311,f869(x42314,a852)),x42313),x42315)),x42316))
% 11.41/11.17 [4280]E(f784(f261(x42801,x42802,f868(x42803,x42804)),f784(f784(f9(x42801,f869(x42802,x42804),f869(x42802,f868(x42803,x42804))),f784(f784(f10(f869(x42804,f868(x42803,x42804)),f869(f869(x42802,x42804),f869(x42802,f868(x42803,x42804))),x42801),f10(x42804,f868(x42803,x42804),x42802)),f784(f784(f10(x42803,f869(x42804,f868(x42803,x42804)),x42801),f251(x42803,x42804)),x42805))),x42806)),f262(x42801,x42803,x42802,x42804,x42805,x42806))
% 11.41/11.17 [4205]E(f784(f784(f784(f81(x42051,f864(x42052)),f179(x42051,x42052,x42053,f784(f784(f3(f869(x42051,a852)),x42054),f784(f784(f312(x42051),x42055),f187(f869(x42051,a852)))))),x42055),x42056),f784(f784(f784(f81(x42051,f864(x42052)),f179(x42051,x42052,x42053,x42054)),x42055),x42056))
% 11.41/11.17 [4303]E(f784(f313(x43031,x43032,f784(f784(f20(x43031,x43032,x43032),f784(f784(f20(x43031,x43032,f869(x43032,x43032)),f784(f784(f10(a852,f869(x43032,f869(x43032,x43032)),x43031),f105(x43032)),x43033)),x43034)),x43035)),x43036),f784(f784(f110(f869(x43032,a852)),f784(f313(x43031,x43032,x43034),f784(f784(f111(f869(x43031,a852)),x43036),f784(f266(x43031),x43033)))),f784(f313(x43031,x43032,x43035),f784(f784(f111(f869(x43031,a852)),x43036),f784(f266(x43031),f784(f784(f10(a852,a852,x43031),a341),x43033))))))
% 11.41/11.17 [4314]E(f784(f313(x43141,f868(x43142,x43143),f784(f784(f20(x43141,x43143,f868(x43142,x43143)),f784(f784(f10(x43142,f869(x43143,f868(x43142,x43143)),x43141),f251(x43142,x43143)),x43144)),x43145)),x43146),f784(f784(f258(x43142,x43143),f784(f313(x43141,x43142,x43144),x43146)),f784(f784(f10(f869(x43141,a852),f869(x43143,a852),x43142),f313(x43141,x43143,x43145)),f784(f784(f9(x43142,f869(x43141,a852),f869(x43141,a852)),f784(f784(f10(f869(x43141,a852),f869(f869(x43141,a852),f869(x43141,a852)),x43142),f111(f869(x43141,a852))),f784(f784(f10(f869(x43142,a852),f869(x43141,a852),x43142),f315(x43141,x43142,x43144)),f784(f784(f9(x43142,f869(x43142,a852),f869(x43142,a852)),f312(x43142)),f187(f869(x43142,a852)))))),x43146))))
% 11.41/11.17 [4263]E(f784(f260(x42631,x42632),f784(f262(x42633,x42631,x42634,x42632,x42635,x42636),x42637)),f784(x42636,f784(f260(x42633,x42634),x42637)))
% 11.41/11.17 [4264]E(f784(f250(x42641,x42642),f784(f262(x42643,x42641,x42644,x42642,x42645,x42646),x42647)),f784(x42645,f784(f250(x42643,x42644),x42647)))
% 11.41/11.17 [3971]E(f784(f784(f173(x39711,x39712),f784(f784(f151(x39711,x39713),x39714),x39715)),f784(f784(f151(x39712,x39716),x39714),x39717)),f784(f784(f151(f868(x39711,x39712),f784(f784(f173(x39711,x39712),x39713),x39716)),x39714),f784(f784(f251(x39711,x39712),x39715),x39717)))
% 11.41/11.17 [4040]E(f784(f784(f784(f263(x40401,x40402,x40403,x40404),x40405),x40406),x40407),f784(f784(f261(x40402,x40403,x40404),x40406),f784(x40405,x40407)))
% 11.41/11.17 [4041]E(f784(f784(f784(f263(x40411,x40412,x40413,x40414),x40415),x40416),x40417),f784(f784(f261(x40412,x40413,x40414),x40416),f784(x40415,x40417)))
% 11.41/11.17 [4051]E(f784(f784(f784(f263(x40511,x40512,x40513,x40514),x40515),x40516),x40517),f784(f784(x40516,f784(f250(x40512,x40513),f784(x40515,x40517))),f784(f260(x40512,x40513),f784(x40515,x40517))))
% 11.41/11.17 [4087]E(f178(x40871,x40872,f784(f784(f784(f81(x40871,f864(x40872)),x40873),x40874),f784(f237(x40872),x40875)),x40876,x40877),f178(x40871,x40872,x40873,f784(f784(f144(x40871),x40874),x40876),f784(f784(f144(x40872),x40875),x40877)))
% 11.41/11.17 [4104]E(f784(f82(x41041,x41042,x41043,x41044),f784(f82(x41045,x41041,x41043,x41046),x41047)),f784(f82(x41045,x41042,x41043,f784(f82(x41041,x41042,x41045,x41044),x41046)),x41047))
% 11.41/11.17 [4167]E(f784(f82(f864(x41671),f864(x41672),x41673,f784(f206(x41671,x41672),x41674)),f784(f784(f784(f81(x41673,f864(x41671)),x41675),x41676),f784(f237(x41671),x41677))),f784(f784(f784(f81(x41673,f864(x41672)),f784(f82(f864(x41671),f864(x41672),x41673,f784(f206(x41671,x41672),x41674)),x41675)),x41676),f784(f237(x41672),f784(x41674,x41677))))
% 11.41/11.17 [4287]E(f784(f262(x42871,x42872,x42873,x42873,x42874,f41(x42873)),f784(f262(x42871,x42871,x42875,x42873,f41(x42871),x42876),x42877)),f784(f784(f251(x42872,x42873),f784(x42874,f784(f250(x42871,x42875),x42877))),f784(x42876,f784(f260(x42871,x42875),x42877))))
% 11.41/11.17 [4288]E(f784(f262(x42881,x42881,x42882,x42883,f41(x42881),x42884),f784(f262(x42885,x42881,x42882,x42882,x42886,f41(x42882)),x42887)),f784(f784(f251(x42881,x42883),f784(x42886,f784(f250(x42885,x42882),x42887))),f784(x42884,f784(f260(x42885,x42882),x42887))))
% 11.41/11.17 [4301]E(f784(f262(x43011,x43012,x43013,x43013,x43014,f41(x43013)),f784(f262(x43015,x43011,x43013,x43013,x43016,f41(x43013)),x43017)),f784(f262(x43015,x43012,x43013,x43013,f784(f82(x43011,x43012,x43015,x43014),x43016),f41(x43013)),x43017))
% 11.41/11.17 [4302]E(f784(f262(x43021,x43021,x43022,x43023,f41(x43021),x43024),f784(f262(x43021,x43021,x43025,x43022,f41(x43021),x43026),x43027)),f784(f262(x43021,x43021,x43025,x43023,f41(x43021),f784(f82(x43022,x43023,x43025,x43024),x43026)),x43027))
% 11.41/11.17 [4311]E(f784(f262(x43111,x43112,x43113,x43113,x43114,f41(x43113)),f784(f262(x43111,x43111,x43115,x43113,f41(x43111),x43116),x43117)),f784(f262(x43112,x43112,x43115,x43113,f41(x43112),x43116),f784(f262(x43111,x43112,x43115,x43115,x43114,f41(x43115)),x43117)))
% 11.41/11.17 [4007]E(f784(f784(f291(x40071,x40072,x40073),f784(f784(f291(x40071,x40074,x40072),x40075),x40076)),x40077),f784(f784(f291(x40071,x40074,x40073),x40075),f784(f784(f291(x40074,x40072,x40073),x40076),x40077)))
% 11.41/11.17 [4079]E(f784(f784(f261(x40791,x40792,x40793),f784(f82(x40794,f869(x40792,x40793),x40791,x40795),x40796)),x40797),f784(f784(x40795,f784(x40796,f784(f250(x40791,x40792),x40797))),f784(f260(x40791,x40792),x40797)))
% 11.41/11.17 [4129]E(f784(f82(x41291,x41292,x41293,x41294),f784(f784(f784(f81(x41293,x41291),x41295),x41296),x41297)),f784(f784(f784(f81(x41293,x41292),f784(f82(x41291,x41292,x41293,x41294),x41295)),x41296),f784(x41294,x41297)))
% 11.41/11.17 [4163]E(f784(f136(x41631,x41632,f784(f9(x41632,x41631,x41631),x41633),x41634),f784(f162(x41632),f784(f784(f146(x41635,x41632),x41636),x41637))),f784(f136(x41631,x41635,f784(f9(x41635,x41631,x41631),f784(f82(x41632,f869(x41631,x41631),x41635,x41633),x41636)),x41634),f784(f162(x41635),x41637)))
% 11.41/11.17 [4168]E(f332(x41681,f864(x41682),x41683,f784(f82(f864(x41684),f864(x41682),x41681,f784(f206(x41684,x41682),x41685)),x41686),f784(f82(f864(x41684),f864(x41682),x41683,f784(f206(x41684,x41682),x41685)),x41687)),f784(f82(f864(x41684),f864(x41682),f870(x41681,x41683),f784(f206(x41684,x41682),x41685)),f332(x41681,f864(x41684),x41683,x41686,x41687)))
% 11.41/11.17 [4105]E(f784(f784(f54(x41051,f869(f868(x41052,x41053),a852)),x41054),f784(f784(f10(f869(f868(x41055,x41053),a852),f869(f868(x41052,x41053),a852),x41051),f784(f291(x41052,x41055,x41053),x41056)),x41057)),f784(f784(f291(x41052,x41055,x41053),x41056),f784(f784(f54(x41051,f869(f868(x41055,x41053),a852)),x41054),x41057)))
% 11.41/11.17 [4250]E(f784(f784(f54(x42501,f869(f868(x42502,x42503),a852)),x42504),f784(f784(f9(x42501,f869(f868(x42505,x42503),a852),f869(f868(x42502,x42503),a852)),f784(f784(f10(f869(f868(x42502,x42505),a852),f869(f869(f868(x42505,x42503),a852),f869(f868(x42502,x42503),a852)),x42501),f291(x42502,x42505,x42503)),x42506)),x42507)),f784(f784(f291(x42502,x42505,x42503),f784(f784(f54(x42501,f869(f868(x42502,x42505),a852)),x42504),x42506)),x42507))
% 11.41/11.17 [4251]E(f784(f136(x42511,x42512,f784(f784(f9(x42511,f869(x42512,x42513),f869(x42512,x42511)),f784(f784(f10(f869(x42513,x42511),f869(f869(x42512,x42513),f869(x42512,x42511)),x42511),f10(x42513,x42511,x42512)),x42514)),x42515),x42516),x42517),f784(f136(x42511,x42513,x42514,x42516),f784(f784(f146(x42512,x42513),x42515),x42517)))
% 11.41/11.17 [4312]E(f784(f784(f55(x43121,f869(x43122,a852)),x43123),f784(f784(f10(f869(x43124,f869(x43122,a852)),f869(x43122,a852),x43121),f784(f55(x43124,f869(x43122,a852)),x43125)),f784(f784(f9(x43121,f869(x43124,f869(x43122,a852)),f869(x43124,f869(x43122,a852))),f784(f784(f10(f869(f869(x43122,a852),f869(x43122,a852)),f869(f869(x43124,f869(x43122,a852)),f869(x43124,f869(x43122,a852))),x43121),f10(f869(x43122,a852),f869(x43122,a852),x43124)),f784(f784(f10(f869(x43122,a852),f869(f869(x43122,a852),f869(x43122,a852)),x43121),f110(f869(x43122,a852))),x43126))),x43127))),f784(f784(f110(f869(x43122,a852)),f784(f784(f55(x43121,f869(x43122,a852)),x43123),x43126)),f784(f784(f55(x43124,f869(x43122,a852)),x43125),x43127)))
% 11.41/11.17 [4313]E(f784(f784(f54(x43131,f869(x43132,a852)),x43133),f784(f784(f10(f869(x43134,f869(x43132,a852)),f869(x43132,a852),x43131),f784(f54(x43134,f869(x43132,a852)),x43135)),f784(f784(f9(x43131,f869(x43134,f869(x43132,a852)),f869(x43134,f869(x43132,a852))),f784(f784(f10(f869(f869(x43132,a852),f869(x43132,a852)),f869(f869(x43134,f869(x43132,a852)),f869(x43134,f869(x43132,a852))),x43131),f10(f869(x43132,a852),f869(x43132,a852),x43134)),f784(f784(f10(f869(x43132,a852),f869(f869(x43132,a852),f869(x43132,a852)),x43131),f111(f869(x43132,a852))),x43136))),x43137))),f784(f784(f111(f869(x43132,a852)),f784(f784(f54(x43131,f869(x43132,a852)),x43133),x43136)),f784(f784(f54(x43134,f869(x43132,a852)),x43135),x43137)))
% 11.41/11.17 [4306]E(f202(x43061,x43062,f784(f784(f784(x43063,x43064),x43065),x43066),f784(f784(f9(x43061,f868(a108,a108),f869(a108,f861(x43062))),f784(f784(f9(x43061,a108,f869(f868(a108,a108),f869(a108,f861(x43062)))),f784(f784(f9(x43061,a108,f869(a108,f869(f868(a108,a108),f869(a108,f861(x43062))))),x43067),x43064)),x43065)),x43066)),f784(f784(f784(f214(x43061,x43062,x43063,x43067),x43064),x43065),x43066))
% 11.41/11.17 [4319]E(f203(x43191,x43192,f784(f784(f784(x43193,x43194),x43195),x43196),f784(f784(f9(x43191,f868(a108,a108),f869(a108,f861(x43192))),f784(f784(f9(x43191,a108,f869(f868(a108,a108),f869(a108,f861(x43192)))),f784(f784(f9(x43191,a108,f869(a108,f869(f868(a108,a108),f869(a108,f861(x43192))))),x43197),x43194)),x43195)),x43196)),f216(x43191,x43192,x43193,x43197,x43194,x43195,x43196))
% 11.41/11.17 [4310]E(f200(x43101,x43102,f784(f784(f784(x43103,x43104),x43105),x43106),f784(f784(f9(x43101,f868(a108,a108),f869(a108,f861(f864(x43102)))),f784(f784(f9(x43101,a108,f869(f868(a108,a108),f869(a108,f861(f864(x43102))))),f784(f784(f9(x43101,a108,f869(a108,f869(f868(a108,a108),f869(a108,f861(f864(x43102)))))),x43107),x43104)),x43105)),x43106)),f784(f784(f784(f211(x43101,x43102,x43103,x43107),x43104),x43105),x43106))
% 11.41/11.17 [4321]E(f201(x43211,x43212,f784(f784(f784(x43213,x43214),x43215),x43216),f784(f784(f9(x43211,f868(a108,a108),f869(a108,f861(f864(x43212)))),f784(f784(f9(x43211,a108,f869(f868(a108,a108),f869(a108,f861(f864(x43212))))),f784(f784(f9(x43211,a108,f869(a108,f869(f868(a108,a108),f869(a108,f861(f864(x43212)))))),x43217),x43214)),x43215)),x43216)),f213(x43211,x43212,x43213,x43217,x43214,x43215,x43216))
% 11.41/11.17 [4224]E(f784(f262(x42241,x42242,x42243,x42244,x42245,x42246),f784(f784(f251(x42241,x42243),x42247),x42248)),f784(f784(f251(x42242,x42244),f784(x42245,x42247)),f784(x42246,x42248)))
% 11.41/11.17 [4323]E(f784(f784(f146(f868(x43231,x43232),f868(x43233,x43234)),f784(f261(x43231,x43232,f868(x43233,x43234)),f784(f784(f9(x43231,f869(x43232,x43234),f869(x43232,f868(x43233,x43234))),f784(f784(f10(f869(x43234,f868(x43233,x43234)),f869(f869(x43232,x43234),f869(x43232,f868(x43233,x43234))),x43231),f10(x43234,f868(x43233,x43234),x43232)),f784(f784(f10(x43233,f869(x43234,f868(x43233,x43234)),x43231),f251(x43233,x43234)),x43235))),x43236))),f784(f784(f173(x43231,x43232),x43237),x43238)),f784(f784(f173(x43233,x43234),f784(f784(f146(x43231,x43233),x43235),x43237)),f784(f784(f146(x43232,x43234),x43236),x43238)))
% 11.41/11.17 [4327]E(f784(f784(f146(f868(x43271,x43272),x43273),f784(f261(x43271,x43272,x43273),f784(f784(f10(f869(x43272,f868(x43271,x43274)),f869(x43272,x43273),x43271),f784(f10(f868(x43271,x43274),x43273,x43272),x43275)),f784(f784(f9(x43271,f869(x43272,x43274),f869(x43272,f868(x43271,x43274))),f784(f784(f10(f869(x43274,f868(x43271,x43274)),f869(f869(x43272,x43274),f869(x43272,f868(x43271,x43274))),x43271),f10(x43274,f868(x43271,x43274),x43272)),f251(x43271,x43274))),x43276)))),f784(f784(f173(x43271,x43272),x43277),x43278)),f784(f784(f146(f868(x43271,x43274),x43273),x43275),f784(f784(f173(x43271,x43274),x43277),f784(f784(f146(x43272,x43274),x43276),x43278))))
% 11.41/11.17 [4255]E(f784(f784(f146(f868(x42551,x42552),x42553),f784(f261(x42551,x42552,x42553),f784(f784(f10(f869(x42552,f868(x42554,x42552)),f869(x42552,x42553),x42551),f784(f10(f868(x42554,x42552),x42553,x42552),x42555)),f784(f784(f10(x42554,f869(x42552,f868(x42554,x42552)),x42551),f251(x42554,x42552)),x42556)))),f784(f784(f173(x42551,x42552),x42557),x42558)),f784(f784(f146(f868(x42554,x42552),x42553),x42555),f784(f784(f173(x42554,x42552),f784(f784(f146(x42551,x42554),x42556),x42557)),x42558)))
% 11.41/11.17 [4215]E(f784(f784(f261(x42151,x42152,x42153),f784(f784(f10(f869(x42152,f868(x42154,x42155)),f869(x42152,x42153),x42151),f784(f10(f868(x42154,x42155),x42153,x42152),f784(f261(x42154,x42155,x42153),x42156))),x42157)),x42158),f784(f784(f261(x42154,x42155,x42153),x42156),f784(f784(f261(x42151,x42152,f868(x42154,x42155)),x42157),x42158)))
% 11.41/11.17 [4328]E(f784(f784(f54(f868(x43281,x43282),f869(f868(x43283,x43284),a852)),f784(f784(f258(x43281,x43282),x43285),f784(f18(f869(x43282,a852),x43281),x43286))),f784(f261(x43281,x43282,f869(f868(x43283,x43284),a852)),f784(f784(f9(x43281,f869(x43282,f869(x43283,f869(x43284,a852))),f869(x43282,f869(f868(x43283,x43284),a852))),f784(f784(f10(f869(f869(x43283,f869(x43284,a852)),f869(f868(x43283,x43284),a852)),f869(f869(x43282,f869(x43283,f869(x43284,a852))),f869(x43282,f869(f868(x43283,x43284),a852))),x43281),f10(f869(x43283,f869(x43284,a852)),f869(f868(x43283,x43284),a852),x43282)),f784(f784(f10(f869(x43283,a852),f869(f869(x43283,f869(x43284,a852)),f869(f868(x43283,x43284),a852)),x43281),f258(x43283,x43284)),x43287))),f784(f784(f10(f869(x43284,a852),f869(x43283,f869(x43284,a852)),x43282),f18(f869(x43284,a852),x43283)),x43288)))),f784(f784(f258(x43283,x43284),f784(f784(f54(x43281,f869(x43283,a852)),x43285),x43287)),f784(f18(f869(x43284,a852),x43283),f784(f784(f54(x43282,f869(x43284,a852)),x43286),x43288))))
% 11.41/11.17 [4357]E(f39(x43571,x43572,x43573,x43574,x43575,x43576,x43577,x43578,x43579,a25),x43572)
% 11.41/11.17 [4358]E(f40(x43581,x43582,x43583,x43584,x43585,x43586,x43587,x43588,x43589,a25),x43582)
% 11.41/11.17 [4269]E(f784(f784(f263(x42691,x42692,x42693,x42694),f784(f784(f263(x42691,x42695,x42696,f868(x42692,x42693)),x42697),x42698)),x42699),f784(f784(f263(x42691,x42695,x42696,x42694),x42697),f784(f784(f9(x42695,f869(x42692,f869(x42693,x42694)),f869(x42696,x42694)),f784(f784(f10(f869(x42696,f868(x42692,x42693)),f869(f869(x42692,f869(x42693,x42694)),f869(x42696,x42694)),x42695),f263(x42696,x42692,x42693,x42694)),x42698)),x42699)))
% 11.41/11.17 [4359]E(f39(x43591,x43592,x43593,x43594,x43595,x43596,x43597,x43598,x43599,f784(a29,x435910)),f784(x43598,x435910))
% 11.41/11.17 [4360]E(f40(x43601,x43602,x43603,x43604,x43605,x43606,x43607,x43608,x43609,f784(a29,x436010)),f784(x43608,x436010))
% 11.41/11.17 [4298]E(f784(f82(f868(x42981,x42982),f868(x42983,x42984),f868(x42985,x42986),f262(x42981,x42983,x42982,x42984,x42987,x42988)),f262(x42985,x42981,x42986,x42982,x42989,x429810)),f262(x42985,x42983,x42986,x42984,f784(f82(x42981,x42983,x42985,x42987),x42989),f784(f82(x42982,x42984,x42986,x42988),x429810)))
% 11.41/11.17 [4299]E(f784(f82(f868(x42991,x42992),f868(x42993,x42994),f868(x42995,x42996),f262(x42991,x42993,x42992,x42994,x42997,x42998)),f262(x42995,x42991,x42996,x42992,x42999,x429910)),f262(x42995,x42993,x42996,x42994,f784(f82(x42991,x42993,x42995,x42997),x42999),f784(f82(x42992,x42994,x42996,x42998),x429910)))
% 11.41/11.17 [4361]E(f39(x43611,x43612,x43613,x43614,x43615,x43616,x43617,x43618,x43619,f30(x436110,x436111)),f784(f784(x43613,x436110),x436111))
% 11.41/11.17 [4362]E(f39(x43621,x43622,x43623,x43624,x43625,x43626,x43627,x43628,x43629,f38(x436210,x436211)),f784(f784(x43625,x436210),x436211))
% 11.41/11.17 [4363]E(f39(x43631,x43632,x43633,x43634,x43635,x43636,x43637,x43638,x43639,f37(x436310,x436311)),f784(f784(x43637,x436310),x436311))
% 11.41/11.17 [4364]E(f40(x43641,x43642,x43643,x43644,x43645,x43646,x43647,x43648,x43649,f30(x436410,x436411)),f784(f784(x43643,x436410),x436411))
% 11.41/11.17 [4370]E(f784(f784(f784(x43701,x43702),x43703),f40(x43704,x43705,x43706,x43707,x43708,x43709,x43701,x437010,x437011,x43703)),f40(x43704,x43705,x43706,x43707,x43708,x43709,x43701,x437010,x437011,f37(x43702,x43703)))
% 11.41/11.17 [4374]E(f784(f784(f784(f784(x43741,x43742),x43743),f40(x43744,x43745,x43746,x43747,x43741,x43748,x43749,x437410,x437411,x43742)),f40(x43744,x43745,x43746,x43747,x43741,x43748,x43749,x437410,x437411,x43743)),f40(x43744,x43745,x43746,x43747,x43741,x43748,x43749,x437410,x437411,f38(x43742,x43743)))
% 11.41/11.17 [4304]E(f784(f262(x43041,x43042,x43043,x43044,x43045,x43046),f784(f262(x43047,x43041,x43048,x43043,x43049,x430410),x430411)),f784(f262(x43047,x43042,x43048,x43044,f784(f82(x43041,x43042,x43047,x43045),x43049),f784(f82(x43043,x43044,x43048,x43046),x430410)),x430411))
% 11.41/11.17 [4371]E(f784(f784(f784(f784(x43711,x43712),x43713),x43714),f40(x43715,x43716,x43717,x43711,x43718,x43719,x437110,x437111,x437112,x43714)),f40(x43715,x43716,x43717,x43711,x43718,x43719,x437110,x437111,x437112,f34(x43712,x43713,x43714)))
% 11.41/11.17 [4375]E(f784(f784(f784(f784(f784(x43751,x43752),x43753),x43754),f40(x43755,x43756,x43757,x43758,x43759,x43751,x437510,x437511,x437512,x43753)),f40(x43755,x43756,x43757,x43758,x43759,x43751,x437510,x437511,x437512,x43754)),f40(x43755,x43756,x43757,x43758,x43759,x43751,x437510,x437511,x437512,f35(x43752,x43753,x43754)))
% 11.41/11.17 [4365]E(f39(x43651,x43652,x43653,x43654,x43655,x43656,x43657,x43658,x43659,f33(x436510,x436511,x436512)),f784(f784(f784(x43659,x436510),x436511),x436512))
% 11.41/11.17 [4366]E(f39(x43661,x43662,x43663,x43664,x43665,x43666,x43667,x43668,x43669,f35(x436610,x436611,x436612)),f784(f784(f784(x43666,x436610),x436611),x436612))
% 11.41/11.17 [4367]E(f39(x43671,x43672,x43673,x43674,x43675,x43676,x43677,x43678,x43679,f34(x436710,x436711,x436712)),f784(f784(f784(x43674,x436710),x436711),x436712))
% 11.41/11.17 [4368]E(f40(x43681,x43682,x43683,x43684,x43685,x43686,x43687,x43688,x43689,f33(x436810,x436811,x436812)),f784(f784(f784(x43689,x436810),x436811),x436812))
% 11.41/11.17 [6375]P10(a500)+P85(f784(f784(f347(f868(a855,a853)),a707),f784(f164(f868(a855,a853)),a31)))
% 11.41/11.17 [8406]P10(a500)+~P85(f784(f784(f261(a855,a853,a852),f784(f18(f869(a853,a852),a855),a26)),a707))
% 11.41/11.17 [4509]~P58(x45091)+P58(f864(x45091))
% 11.41/11.17 [4511]~P140(x45111)+~E(f87(x45111),f2(x45111))
% 11.41/11.17 [4512]~P140(x45121)+~E(f87(x45121),f2(x45121))
% 11.41/11.17 [4514]~E(x45141,f2(a108))+E(f784(a23,x45141),f2(a1))
% 11.41/11.17 [4515]~E(x45151,f2(a1))+E(f91(a1,x45151),f2(a1))
% 11.41/11.17 [4521]~P112(x45211)+P30(x45211,f2(x45211))
% 11.41/11.17 [4522]~P101(x45221)+P15(x45221,f120(x45221))
% 11.41/11.17 [4523]~P101(x45231)+P15(x45231,f120(x45231))
% 11.41/11.17 [4532]P85(x45321)+P85(f784(a341,x45321))
% 11.41/11.17 [4573]~P112(x45731)+~P30(x45731,f87(x45731))
% 11.41/11.17 [4617]~P85(x46171)+~P85(f784(a341,x46171))
% 11.41/11.17 [4641]E(f784(a114,x46411),f2(a859))+~P85(f784(a193,x46411))
% 11.41/11.17 [4701]~P92(x47011)+P16(x47011,x47011,f90(x47011))
% 11.41/11.17 [4702]~P101(x47021)+P16(x47021,x47021,f246(x47021))
% 11.41/11.17 [4703]~P101(x47031)+P16(x47031,x47031,f186(x47031))
% 11.41/11.17 [4704]~P98(x47041)+P16(x47041,x47041,f110(x47041))
% 11.41/11.17 [4705]~P99(x47051)+P16(x47051,x47051,f111(x47051))
% 11.41/11.17 [4706]~P65(x47061)+P17(x47061,x47061,f90(x47061))
% 11.41/11.17 [4519]E(x45191,f2(a859))+E(f784(a160,f552(x45191)),x45191)
% 11.41/11.17 [4520]~E(x45201,f2(a859))+E(f784(f109(a1),x45201),f2(a1))
% 11.41/11.17 [4525]~P89(x45251)+E(f784(f113(x45251),a92),f2(x45251))
% 11.41/11.17 [4526]~P89(x45261)+E(f784(f113(x45261),a92),f2(x45261))
% 11.41/11.17 [4528]~E(f609(x45281),f2(a859))+E(f784(f157(a859),x45281),f2(a859))
% 11.41/11.17 [4529]~P103(x45291)+E(f244(x45291,f242(x45291)),f246(x45291))
% 11.41/11.17 [4530]~P103(x45301)+E(f245(x45301,f242(x45301)),f186(x45301))
% 11.41/11.17 [4531]~P82(x45311)+E(f91(x45311,f2(x45311)),f2(x45311))
% 11.41/11.17 [4538]~P112(x45381)+E(f784(f109(x45381),f2(a859)),f2(x45381))
% 11.41/11.17 [4539]~P112(x45391)+E(f784(f109(x45391),f87(a859)),f87(x45391))
% 11.41/11.17 [4540]~P136(x45401)+E(f784(f112(x45401),f2(a1)),f2(x45401))
% 11.41/11.17 [4541]~P136(x45411)+E(f784(f112(x45411),f87(a1)),f87(x45411))
% 11.41/11.17 [4542]E(x45421,f2(a859))+~E(f784(f109(a1),x45421),f2(a1))
% 11.41/11.17 [4567]~P70(x45671)+E(f784(f88(x45671),f2(x45671)),f2(x45671))
% 11.41/11.17 [4568]~P91(x45681)+E(f784(f88(x45681),f249(x45681)),f187(x45681))
% 11.41/11.17 [4569]~P91(x45691)+E(f784(f88(x45691),f187(x45691)),f249(x45691))
% 11.41/11.17 [4570]~P79(x45701)+E(f784(f84(x45701),f2(x45701)),f2(x45701))
% 11.41/11.17 [4571]~P113(x45711)+E(f784(f84(x45711),f87(x45711)),f87(x45711))
% 11.41/11.17 [4572]~P67(x45721)+E(f784(f157(x45721),f120(x45721)),f2(x45721))
% 11.41/11.17 [4593]~P34(x45931)+P37(f784(f164(a1),x45931))
% 11.41/11.17 [4621]~P89(x46211)+E(f784(f88(x46211),f87(x46211)),f784(f113(x46211),a106))
% 11.41/11.17 [4622]~P89(x46221)+E(f784(f88(x46221),f87(x46221)),f784(f113(x46221),a106))
% 11.41/11.17 [4640]~P89(x46401)+P30(x46401,f784(f113(x46401),a92))
% 11.41/11.17 [4665]P34(x46651)+~P37(f784(f164(a1),x46651))
% 11.41/11.17 [4707]E(f784(f109(a1),f784(a114,x47071)),x47071)+P85(f784(a193,x47071))
% 11.41/11.17 [4773]~P106(x47731)+E(f253(x47731,f87(x47731),f90(x47731)),f252(x47731))
% 11.41/11.17 [4801]~P89(x48011)+~P30(x48011,f784(f113(x48011),a106))
% 11.41/11.17 [4811]E(f784(a32,x48111),f190(a853))+P85(f784(a26,f784(a29,x48111)))
% 11.41/11.17 [4888]~E(x48881,f2(a859))+P85(f784(f784(f242(a859),x48881),f2(a859)))
% 11.41/11.17 [4889]~E(x48891,f87(a859))+P85(f784(f784(f289(a859),x48891),f87(a859)))
% 11.41/11.17 [4943]E(f784(f84(a1),x49431),x49431)+P85(f784(f784(f243(a1),x49431),f2(a1)))
% 11.41/11.17 [4963]~E(f784(a114,x49631),f2(a859))+P85(f784(f784(f242(a1),x49631),f2(a1)))
% 11.41/11.17 [4999]~E(f784(f84(a1),x49991),f87(a1))+P85(f784(f784(f289(a1),x49991),f87(a1)))
% 11.41/11.17 [5029]~P85(f784(a193,x50291))+P85(f784(f784(f243(a1),x50291),f2(a1)))
% 11.41/11.17 [5069]~P120(x50691)+P85(f784(f784(f243(x50691),f2(x50691)),f87(x50691)))
% 11.41/11.17 [5070]~P120(x50701)+P85(f784(f784(f242(x50701),f2(x50701)),f87(x50701)))
% 11.41/11.17 [5071]~P112(x50711)+P85(f784(f784(f347(x50711),f2(x50711)),f183(x50711)))
% 11.41/11.17 [5072]~P136(x50721)+P85(f784(f784(f347(x50721),f2(x50721)),f119(x50721)))
% 11.41/11.17 [5073]~P112(x50731)+P85(f784(f784(f347(x50731),f87(x50731)),f183(x50731)))
% 11.41/11.17 [5074]~P136(x50741)+P85(f784(f784(f347(x50741),f87(x50741)),f119(x50741)))
% 11.41/11.17 [5077]E(f784(f237(a853),f387(x50771)),f784(a32,x50771))+~P85(f784(a26,f784(a29,x50771)))
% 11.41/11.17 [5078]E(f784(f237(a853),f462(x50781)),f784(a32,x50781))+~P85(f784(a26,f784(a29,x50781)))
% 11.41/11.17 [5127]E(x51271,f2(a859))+~P85(f784(f784(f242(a859),x51271),f2(a859)))
% 11.41/11.17 [5128]E(x51281,f87(a859))+~P85(f784(f784(f289(a859),x51281),f87(a859)))
% 11.41/11.17 [5168]E(f784(a114,x51681),f2(a859))+~P85(f784(f784(f242(a1),x51681),f2(a1)))
% 11.41/11.17 [5169]E(f784(a114,x51691),f2(a859))+~P85(f784(f784(f242(a1),x51691),f2(a1)))
% 11.41/11.17 [5196]E(f784(f84(a1),x51961),f87(a1))+~P85(f784(f784(f289(a1),x51961),f87(a1)))
% 11.41/11.17 [5223]P85(f784(a193,x52231))+~P85(f784(f784(f243(a1),x52231),f2(a1)))
% 11.41/11.17 [5228]~P101(x52281)+P17(x52281,f860(x52281),f142(x52281,x52281,f7(x52281)))
% 11.41/11.17 [5245]P37(x52451)+~P85(f784(f784(f242(a1),f2(a1)),f351(x52451)))
% 11.41/11.17 [5251]E(f784(f84(a1),x52511),f784(f88(a1),x52511))+~P85(f784(f784(f243(a1),x52511),f2(a1)))
% 11.41/11.17 [5421]~P120(x54211)+~P85(f784(f784(f243(x54211),f87(x54211)),f2(x54211)))
% 11.41/11.17 [5422]~P120(x54221)+~P85(f784(f784(f242(x54221),f87(x54221)),f2(x54221)))
% 11.41/11.17 [5434]~E(x54341,f2(a1))+P85(f784(f784(f243(a1),f784(f84(a1),x54341)),f87(a1)))
% 11.41/11.17 [5435]~E(x54351,f2(a859))+P85(f784(f784(f242(a1),f784(f109(a1),x54351)),f2(a1)))
% 11.41/11.17 [5549]~P67(x55491)+E(f136(x55491,x55491,f89(x55491),f2(x55491)),f157(x55491))
% 11.41/11.17 [5724]~P87(x57241)+P26(a859,x57241,f109(x57241),f249(f869(a859,a852)))
% 11.41/11.17 [5921]E(x59211,f2(a859))+~P85(f784(f784(f242(a1),f784(f109(a1),x59211)),f2(a1)))
% 11.41/11.17 [5922]E(x59221,f2(a1))+~P85(f784(f784(f243(a1),f784(f84(a1),x59221)),f87(a1)))
% 11.41/11.17 [6745]~P85(f784(f784(f243(a1),x67451),f2(a1)))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x67451),x67451)),f2(a1)))
% 11.41/11.17 [7316]P85(f784(f784(f243(a1),x73161),f2(a1)))+~P85(f784(f784(f243(a1),f784(f784(f89(a1),x73161),x73161)),f2(a1)))
% 11.41/11.17 [7879]E(x78791,f784(a5,f2(a859)))+P85(f784(f784(f243(a859),f784(f784(f3(a859),f784(a22,x78791)),f784(a160,f2(a859)))),f784(a22,x78791)))
% 11.41/11.17 [8617]~P85(f784(f784(f243(a1),x86171),f2(a1)))+P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x86171),x86171)),a106)),f2(a1)))
% 11.41/11.17 [8701]~P85(f784(f784(f243(a1),x87011),f2(a1)))+P85(f784(f784(f243(a1),f784(f784(f89(a1),f784(f784(f89(a1),f87(a1)),x87011)),x87011)),f2(a1)))
% 11.41/11.17 [8986]P85(f784(f784(f243(a1),x89861),f2(a1)))+~P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x89861),x89861)),a106)),f2(a1)))
% 11.41/11.17 [9052]P85(f784(f784(f243(a1),x90521),f2(a1)))+~P85(f784(f784(f243(a1),f784(f784(f89(a1),f784(f784(f89(a1),f87(a1)),x90521)),x90521)),f2(a1)))
% 11.41/11.17 [4610]~E(a92,x46101)+E(f784(f784(f89(a1),x46101),x46101),a92)
% 11.41/11.17 [4611]~E(x46111,a92)+E(f784(f784(f89(a1),x46111),x46111),a92)
% 11.41/11.17 [4626]E(x46261,f2(a1))+E(f784(f784(f51(a1),x46261),x46261),f87(a1))
% 11.41/11.17 [4751]E(x47511,a92)+~E(f784(f784(f89(a1),x47511),x47511),a92)
% 11.41/11.17 [4752]E(a92,x47521)+~E(f784(f784(f89(a1),x47521),x47521),a92)
% 11.41/11.17 [4753]~P89(x47531)+E(f784(f112(x47531),f784(f113(a1),a106)),f784(f113(x47531),a106))
% 11.41/11.17 [4763]~P6(x47631)+E(f53(x47631,f249(f869(x47631,a852))),f187(x47631))
% 11.41/11.17 [4764]~P6(x47641)+E(f53(x47641,f187(f869(x47641,a852))),f249(x47641))
% 11.41/11.17 [4765]~P6(x47651)+E(f52(x47651,f249(f869(x47651,a852))),f249(x47651))
% 11.41/11.17 [4766]~P6(x47661)+E(f52(x47661,f187(f869(x47661,a852))),f187(x47661))
% 11.41/11.17 [4767]~P101(x47671)+E(f134(x47671,f187(f869(x47671,a852))),f120(x47671))
% 11.41/11.17 [4900]E(x49001,f2(a859))+P85(f784(f784(f243(a859),f2(a859)),x49001))
% 11.41/11.17 [4901]E(x49011,f2(a859))+P85(f784(f784(f243(a859),f2(a859)),x49011))
% 11.41/11.17 [4921]~P7(x49211)+P85(f784(f784(f242(a1),f2(a1)),x49211))
% 11.41/11.17 [4953]~E(f784(f113(a859),x49531),f2(a859))+P85(f784(f784(f242(a1),x49531),a92))
% 11.41/11.17 [4954]~E(f784(f113(a859),x49541),f2(a859))+P85(f784(f784(f242(a1),x49541),a92))
% 11.41/11.17 [4959]P37(x49591)+P85(f784(f784(f347(a1),f351(x49591)),x49591))
% 11.41/11.17 [4960]E(x49601,f784(a5,f2(a859)))+P85(f784(f784(f242(a108),f87(a108)),x49601))
% 11.41/11.17 [5004]P85(f784(a193,x50041))+P85(f784(f784(f242(a1),f2(a1)),x50041))
% 11.41/11.17 [5051]E(f784(f109(a1),f784(a114,x50511)),f2(a1))+P85(f784(f784(f242(a1),f2(a1)),x50511))
% 11.41/11.17 [5102]~P58(x51021)+P85(f784(f71(x51021),f249(f869(x51021,a852))))
% 11.41/11.17 [5115]E(f784(f109(a1),f784(f113(a859),x51151)),f784(f113(a1),x51151))+P85(f784(a193,f784(f113(a1),x51151)))
% 11.41/11.17 [5117]~E(x51171,f2(a859))+P85(f784(f784(f243(a859),x51171),f784(a160,f2(a859))))
% 11.41/11.17 [5133]E(f784(f113(a859),x51331),f2(a859))+~P85(f784(f784(f242(a1),x51331),a92))
% 11.41/11.17 [5134]E(f784(f113(a859),x51341),f2(a859))+~P85(f784(a193,f784(f113(a1),x51341)))
% 11.41/11.17 [5135]E(f784(f113(a859),x51351),f2(a859))+~P85(f784(f784(f242(a1),x51351),a92))
% 11.41/11.17 [5166]P7(x51661)+~P85(f784(f784(f242(a1),f2(a1)),x51661))
% 11.41/11.17 [5184]~E(x51841,f2(a859))+~P85(f784(f784(f243(a859),f2(a859)),x51841))
% 11.41/11.17 [5206]~E(x52061,f784(a160,f2(a859)))+P85(f784(f784(f289(a859),x52061),f784(a160,f2(a859))))
% 11.41/11.17 [5231]E(f784(a160,f561(x52311)),x52311)+~P85(f784(f784(f243(a859),f2(a859)),x52311))
% 11.41/11.17 [5232]E(f784(a160,f629(x52321)),x52321)+~P85(f784(f784(f243(a859),f2(a859)),x52321))
% 11.41/11.17 [5240]E(f784(a160,f784(f113(a859),x52401)),f87(a859))+~P85(f784(a193,f784(f113(a1),x52401)))
% 11.41/11.17 [5247]E(f784(f109(a1),f638(x52471)),x52471)+~P85(f784(f784(f243(a1),f2(a1)),x52471))
% 11.41/11.17 [5254]~E(x52541,f784(a5,f2(a859)))+~P85(f784(f784(f242(a108),f87(a108)),x52541))
% 11.41/11.17 [5261]E(f784(f109(a1),f784(f113(a859),x52611)),f2(a1))+~P85(f784(a193,f784(f113(a1),x52611)))
% 11.41/11.17 [5285]E(f784(f157(a859),x52851),f2(a859))+P85(f784(f784(f347(a859),f609(x52851)),f784(f164(a859),x52851)))
% 11.41/11.17 [5304]E(f784(f109(a1),f784(a114,x53041)),x53041)+~P85(f784(f784(f242(a1),f2(a1)),x53041))
% 11.41/11.17 [5305]E(f784(f109(a1),f784(a114,x53051)),x53051)+~P85(f784(f784(f242(a1),f2(a1)),x53051))
% 11.41/11.17 [5314]~P85(f784(a193,x53141))+~P85(f784(f784(f242(a1),f2(a1)),x53141))
% 11.41/11.17 [5414]E(f784(f784(f89(a859),f87(a859)),f784(f113(a859),x54141)),f87(a859))+~P85(f784(f784(f243(a1),x54141),a92))
% 11.41/11.17 [5471]E(x54711,f2(a859))+~P85(f784(f784(f243(a859),x54711),f784(a160,f2(a859))))
% 11.41/11.17 [5491]E(x54911,f784(a160,f2(a859)))+~P85(f784(f784(f289(a859),x54911),f784(a160,f2(a859))))
% 11.41/11.17 [5509]E(f784(f784(f89(a859),f784(f113(a859),x55091)),f87(a859)),f87(a859))+~P85(f784(f784(f243(a1),x55091),a92))
% 11.41/11.17 [5510]E(f784(f784(f3(a859),f784(f113(a859),x55101)),f87(a859)),f2(a859))+~P85(f784(f784(f242(a1),x55101),a92))
% 11.41/11.17 [5520]~P37(x55201)+E(f784(f50(a859),f784(f313(a1,a859,a114),x55201)),f784(f50(a1),x55201))
% 11.41/11.17 [5550]~P101(x55501)+E(f244(x55501,f784(f9(x55501,x55501,a852),f242(x55501))),f186(x55501))
% 11.41/11.17 [5551]~P101(x55511)+E(f245(x55511,f784(f9(x55511,x55511,a852),f242(x55511))),f246(x55511))
% 11.41/11.17 [5560]E(f60(a859,f784(a160,f2(a859)),f784(f113(a859),x55601)),f784(a160,f2(a859)))+~P85(f784(a193,f784(f113(a1),x55601)))
% 11.41/11.17 [5568]P85(f784(f784(f243(a1),f2(a1)),x55681))+~P85(f784(f784(f242(a1),f87(a1)),x55681))
% 11.41/11.17 [5569]~P85(f784(f784(f243(a1),f2(a1)),x55691))+P85(f784(f784(f242(a1),f87(a1)),x55691))
% 11.41/11.17 [5578]E(f784(a160,f784(f784(f3(a859),x55781),f87(a859))),x55781)+~P85(f784(f784(f243(a859),f2(a859)),x55781))
% 11.41/11.17 [5579]E(f784(a160,f784(f784(f3(a859),x55791),f87(a859))),x55791)+~P85(f784(f784(f243(a859),f2(a859)),x55791))
% 11.41/11.17 [5637]P85(f784(f784(f243(a859),f2(a859)),f638(x56371)))+~P85(f784(f784(f243(a1),f2(a1)),x56371))
% 11.41/11.17 [5694]E(f60(a1,f784(f113(a1),a106),x56941),f784(f784(f3(a1),x56941),f87(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x56941))
% 11.41/11.17 [5739]~P85(f784(f784(f243(a1),a92),x57391))+P85(f784(f784(f243(a859),f2(a859)),f784(f113(a859),x57391)))
% 11.41/11.17 [5793]P85(f784(f784(f243(a859),f2(a859)),f784(a114,x57931)))+~P85(f784(f784(f243(a1),f2(a1)),x57931))
% 11.41/11.17 [5814]E(f784(a22,f784(a5,x58141)),x58141)+~P85(f784(f784(f347(a859),x58141),f249(f869(a859,a852))))
% 11.41/11.17 [5840]~P85(f784(f784(f243(a859),f2(a859)),x58401))+P85(f784(f784(f243(a1),f2(a1)),f784(f109(a1),x58401)))
% 11.41/11.17 [5875]~P85(f784(f784(f243(a859),f2(a859)),f784(a114,x58751)))+P85(f784(f784(f243(a1),f2(a1)),x58751))
% 11.41/11.17 [5890]~P37(x58901)+E(f784(f313(a859,a1,f109(a1)),f784(f313(a1,a859,a114),x58901)),x58901)
% 11.41/11.17 [5901]P85(f784(f784(f243(a1),a92),x59011))+~P85(f784(f784(f243(a859),f2(a859)),f784(f113(a859),x59011)))
% 11.41/11.17 [5962]P85(f784(f784(f243(a859),f2(a859)),x59621))+~P85(f784(f784(f243(a1),f2(a1)),f784(f109(a1),x59621)))
% 11.41/11.17 [5993]E(f170(x59931,f120(f860(x59931))),f120(f860(x59931)))+~P85(f784(f334(f860(f860(x59931)),f171(x59931)),f120(f860(x59931))))
% 11.41/11.17 [6076]E(f784(f313(a859,a1,f109(a1)),f784(f267(a859),f784(a114,x60761))),f784(f304(a1,f2(a1)),x60761))+~P85(f784(f784(f242(a1),f2(a1)),x60761))
% 11.41/11.17 [6092]~P120(x60921)+P85(f784(f784(f243(x60921),f2(x60921)),f784(f784(f89(x60921),f87(x60921)),f87(x60921))))
% 11.41/11.17 [6143]P85(f784(f784(f243(a859),f784(a160,f2(a859))),f784(a114,x61431)))+~P85(f784(f784(f243(a1),f87(a1)),x61431))
% 11.41/11.17 [6238]E(x62381,f2(a1))+P85(f784(f64(f2(a1),x62381),f784(f784(f251(a1,a1),f2(a1)),f2(a1))))
% 11.41/11.17 [6418]~P85(f784(f784(f243(a859),f784(a160,f2(a859))),f784(a114,x64181)))+P85(f784(f784(f243(a1),f87(a1)),x64181))
% 11.41/11.17 [6469]E(f784(a160,f784(f784(f3(a859),f784(f113(a859),x64691)),f87(a859))),f784(f113(a859),x64691))+~P85(f784(f784(f243(a859),f2(a859)),f784(f113(a859),x64691)))
% 11.41/11.17 [6866]~P108(x68661)+P35(x68661,f784(f266(f868(x68661,x68661)),f784(f261(x68661,x68661,a852),f243(x68661))))
% 11.41/11.17 [5461]E(f784(f113(a859),f784(f784(f3(a1),x54611),a106)),f784(a160,f784(f113(a859),x54611)))+P85(f784(a193,f784(f113(a1),x54611)))
% 11.41/11.17 [5585]E(f784(f88(a1),f784(f109(a1),f784(a160,f696(x55851)))),x55851)+~P85(f784(f784(f243(a1),x55851),f2(a1)))
% 11.41/11.17 [5595]E(f784(f784(f89(a859),f87(a859)),f784(f113(a859),x55951)),f784(f113(a859),f784(f784(f3(a1),x55951),a106)))+P85(f784(f784(f243(a1),x55951),a92))
% 11.41/11.17 [5639]E(f784(f784(f51(a1),f784(f113(a1),a106)),x56391),f784(f113(a1),a106))+~P85(f784(f784(f243(a1),f2(a1)),x56391))
% 11.41/11.17 [5735]E(f784(f784(f89(a859),f784(f113(a859),x57351)),f87(a859)),f784(f113(a859),f784(f784(f3(a1),x57351),a106)))+P85(f784(f784(f243(a1),x57351),a92))
% 11.41/11.17 [5736]E(f784(f784(f3(a859),f784(f113(a859),x57361)),f87(a859)),f784(f113(a859),f784(f784(f89(a1),x57361),a106)))+P85(f784(f784(f242(a1),x57361),a92))
% 11.41/11.17 [5779]E(f784(a114,f784(f784(f89(a1),f87(a1)),x57791)),f784(a160,f784(a114,x57791)))+~P85(f784(f784(f242(a1),f2(a1)),x57791))
% 11.41/11.17 [5816]E(f784(a160,f784(f784(f3(a859),x58161),f784(a160,f2(a859)))),x58161)+~P85(f784(f784(f243(a859),f2(a859)),x58161))
% 11.41/11.17 [6022]E(f60(a859,f784(a160,f2(a859)),f784(f113(a859),x60221)),f784(a114,f60(a1,f87(a1),f784(f113(a1),x60221))))+P85(f784(a193,f784(f113(a1),x60221)))
% 11.41/11.17 [6067]~P85(f784(f784(f243(a1),a106),x60671))+P85(f784(f784(f243(a1),a106),f784(f784(f89(a1),x60671),x60671)))
% 11.41/11.17 [6068]~P85(f784(f784(f243(a1),a92),x60681))+P85(f784(f784(f243(a1),a92),f784(f784(f89(a1),x60681),x60681)))
% 11.41/11.17 [6069]~P85(f784(f784(f243(a1),a106),x60691))+P85(f784(f784(f242(a1),a106),f784(f784(f89(a1),x60691),x60691)))
% 11.41/11.17 [6070]~P85(f784(f784(f242(a1),a92),x60701))+P85(f784(f784(f242(a1),a92),f784(f784(f89(a1),x60701),x60701)))
% 11.41/11.17 [6252]~P85(f784(f71(x62521),f249(f869(x62521,a852))))+P85(f784(f71(f864(x62521)),f249(f869(f864(x62521),a852))))
% 11.41/11.17 [6343]~P85(f784(f784(f242(a1),f2(a1)),x63431))+P85(f784(f784(f243(a1),f2(a1)),f784(f784(f89(a1),f87(a1)),x63431)))
% 11.41/11.17 [6349]E(f784(f250(a1,a1),f62(f87(a1),f784(f113(a1),x63491))),f784(f784(f51(a1),f87(a1)),f784(f113(a1),x63491)))+~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x63491)))
% 11.41/11.17 [6374]E(f784(f260(a1,a1),f62(f87(a1),f784(f113(a1),x63741))),f60(a1,f87(a1),f784(f113(a1),x63741)))+~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x63741)))
% 11.41/11.17 [6387]P85(f784(f71(x63871),f249(f869(x63871,a852))))+~P85(f784(f71(f864(x63871)),f249(f869(f864(x63871),a852))))
% 11.41/11.17 [6419]P85(f784(f784(f243(a1),a106),x64191))+~P85(f784(f784(f243(a1),a106),f784(f784(f89(a1),x64191),x64191)))
% 11.41/11.17 [6420]P85(f784(f784(f243(a1),a106),x64201))+~P85(f784(f784(f242(a1),a106),f784(f784(f89(a1),x64201),x64201)))
% 11.41/11.17 [6421]P85(f784(f784(f243(a1),a92),x64211))+~P85(f784(f784(f243(a1),a92),f784(f784(f89(a1),x64211),x64211)))
% 11.41/11.17 [6422]P85(f784(f784(f242(a1),a92),x64221))+~P85(f784(f784(f242(a1),a92),f784(f784(f89(a1),x64221),x64221)))
% 11.41/11.17 [6616]~P85(f784(f71(a859),x66161))+P85(f784(f71(a1),f784(f313(a859,a1,f109(a1)),x66161)))
% 11.41/11.17 [6750]~P85(f784(f71(x67501),f249(f869(x67501,a852))))+P85(f784(f784(f243(a859),f2(a859)),f784(f50(x67501),f249(f869(x67501,a852)))))
% 11.41/11.17 [7361]P85(f784(f71(a859),x73611))+~P85(f784(f71(a1),f784(f313(a859,a1,f109(a1)),x73611)))
% 11.41/11.17 [5389]~E(a106,x53891)+E(f784(f784(f3(a1),f784(f784(f89(a1),x53891),x53891)),a106),a106)
% 11.41/11.17 [5390]~E(x53901,a106)+E(f784(f784(f3(a1),f784(f784(f89(a1),x53901),x53901)),a106),a106)
% 11.41/11.17 [5895]E(x58951,a106)+~E(f784(f784(f3(a1),f784(f784(f89(a1),x58951),x58951)),a106),a106)
% 11.41/11.17 [5896]E(a106,x58961)+~E(f784(f784(f3(a1),f784(f784(f89(a1),x58961),x58961)),a106),a106)
% 11.41/11.17 [6312]~E(f784(f113(a859),x63121),f2(a859))+P85(f784(a193,f784(f113(a1),f784(f784(f89(a1),x63121),a106))))
% 11.41/11.17 [6675]~P85(f784(a193,f784(f113(a1),x66751)))+P85(f784(a193,f784(f113(a1),f784(f784(f89(a1),x66751),x66751))))
% 11.41/11.17 [6676]~P85(f784(f784(f242(a1),x66761),a106))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x66761),x66761)),a106))
% 11.41/11.17 [6677]~P85(f784(f784(f243(a1),x66771),a92))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x66771),x66771)),a92))
% 11.41/11.17 [6678]~P85(f784(f784(f242(a1),x66781),a106))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x66781),x66781)),a106))
% 11.41/11.17 [6679]~P85(f784(f784(f242(a1),x66791),a92))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x66791),x66791)),a92))
% 11.41/11.17 [7006]E(f784(f113(a859),x70061),f2(a859))+~P85(f784(a193,f784(f113(a1),f784(f784(f89(a1),x70061),a106))))
% 11.41/11.17 [7264]~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x72641)))+P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),f784(f784(f89(a1),x72641),x72641))))
% 11.41/11.17 [7265]P85(f784(a193,f784(f113(a1),x72651)))+~P85(f784(a193,f784(f113(a1),f784(f784(f89(a1),x72651),x72651))))
% 11.41/11.17 [7266]P85(f784(f784(f243(a1),x72661),a92))+~P85(f784(f784(f243(a1),f784(f784(f89(a1),x72661),x72661)),a92))
% 11.41/11.17 [7267]P85(f784(f784(f242(a1),x72671),a106))+~P85(f784(f784(f243(a1),f784(f784(f89(a1),x72671),x72671)),a106))
% 11.41/11.17 [7268]P85(f784(f784(f242(a1),x72681),a106))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),x72681),x72681)),a106))
% 11.41/11.17 [7269]P85(f784(f784(f242(a1),x72691),a92))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),x72691),x72691)),a92))
% 11.41/11.17 [7647]E(f784(a116,f573(x76471)),x76471)+~P85(f784(f784(f347(f869(f868(a859,a859),a852)),x76471),a107))
% 11.41/11.17 [6225]~P89(x62251)+E(f784(f113(x62251),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f87(x62251))
% 11.41/11.17 [6226]~P89(x62261)+E(f784(f113(x62261),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f87(x62261))
% 11.41/11.17 [6729]~P85(f784(a193,f784(f113(a1),x67291)))+E(f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),x67291),x67291)),a106)),f2(a859))
% 11.41/11.17 [7825]~P85(f784(f784(f243(a1),f784(f113(a1),x78251)),f2(a1)))+E(f784(f250(a1,a1),f784(a66,f65(f784(f88(a1),f87(a1)),f784(f88(a1),f784(f113(a1),x78251))))),f784(f784(f51(a1),f87(a1)),f784(f113(a1),x78251)))
% 11.41/11.17 [7838]~P85(f784(f784(f243(a1),f784(f113(a1),x78381)),f2(a1)))+E(f784(f260(a1,a1),f784(a66,f65(f784(f88(a1),f87(a1)),f784(f88(a1),f784(f113(a1),x78381))))),f60(a1,f87(a1),f784(f113(a1),x78381)))
% 11.41/11.17 [7885]~P85(f784(f784(f243(a1),a106),x78851))+P85(f784(f784(f243(a1),a106),f784(f784(f3(a1),f784(f784(f89(a1),x78851),x78851)),a106)))
% 11.41/11.17 [7886]~P85(f784(f784(f242(a1),a92),x78861))+P85(f784(f784(f243(a1),a92),f784(f784(f3(a1),f784(f784(f89(a1),x78861),x78861)),a106)))
% 11.41/11.17 [7887]~P85(f784(f784(f242(a1),a106),x78871))+P85(f784(f784(f242(a1),a106),f784(f784(f3(a1),f784(f784(f89(a1),x78871),x78871)),a106)))
% 11.41/11.17 [7888]~P85(f784(f784(f242(a1),a92),x78881))+P85(f784(f784(f242(a1),a92),f784(f784(f3(a1),f784(f784(f89(a1),x78881),x78881)),a106)))
% 11.41/11.17 [8181]~P89(x81811)+~P30(x81811,f784(f113(x81811),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))
% 11.41/11.17 [8362]P85(f784(f784(f243(a1),a106),x83621))+~P85(f784(f784(f243(a1),a106),f784(f784(f3(a1),f784(f784(f89(a1),x83621),x83621)),a106)))
% 11.41/11.17 [8363]P85(f784(f784(f242(a1),a106),x83631))+~P85(f784(f784(f242(a1),a106),f784(f784(f3(a1),f784(f784(f89(a1),x83631),x83631)),a106)))
% 11.41/11.17 [8364]P85(f784(f784(f242(a1),a92),x83641))+~P85(f784(f784(f243(a1),a92),f784(f784(f3(a1),f784(f784(f89(a1),x83641),x83641)),a106)))
% 11.41/11.17 [8365]P85(f784(f784(f242(a1),a92),x83651))+~P85(f784(f784(f242(a1),a92),f784(f784(f3(a1),f784(f784(f89(a1),x83651),x83651)),a106)))
% 11.41/11.17 [8660]E(f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),x86601),x86601)),a106)),f784(f784(f95(a859,a859),f784(f113(a859),x86601)),f784(f784(f10(a859,a859,a859),a160),f784(f784(f20(a859,a859,a859),f89(a859)),f7(a859)))))+P85(f784(a193,f784(f113(a1),x86601)))
% 11.41/11.17 [9433]E(x94331,f187(f869(f868(a859,a859),a852)))+P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),x94331),f187(f869(f868(a859,a859),a852)))),a48))
% 11.41/11.17 [8594]~P85(f784(a193,f784(f113(a1),x85941)))+P85(f784(a193,f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),x85941),x85941)),a106))))
% 11.41/11.17 [8595]~P85(f784(f784(f243(a1),x85951),a106))+P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x85951),x85951)),a106)),a106))
% 11.41/11.17 [8596]~P85(f784(f784(f243(a1),x85961),a92))+P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x85961),x85961)),a106)),a92))
% 11.41/11.17 [8597]~P85(f784(f784(f242(a1),x85971),a106))+P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x85971),x85971)),a106)),a106))
% 11.41/11.17 [8598]~P85(f784(f784(f243(a1),x85981),a92))+P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x85981),x85981)),a106)),a92))
% 11.41/11.17 [8694]~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x86941)))+P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),x86941),x86941)),a106))))
% 11.41/11.17 [8827]~P89(x88271)+E(f784(f784(f89(x88271),f87(x88271)),f87(x88271)),f784(f113(x88271),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))
% 11.41/11.17 [8972]P85(f784(a193,f784(f113(a1),x89721)))+~P85(f784(a193,f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),x89721),x89721)),a106))))
% 11.41/11.18 [8973]P85(f784(f784(f243(a1),x89731),a106))+~P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x89731),x89731)),a106)),a106))
% 11.41/11.18 [8974]P85(f784(f784(f243(a1),x89741),a92))+~P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x89741),x89741)),a106)),a92))
% 11.41/11.18 [8975]P85(f784(f784(f243(a1),x89751),a92))+~P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x89751),x89751)),a106)),a92))
% 11.41/11.18 [8976]P85(f784(f784(f242(a1),x89761),a106))+~P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x89761),x89761)),a106)),a106))
% 11.41/11.18 [9483]~P85(f784(f71(f868(a859,a859)),x94831))+P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),f187(f869(f868(a859,a859),a852))),x94831)),a78))
% 11.41/11.18 [9268]~P112(x92681)+E(f784(f784(f252(x92681),f2(x92681)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f2(x92681))
% 11.41/11.18 [9269]~P112(x92691)+E(f784(f784(f252(x92691),f87(x92691)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f87(x92691))
% 11.41/11.18 [9688]~P85(f784(f784(f243(a859),f87(a859)),x96881))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f51(a859),x96881),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.18 [9694]~P85(f784(f784(f243(a859),f2(a859)),x96941))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f51(a859),f784(f784(f89(a859),x96941),f87(a859))),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.18 [9733]~E(f60(a859,x97331,f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f87(a859))+P85(f784(f784(f243(a859),f2(a859)),f60(a859,x97331,f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.18 [9768]E(f60(a859,x97681,f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f87(a859))+~P85(f784(f784(f243(a859),f2(a859)),f60(a859,x97681,f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.18 [4546]~P35(x45461,x45462)+P55(x45461,x45462)
% 11.41/11.18 [4547]~P41(x45471,x45472)+P55(x45471,x45472)
% 11.41/11.18 [4507]E(x45071,x45072)+~E(f42(x45071),f42(x45072))
% 11.41/11.18 [4508]E(x45081,x45082)+~E(f43(x45081),f43(x45082))
% 11.41/11.18 [4510]~E(x45101,x45102)+E(f276(x45101,x45102),f87(a108))
% 11.41/11.18 [4513]E(f221(x45131,x45132),x45131)+~E(x45132,f2(a859))
% 11.41/11.18 [4518]P36(x45181,x45182)+~E(x45182,f190(x45181))
% 11.41/11.18 [4524]~P36(x45242,x45241)+E(x45241,f190(x45242))
% 11.41/11.18 [4551]~P100(x45512)+P100(f869(x45511,x45512))
% 11.41/11.18 [4552]~P104(x45522)+P104(f869(x45521,x45522))
% 11.41/11.18 [4553]~P103(x45532)+P103(f869(x45531,x45532))
% 11.41/11.18 [4554]~P91(x45542)+P91(f869(x45541,x45542))
% 11.41/11.18 [4555]~P84(x45552)+P84(f869(x45551,x45552))
% 11.41/11.18 [4556]~P72(x45562)+P72(f869(x45561,x45562))
% 11.41/11.18 [4557]~P93(x45572)+P93(f869(x45571,x45572))
% 11.41/11.18 [4558]~P93(x45582)+P98(f869(x45581,x45582))
% 11.41/11.18 [4559]~P6(x45592)+P6(f869(x45591,x45592))
% 11.41/11.18 [4560]~P107(x45602)+P107(f869(x45601,x45602))
% 11.41/11.18 [4561]~P96(x45612)+P94(f869(x45611,x45612))
% 11.41/11.18 [4562]~P102(x45622)+P102(f869(x45621,x45622))
% 11.41/11.18 [4563]~P96(x45632)+P95(f869(x45631,x45632))
% 11.41/11.18 [4564]~P93(x45642)+P99(f869(x45641,x45642))
% 11.41/11.18 [4565]~P97(x45652)+P97(f869(x45651,x45652))
% 11.41/11.18 [4566]~P96(x45662)+P96(f869(x45661,x45662))
% 11.41/11.18 [4578]E(x45781,x45782)+~E(f784(a29,x45781),f784(a29,x45782))
% 11.41/11.18 [4579]E(x45791,x45792)+~E(f784(a160,x45791),f784(a160,x45792))
% 11.41/11.18 [4580]E(x45801,x45802)+~E(f784(a160,x45801),f784(a160,x45802))
% 11.41/11.18 [4581]E(x45811,x45812)+~E(f784(a5,x45811),f784(a5,x45812))
% 11.41/11.18 [4582]E(x45821,x45822)+~E(f784(a22,x45821),f784(a22,x45822))
% 11.41/11.18 [4583]E(x45831,x45832)+~E(f784(a22,x45831),f784(a22,x45832))
% 11.41/11.18 [4584]E(x45841,x45842)+~E(f784(a116,x45841),f784(a116,x45842))
% 11.41/11.18 [4681]~P4(x46811)+E(f60(x46811,x46812,x46812),f2(x46811))
% 11.41/11.18 [4714]~P35(x47141,x47142)+P35(f860(x47141),f140(x47141,x47142))
% 11.41/11.18 [4715]~P35(x47151,x47152)+P35(f860(x47151),f139(x47151,x47152))
% 11.41/11.18 [4806]~P35(x48061,x48062)+P35(f869(x48061,a852),f337(x48061,x48062))
% 11.41/11.18 [4807]~P35(x48071,x48072)+P35(f869(x48071,a852),f338(x48071,x48072))
% 11.41/11.18 [4926]~P7(x49261)+P37(f305(a1,x49261,x49262))
% 11.41/11.18 [5032]~P35(x50321,x50322)+P57(x50321,f77(x50321,x50321,x50322))
% 11.41/11.18 [5514]~P77(x55141)+P26(x55141,x55141,f88(x55141),x55142)
% 11.41/11.18 [4533]~E(x45332,f120(x45331))+E(f784(f162(x45331),x45332),f120(x45331))
% 11.41/11.18 [4534]~E(x45342,f120(x45341))+E(f784(f161(x45341),x45342),f120(x45341))
% 11.41/11.18 [4535]~E(x45352,f120(x45351))+E(f784(f162(x45351),x45352),f120(x45351))
% 11.41/11.18 [4588]E(x45881,f784(a114,x45882))+~E(f784(f109(a1),x45881),x45882)
% 11.41/11.18 [4590]E(x45901,f120(x45902))+~E(f784(f162(x45902),x45901),f120(x45902))
% 11.41/11.18 [4591]E(x45911,f120(x45912))+~E(f784(f161(x45912),x45911),f120(x45912))
% 11.41/11.18 [4592]E(x45921,f120(x45922))+~E(f784(f162(x45922),x45921),f120(x45922))
% 11.41/11.18 [4607]~P89(x46071)+E(f784(f113(x46071),x46072),f784(f112(x46071),x46072))
% 11.41/11.18 [4614]~E(x46142,f190(x46141))+E(f236(x46141,x46142),f187(f869(x46141,a852)))
% 11.41/11.18 [4615]~P58(x46151)+P85(f784(f71(x46151),x46152))
% 11.41/11.18 [4616]~P58(x46161)+P85(f784(f71(x46161),x46162))
% 11.41/11.18 [4623]E(x46231,f190(x46232))+E(f784(f237(x46232),f504(x46232,x46231)),x46231)
% 11.41/11.18 [4624]E(x46241,f190(x46242))+E(f784(f237(x46242),f505(x46242,x46241)),x46241)
% 11.41/11.18 [4625]E(x46251,f190(x46252))+E(f784(f237(x46252),f516(x46252,x46251)),x46251)
% 11.41/11.18 [4627]~E(f733(x46272,x46271),f120(x46271))+E(f170(x46271,x46272),f120(f860(x46271)))
% 11.41/11.18 [4636]~E(x46362,f120(x46361))+E(f784(f164(x46361),x46362),f187(f869(x46361,a852)))
% 11.41/11.18 [4637]~E(x46372,f120(x46371))+E(f187(f869(x46371,a852)),f784(f164(x46371),x46372))
% 11.41/11.18 [4638]E(x46381,x46382)+~E(f784(f109(a1),x46381),f784(f109(a1),x46382))
% 11.41/11.18 [4639]E(x46391,x46392)+~E(f784(f109(a1),x46391),f784(f109(a1),x46392))
% 11.41/11.18 [4642]E(f219(x46421,x46422),f2(a859))+P85(f784(f71(x46421),x46422))
% 11.41/11.18 [4660]~P113(x46601)+E(f91(x46601,f91(x46601,x46602)),f91(x46601,x46602))
% 11.41/11.18 [4672]~P86(x46721)+E(f784(f784(f252(x46721),x46722),f87(a859)),x46722)
% 11.41/11.18 [4673]~P75(x46731)+E(f784(f784(f252(x46731),x46732),f87(a859)),x46732)
% 11.41/11.18 [4675]E(x46751,x46752)+E(f276(x46751,x46752),f784(f784(f89(a108),x46752),f87(a108)))
% 11.41/11.18 [4676]E(f784(f50(x46761),x46762),f2(a859))+P85(f784(f71(x46761),x46762))
% 11.41/11.18 [4677]E(f784(f50(x46771),x46772),f2(a859))+P85(f784(f71(x46771),x46772))
% 11.41/11.18 [4678]E(f784(f50(x46781),x46782),f2(a859))+P85(f784(f71(x46781),x46782))
% 11.41/11.18 [4684]~P67(x46841)+E(f784(f784(f89(x46841),x46842),f2(x46841)),x46842)
% 11.41/11.18 [4685]~P68(x46851)+E(f784(f784(f89(x46851),x46852),f2(x46851)),x46852)
% 11.41/11.18 [4686]~P86(x46861)+E(f784(f784(f89(x46861),x46862),f2(x46861)),x46862)
% 11.41/11.18 [4687]~P86(x46871)+E(f784(f784(f90(x46871),x46872),f87(x46871)),x46872)
% 11.41/11.18 [4688]~P75(x46881)+E(f784(f784(f90(x46881),x46882),f87(x46881)),x46882)
% 11.41/11.18 [4689]~P71(x46891)+E(f784(f784(f90(x46891),x46892),f87(x46891)),x46892)
% 11.41/11.18 [4690]~P4(x46901)+E(f784(f784(f51(x46901),x46902),f87(x46901)),x46902)
% 11.41/11.18 [4691]~P70(x46911)+E(f784(f784(f3(x46911),x46912),f2(x46911)),x46912)
% 11.41/11.18 [4692]~P116(x46921)+E(f784(f784(f293(x46921),x46922),f87(x46921)),x46922)
% 11.41/11.18 [4693]~P95(x46931)+E(f784(f784(f110(x46931),x46932),f187(x46931)),x46932)
% 11.41/11.18 [4694]~P94(x46941)+E(f784(f784(f111(x46941),x46942),f249(x46941)),x46942)
% 11.41/11.18 [4695]~P86(x46951)+E(f784(f784(f252(x46951),x46952),f2(a859)),f87(x46951))
% 11.41/11.18 [4696]~P106(x46961)+E(f784(f784(f252(x46961),x46962),f2(a859)),f87(x46961))
% 11.41/11.18 [4697]~E(x46972,f187(f869(x46971,a852)))+E(f784(f50(x46971),x46972),f2(a859))
% 11.41/11.18 [4708]~P4(x47081)+E(f60(x47081,x47082,f2(x47081)),x47082)
% 11.41/11.18 [4716]~P86(x47161)+E(f784(f784(f90(x47161),x47162),f2(x47161)),f2(x47161))
% 11.41/11.18 [4717]~P124(x47171)+E(f784(f784(f90(x47171),x47172),f2(x47171)),f2(x47171))
% 11.41/11.18 [4718]~P4(x47181)+E(f784(f784(f51(x47181),x47182),f2(x47181)),f2(x47181))
% 11.41/11.18 [4719]~P117(x47191)+E(f784(f784(f293(x47191),x47192),f2(x47191)),f2(x47191))
% 11.41/11.18 [4720]~P94(x47201)+E(f784(f784(f110(x47201),x47202),f249(x47201)),f249(x47201))
% 11.41/11.18 [4721]~P95(x47211)+E(f784(f784(f111(x47211),x47212),f187(x47211)),f187(x47211))
% 11.41/11.18 [4722]E(x47221,f190(x47222))+~E(f236(x47222,x47221),f187(f869(x47222,a852)))
% 11.41/11.18 [4723]~P4(x47231)+E(f60(x47231,x47232,f87(x47231)),f2(x47231))
% 11.41/11.18 [4724]~P4(x47241)+E(f60(x47241,f2(x47241),x47242),f2(x47241))
% 11.41/11.18 [4775]P35(x47751,x47752)+~E(f610(x47752,x47751),f187(f869(x47751,a852)))
% 11.41/11.18 [4776]E(x47761,f120(x47762))+~E(f784(f164(x47762),x47761),f187(f869(x47762,a852)))
% 11.41/11.18 [4777]E(x47771,f120(x47772))+~E(f187(f869(x47772,a852)),f784(f164(x47772),x47771))
% 11.41/11.18 [4780]~E(x47801,x47802)+P85(f784(f784(a343,x47801),x47802))
% 11.41/11.18 [4790]P85(x47901)+P85(f784(f784(a348,x47901),x47902))
% 11.41/11.18 [4791]E(x47911,f120(x47912))+E(f784(f784(f155(x47912),x47911),f2(a859)),f784(f135(x47912),x47911))
% 11.41/11.18 [4797]~P85(x47972)+P85(f784(f784(a348,x47971),x47972))
% 11.41/11.18 [4798]~P85(x47982)+P85(f784(f784(a345,x47981),x47982))
% 11.41/11.18 [4799]~P85(x47991)+P85(f784(f784(a345,x47991),x47992))
% 11.41/11.18 [4809]~E(f734(x48092,x48091),f738(x48092,x48091))+P85(f784(f132(x48091),x48092))
% 11.41/11.18 [4817]E(f784(f266(x48171),x48172),f187(f869(x48171,a852)))+P85(f784(x48172,f559(x48172)))
% 11.41/11.18 [4818]E(f187(f869(x48181,a852)),f784(f266(x48181),x48182))+P85(f784(x48182,f560(x48182)))
% 11.41/11.18 [4882]~P113(x48821)+E(f784(f784(f90(x48821),x48822),f91(x48821,x48822)),f784(f84(x48821),x48822))
% 11.41/11.18 [4893]~E(x48931,f2(a1))+E(f61(x48931,x48932),f784(f784(f251(a1,a1),f2(a1)),f2(a1)))
% 11.41/11.18 [4894]~E(x48941,f2(a1))+E(f61(x48941,x48942),f784(f784(f251(a1,a1),f2(a1)),f2(a1)))
% 11.41/11.18 [4925]~P55(x49251,x49252)+P55(x49251,f784(f288(x49251,x49251),x49252))
% 11.41/11.18 [4944]~E(f784(a32,x49441),f784(f237(a853),x49442))+P85(f784(a26,f784(a29,x49441)))
% 11.41/11.18 [4948]E(x49481,x49482)+~P85(f784(f784(a343,x49481),x49482))
% 11.41/11.18 [4951]~P85(f784(a26,x49512))+P85(f784(a26,f37(x49511,x49512)))
% 11.41/11.18 [4952]~P85(f784(a26,x49522))+P85(f784(a26,f37(x49521,x49522)))
% 11.41/11.18 [4961]P85(x49611)+~P85(f784(f784(a344,x49612),x49611))
% 11.41/11.18 [4962]P85(x49621)+~P85(f784(f784(a344,x49621),x49622))
% 11.41/11.18 [4966]~P107(x49661)+P85(f784(f784(f242(x49661),x49662),f249(x49661)))
% 11.41/11.18 [4967]~P86(x49671)+P85(f784(f784(f289(x49671),x49672),f2(x49671)))
% 11.41/11.18 [4972]E(x49721,x49722)+~E(f784(x49721,f385(x49722,x49721)),f784(x49722,f385(x49722,x49721)))
% 11.41/11.18 [5006]E(x50061,f2(a859))+E(f221(x50061,f60(a859,x50062,x50061)),f221(x50062,x50061))
% 11.41/11.18 [5011]~P101(x50111)+P15(x50111,f784(f784(f144(x50111),x50112),f120(x50111)))
% 11.41/11.18 [5013]E(x50131,f2(a1))+P85(f784(f64(x50132,x50131),f61(x50132,x50131)))
% 11.41/11.18 [5030]~E(x50301,x50302)+P85(f784(f784(f243(a859),x50301),f784(a160,x50302)))
% 11.41/11.18 [5040]~E(x50401,f2(a859))+P85(f784(f784(f243(a859),x50401),f784(a160,x50402)))
% 11.41/11.18 [5050]P85(f784(x50501,x50502))+P85(f784(f784(f242(a1),f2(a1)),f786(x50501)))
% 11.41/11.18 [5085]P85(f784(a26,x50851))+~P85(f784(a26,f37(x50852,x50851)))
% 11.41/11.18 [5086]P85(f784(a26,x50861))+~P85(f784(a26,f37(x50862,x50861)))
% 11.41/11.18 [5087]P85(f784(a26,x50871))+~P85(f784(a26,f38(x50872,x50871)))
% 11.41/11.18 [5088]P85(f784(a26,x50881))+~P85(f784(a26,f38(x50882,x50881)))
% 11.41/11.18 [5089]P85(f784(a26,x50891))+~P85(f784(a26,f38(x50891,x50892)))
% 11.41/11.18 [5090]P85(f784(a26,x50901))+~P85(f784(a26,f38(x50901,x50902)))
% 11.41/11.18 [5118]P55(x51181,x51182)+~P55(x51181,f784(f288(x51181,x51181),x51182))
% 11.41/11.18 [5120]~E(f60(a859,x51202,x51201),f2(a859))+E(f784(f784(f90(a859),x51201),f798(x51201,x51202)),x51202)
% 11.41/11.18 [5121]~E(f60(a1,x51212,x51211),f2(a1))+E(f784(f784(f90(a1),x51211),f799(x51211,x51212)),x51212)
% 11.41/11.18 [5126]~E(x51261,f784(a160,x51262))+P85(f784(f784(f242(a859),x51261),f784(a160,x51262)))
% 11.41/11.18 [5147]~P85(f784(x51471,x51472))+P85(f784(f784(f242(a1),f2(a1)),f771(x51471)))
% 11.41/11.18 [5158]E(f784(f784(f3(a859),f784(a114,x51581)),f784(a114,x51582)),f784(a114,x51581))+~P85(f784(a193,x51582))
% 11.41/11.18 [5186]E(f277(x51861,x51862),f87(a108))+~P85(f784(f784(f242(a108),x51861),f87(a108)))
% 11.41/11.18 [5273]E(f784(f784(f155(x52731),x52732),f734(x52732,x52731)),f784(f784(f155(x52731),x52732),f738(x52732,x52731)))+P85(f784(f132(x52731),x52732))
% 11.41/11.18 [5315]~P85(f784(x53151,f99(x53152,x53151)))+P85(f784(x53151,f611(x53152,x53151)))
% 11.41/11.18 [5379]P57(x53791,x53792)+~P85(f784(f334(x53791,x53792),f584(x53792,x53791)))
% 11.41/11.18 [5521]~E(f784(a160,f60(a859,x55211,x55212)),x55212)+E(f60(a859,f784(a160,x55211),x55212),f2(a859))
% 11.41/11.18 [5575]P35(x55751,x55752)+P85(f784(f784(f347(x55751),f694(x55752,x55751)),f695(x55752,x55751)))
% 11.41/11.18 [5581]~P112(x55811)+P85(f784(f784(f347(x55811),f784(f109(x55811),x55812)),f183(x55811)))
% 11.41/11.18 [5582]~P136(x55821)+P85(f784(f784(f347(x55821),f784(f109(x55821),x55822)),f119(x55821)))
% 11.41/11.18 [5583]~P136(x55831)+P85(f784(f784(f347(x55831),f784(f112(x55831),x55832)),f119(x55831)))
% 11.41/11.18 [5584]~P89(x55841)+P85(f784(f784(f347(x55841),f784(f113(x55841),x55842)),f119(x55841)))
% 11.41/11.18 [5738]E(f784(a160,f60(a859,x57381,x57382)),x57382)+E(f60(a859,f784(a160,x57381),x57382),f784(a160,f60(a859,x57381,x57382)))
% 11.41/11.18 [6156]P35(x61561,x61562)+~P85(f784(f784(f347(x61561),f586(x61562,x61561)),f335(x61561,x61562)))
% 11.41/11.18 [6190]~P120(x61901)+~P85(f784(f784(f243(x61901),f784(f109(x61901),x61902)),f2(x61901)))
% 11.41/11.18 [6191]~P79(x61911)+~P85(f784(f784(f243(x61911),f784(f84(x61911),x61912)),f2(x61911)))
% 11.41/11.18 [6280]P85(f784(f784(f243(a1),x62801),f60(a1,x62802,x62801)))+~P85(f784(f784(f243(a1),x62801),f2(a1)))
% 11.41/11.18 [6281]P85(f784(f784(f243(a1),x62811),f60(a1,x62812,x62811)))+~P85(f784(f784(f243(a1),x62811),f2(a1)))
% 11.41/11.18 [6389]E(f784(f784(f312(a859),f784(a160,x63891)),f305(a859,x63892,x63891)),f305(a859,x63892,f784(a160,x63891)))+~P85(f784(f784(f242(a859),x63892),f784(a160,x63891)))
% 11.41/11.18 [6614]E(f784(f161(x66141),x66142),x66142)+~P85(f784(f784(f242(a859),f784(f188(f860(x66141)),x66142)),f87(a859)))
% 11.41/11.18 [6637]~P79(x66371)+P85(f784(f784(f242(x66371),f784(f88(x66371),f784(f84(x66371),x66372))),f2(x66371)))
% 11.41/11.18 [6672]~P35(x66721,x66722)+P35(x66721,f784(f784(f291(x66721,x66721,x66721),x66722),f310(x66721,x66722)))
% 11.41/11.18 [6901]~P85(f784(f784(f243(a1),x69012),f2(a1)))+P85(f784(f784(f242(a1),f60(a1,x69011,x69012)),f2(a1)))
% 11.41/11.18 [6902]~P85(f784(f784(f243(a1),x69022),f2(a1)))+P85(f784(f784(f242(a1),f60(a1,x69021,x69022)),f2(a1)))
% 11.41/11.18 [7311]~P112(x73111)+E(f189(x73111,f784(f784(f9(x73111,x73111,x73111),f89(x73111)),f87(x73111)),x73112,f2(x73111)),f784(f109(x73111),x73112))
% 11.41/11.18 [7344]~P121(x73441)+~P85(f784(f784(f243(x73441),f784(f784(f90(x73441),x73442),x73442)),f2(x73441)))
% 11.41/11.18 [9867]~P113(x98671)+~P85(f784(f784(f243(x98671),f784(f784(f252(x98671),x98672),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f2(x98671)))
% 11.41/11.18 [4589]~E(x45892,f120(x45891))+E(f784(f188(f860(x45891)),x45892),f2(a859))
% 11.41/11.18 [4628]~E(x46281,f2(a859))+E(f784(f784(f89(a859),x46281),x46282),x46282)
% 11.41/11.18 [4629]~E(x46292,f2(a859))+E(f784(f784(f90(a859),x46291),x46292),f2(a859))
% 11.41/11.18 [4630]~E(x46301,f2(a859))+E(f784(f784(f90(a859),x46301),x46302),f2(a859))
% 11.41/11.18 [4631]~E(x46311,f2(a859))+E(f784(f784(f90(a859),x46311),x46312),f2(a859))
% 11.41/11.18 [4632]~E(x46322,f2(a1))+E(f784(f784(f51(a1),x46321),x46322),f2(a1))
% 11.41/11.18 [4633]~E(x46332,f2(a859))+E(f784(f784(f252(a859),x46331),x46332),f87(a859))
% 11.41/11.18 [4643]E(x46431,f120(x46432))+~E(f784(f188(f860(x46432)),x46431),f2(a859))
% 11.41/11.18 [4644]~P92(x46441)+E(f784(f784(f90(x46441),x46442),x46442),x46442)
% 11.41/11.18 [4645]~P92(x46451)+E(f784(f784(f90(x46451),x46452),x46452),x46452)
% 11.41/11.18 [4646]~P101(x46461)+E(f784(f784(f246(x46461),x46462),x46462),x46462)
% 11.41/11.18 [4647]~P101(x46471)+E(f784(f784(f246(x46471),x46472),x46472),x46472)
% 11.41/11.18 [4648]~P101(x46481)+E(f784(f784(f186(x46481),x46482),x46482),x46482)
% 11.41/11.18 [4649]~P101(x46491)+E(f784(f784(f186(x46491),x46492),x46492),x46492)
% 11.41/11.18 [4650]~P93(x46501)+E(f784(f784(f110(x46501),x46502),x46502),x46502)
% 11.41/11.18 [4651]~P98(x46511)+E(f784(f784(f110(x46511),x46512),x46512),x46512)
% 11.41/11.18 [4652]~P98(x46521)+E(f784(f784(f110(x46521),x46522),x46522),x46522)
% 11.41/11.18 [4653]~P93(x46531)+E(f784(f784(f111(x46531),x46532),x46532),x46532)
% 11.41/11.18 [4654]~P99(x46541)+E(f784(f784(f111(x46541),x46542),x46542),x46542)
% 11.41/11.18 [4655]~P99(x46551)+E(f784(f784(f111(x46551),x46552),x46552),x46552)
% 11.41/11.18 [4671]~P70(x46711)+E(f784(f784(f3(x46711),x46712),x46712),f2(x46711))
% 11.41/11.18 [4682]~P70(x46821)+E(f784(f88(x46821),f784(f88(x46821),x46822)),x46822)
% 11.41/11.18 [4683]~P91(x46831)+E(f784(f88(x46831),f784(f88(x46831),x46832)),x46832)
% 11.41/11.18 [4700]~E(x47002,f2(a859))+E(f784(f784(f252(a859),x47001),x47002),f784(a160,f2(a859)))
% 11.41/11.18 [4732]~P67(x47321)+E(f784(f784(f89(x47321),f2(x47321)),x47322),x47322)
% 11.41/11.18 [4733]~P68(x47331)+E(f784(f784(f89(x47331),f2(x47331)),x47332),x47332)
% 11.41/11.18 [4734]~P86(x47341)+E(f784(f784(f89(x47341),f2(x47341)),x47342),x47342)
% 11.41/11.18 [4735]~P86(x47351)+E(f784(f784(f90(x47351),f87(x47351)),x47352),x47352)
% 11.41/11.18 [4736]~P75(x47361)+E(f784(f784(f90(x47361),f87(x47361)),x47362),x47362)
% 11.41/11.18 [4737]~P71(x47371)+E(f784(f784(f90(x47371),f87(x47371)),x47372),x47372)
% 11.41/11.18 [4738]~P95(x47381)+E(f784(f784(f110(x47381),f187(x47381)),x47382),x47382)
% 11.41/11.18 [4739]~P94(x47391)+E(f784(f784(f111(x47391),f249(x47391)),x47392),x47392)
% 11.41/11.18 [4756]~P86(x47561)+E(f784(f784(f90(x47561),f2(x47561)),x47562),f2(x47561))
% 11.41/11.18 [4757]~P124(x47571)+E(f784(f784(f90(x47571),f2(x47571)),x47572),f2(x47571))
% 11.41/11.18 [4758]~P4(x47581)+E(f784(f784(f51(x47581),f2(x47581)),x47582),f2(x47581))
% 11.41/11.18 [4759]~P75(x47591)+E(f784(f784(f252(x47591),f87(x47591)),x47592),f87(x47591))
% 11.41/11.18 [4760]~P116(x47601)+E(f784(f784(f293(x47601),f2(x47601)),x47602),f2(x47601))
% 11.41/11.18 [4761]~P94(x47611)+E(f784(f784(f110(x47611),f249(x47611)),x47612),f249(x47611))
% 11.41/11.18 [4762]~P95(x47621)+E(f784(f784(f111(x47621),f187(x47621)),x47622),f187(x47621))
% 11.41/11.18 [4770]E(x47701,f120(x47702))+E(f138(x47702,f784(f162(x47702),x47701)),f784(f135(x47702),x47701))
% 11.41/11.18 [4771]E(x47711,f120(x47712))+E(f784(f135(x47712),f784(f162(x47712),x47711)),f138(x47712,x47711))
% 11.41/11.18 [4772]E(x47721,f2(a859))+~E(f784(f784(f89(a859),x47722),x47721),x47722)
% 11.41/11.18 [4778]~P136(x47781)+E(f784(f112(x47781),f784(f109(a1),x47782)),f784(f109(x47781),x47782))
% 11.41/11.18 [4779]~P89(x47791)+E(f784(f112(x47791),f784(f113(a1),x47792)),f784(f113(x47791),x47792))
% 11.41/11.18 [4784]E(x47841,f87(a859))+~E(f784(f784(f90(a859),x47842),x47841),f87(a859))
% 11.41/11.18 [4785]E(x47851,f87(a859))+~E(f784(f784(f90(a859),x47851),x47852),f87(a859))
% 11.41/11.18 [4786]E(x47861,f2(a859))+~E(f784(f784(f89(a859),x47862),x47861),f2(a859))
% 11.41/11.18 [4787]E(x47871,f2(a859))+~E(f784(f784(f89(a859),x47871),x47872),f2(a859))
% 11.41/11.18 [4788]E(x47881,f87(a859))+~E(f784(f784(f90(a859),x47882),x47881),f87(a859))
% 11.41/11.18 [4789]E(x47891,f87(a859))+~E(f784(f784(f90(a859),x47891),x47892),f87(a859))
% 11.41/11.18 [4802]~P113(x48021)+E(f784(f84(x48021),f784(f109(x48021),x48022)),f784(f109(x48021),x48022))
% 11.41/11.18 [4803]~P79(x48031)+E(f784(f84(x48031),f784(f88(x48031),x48032)),f784(f84(x48031),x48032))
% 11.41/11.18 [4804]~P79(x48041)+E(f784(f84(x48041),f784(f84(x48041),x48042)),f784(f84(x48041),x48042))
% 11.41/11.18 [4805]~P68(x48051)+E(f784(f157(x48051),f784(f162(x48051),x48052)),f784(f157(x48051),x48052))
% 11.41/11.18 [4810]~E(x48101,f784(a160,f2(a859)))+E(f784(f784(f252(a859),x48101),x48102),f784(a160,f2(a859)))
% 11.41/11.18 [4820]~P70(x48201)+E(f784(f784(f3(x48201),f2(x48201)),x48202),f784(f88(x48201),x48202))
% 11.41/11.18 [4821]~E(x48212,f2(a859))+E(f134(a859,f784(f304(a859,x48211),x48212)),f120(a859))
% 11.41/11.18 [4830]~P89(x48301)+E(f784(f784(f89(x48301),x48302),f784(f113(x48301),a92)),x48302)
% 11.41/11.18 [4831]E(x48311,f2(a1))+E(f62(f784(f84(a1),x48312),f784(f84(a1),x48311)),f68(x48312,x48311))
% 11.41/11.18 [4841]~E(x48411,x48412)+P85(f784(f784(f242(a859),x48411),x48412))
% 11.41/11.18 [4842]~E(x48421,x48422)+P85(f784(f784(f242(a859),x48421),x48422))
% 11.41/11.18 [4843]~E(x48431,x48432)+P85(f784(f784(f242(a859),x48431),x48432))
% 11.41/11.18 [4844]~E(x48441,x48442)+P85(f784(f784(f289(a859),x48441),x48442))
% 11.41/11.18 [4845]~E(x48451,x48452)+P85(f784(f784(f289(a859),x48451),x48452))
% 11.41/11.18 [4846]~E(x48461,x48462)+P85(f784(f784(f289(a859),x48461),x48462))
% 11.41/11.18 [4847]~E(x48471,x48472)+P85(f784(f784(f289(a859),x48471),x48472))
% 11.41/11.18 [4854]~E(x48541,f2(a108))+E(f784(f784(f89(a859),f784(a22,x48541)),x48542),x48542)
% 11.41/11.18 [4855]~E(f784(f113(a1),x48552),f784(f109(a1),x48551))+E(x48551,f784(a114,f784(f113(a1),x48552)))
% 11.41/11.18 [4864]~P7(x48641)+P7(f784(f784(f252(a1),x48641),x48642))
% 11.41/11.18 [4865]~P70(x48651)+E(f784(f784(f89(x48651),x48652),f784(f88(x48651),x48652)),f2(x48651))
% 11.41/11.18 [4866]~P91(x48661)+E(f784(f784(f110(x48661),x48662),f784(f88(x48661),x48662)),f249(x48661))
% 11.41/11.18 [4867]~P91(x48671)+E(f784(f784(f111(x48671),x48672),f784(f88(x48671),x48672)),f187(x48671))
% 11.41/11.18 [4891]E(x48911,f2(a859))+~E(f784(f88(a1),f784(f109(a1),x48912)),f784(f109(a1),x48911))
% 11.41/11.18 [4892]E(x48921,f2(a859))+~E(f784(f88(a1),f784(f109(a1),x48921)),f784(f109(a1),x48922))
% 11.41/11.18 [4902]E(f195(x49021,x49022),f2(a1))+P85(f784(f784(f242(a1),x49022),x49021))
% 11.41/11.18 [4903]E(f248(x49031,x49032),f2(a108))+P85(f784(f784(f243(a108),x49031),x49032))
% 11.41/11.18 [4904]E(f169(x49041,x49042),f120(a1))+P85(f784(f784(f242(a1),x49041),x49042))
% 11.41/11.18 [4917]E(x49171,f784(a160,f2(a859)))+~E(f784(f784(f90(a859),x49172),x49171),f784(a160,f2(a859)))
% 11.41/11.18 [4918]E(x49181,f784(a160,f2(a859)))+~E(f784(f784(f90(a859),x49181),x49182),f784(a160,f2(a859)))
% 11.41/11.18 [4919]~P104(x49191)+P85(f784(f784(f242(x49191),x49192),x49192))
% 11.41/11.18 [4920]~P86(x49201)+P85(f784(f784(f289(x49201),x49202),x49202))
% 11.41/11.18 [4923]~P89(x49231)+E(f784(f784(f90(x49231),x49232),f784(f113(x49231),a106)),f784(f88(x49231),x49232))
% 11.41/11.18 [4938]~P89(x49381)+E(f784(f88(x49381),f784(f113(x49381),x49382)),f784(f113(x49381),f784(f88(a1),x49382)))
% 11.41/11.18 [4939]~P136(x49391)+E(f784(f88(x49391),f784(f112(x49391),x49392)),f784(f112(x49391),f784(f88(a1),x49392)))
% 11.41/11.18 [4940]~P89(x49401)+E(f784(f88(x49401),f784(f113(x49401),x49402)),f784(f113(x49401),f784(f88(a1),x49402)))
% 11.41/11.18 [4977]~E(x49771,f784(a160,x49772))+P85(f784(f784(f243(a859),f2(a859)),x49771))
% 11.41/11.18 [4994]~P101(x49941)+E(f784(f88(f869(x49941,a852)),f784(f267(x49941),x49942)),f784(f268(x49941),x49942))
% 11.41/11.18 [4995]~P101(x49951)+E(f784(f88(f869(x49951,a852)),f784(f306(x49951),x49952)),f784(f303(x49951),x49952))
% 11.41/11.18 [4996]~P101(x49961)+E(f784(f88(f869(x49961,a852)),f784(f303(x49961),x49962)),f784(f306(x49961),x49962))
% 11.41/11.18 [4997]~P101(x49971)+E(f784(f88(f869(x49971,a852)),f784(f268(x49971),x49972)),f784(f267(x49971),x49972))
% 11.41/11.18 [5005]~E(f784(f109(a1),x50052),x50051)+P85(f784(f784(f242(a1),f2(a1)),x50051))
% 11.41/11.18 [5012]~E(x50122,f2(a1))+E(f68(x50121,x50122),f784(f784(f251(a1,a1),f2(a1)),f784(f84(a1),x50121)))
% 11.41/11.18 [5014]~P102(x50141)+P85(f784(f784(f242(x50141),f187(x50141)),x50142))
% 11.41/11.18 [5015]~P86(x50151)+P85(f784(f784(f289(x50151),f87(x50151)),x50152))
% 11.41/11.18 [5045]E(x50451,x50452)+~E(f784(f784(f89(a1),x50451),x50451),f784(f784(f89(a1),x50452),x50452))
% 11.41/11.18 [5049]~P85(f784(x50491,x50492))+P85(f784(x50491,f784(a114,f771(x50491))))
% 11.41/11.18 [5075]~P113(x50751)+E(f784(f784(f90(x50751),f91(x50751,x50752)),f784(f84(x50751),x50752)),x50752)
% 11.41/11.18 [5076]E(x50761,x50762)+~P85(f784(f784(f194(a25),x50761),x50762))
% 11.41/11.18 [5084]~E(x50842,f2(a859))+E(f94(f868(a859,a859),f63(x50841,x50842)),f784(f784(f251(a859,a859),f2(a859)),x50841))
% 11.41/11.18 [5091]~E(x50911,x50912)+~P85(f784(f784(f243(a859),x50911),x50912))
% 11.41/11.18 [5092]~E(x50921,x50922)+~P85(f784(f784(f243(a859),x50921),x50922))
% 11.41/11.18 [5093]~E(x50931,x50932)+~P85(f784(f784(f243(a859),x50931),x50932))
% 11.41/11.18 [5094]~E(x50941,x50942)+~P85(f784(f784(f243(a859),x50941),x50942))
% 11.41/11.18 [5095]~E(x50951,x50952)+~P85(f784(f784(f243(a859),x50951),x50952))
% 11.41/11.18 [5096]~E(x50961,x50962)+~P85(f784(f784(f243(a1),x50961),x50962))
% 11.41/11.18 [5099]~P112(x50991)+E(f784(f784(f89(x50991),f87(x50991)),f784(f109(x50991),x50992)),f784(f109(x50991),f784(a160,x50992)))
% 11.41/11.18 [5103]~E(x51031,f2(a859))+~P85(f784(f784(f243(a859),x51032),x51031))
% 11.41/11.18 [5116]E(f784(f50(x51161),f784(f164(x51161),x51162)),f784(f188(f860(x51161)),x51162))+~P85(f784(f132(x51161),x51162))
% 11.41/11.18 [5125]~P85(f784(x51251,f739(x51251)))+P85(f784(x51251,f784(f109(a1),x51252)))
% 11.41/11.18 [5136]E(f248(x51361,x51362),x51362)+~P85(f784(f784(f243(a108),x51361),x51362))
% 11.41/11.18 [5138]E(f277(x51381,x51382),f87(a108))+~P85(f784(f784(f243(a108),x51382),x51381))
% 11.41/11.18 [5139]E(f169(x51391,x51392),f120(a1))+~P85(f784(f784(f243(a1),x51392),x51391))
% 11.41/11.18 [5142]~P100(x51421)+E(f305(x51421,x51422,x51422),f784(f784(f312(x51421),x51422),f187(f869(x51421,a852))))
% 11.41/11.18 [5161]~E(f784(f784(f3(a859),x51611),x51612),f2(a859))+P85(f784(f784(f242(a859),x51611),x51612))
% 11.41/11.18 [5187]~P104(x51871)+~P85(f784(f784(f243(x51871),x51872),x51872))
% 11.41/11.18 [5189]~E(f60(a1,x51891,x51892),f2(a1))+E(f60(a1,x51891,f784(f88(a1),x51892)),f2(a1))
% 11.41/11.18 [5190]~E(f60(a1,x51901,x51902),f2(a1))+E(f60(a1,x51901,f784(f88(a1),x51902)),f2(a1))
% 11.41/11.18 [5191]~E(f60(a1,x51911,x51912),f2(a1))+E(f60(a1,f784(f88(a1),x51911),x51912),f2(a1))
% 11.41/11.18 [5192]~E(f60(a1,x51921,x51922),f2(a1))+E(f60(a1,f784(f88(a1),x51921),x51922),f2(a1))
% 11.41/11.18 [5198]E(f784(f304(a859,x51981),f784(a160,x51982)),f187(f869(a859,a852)))+P85(f784(f784(f242(a859),x51981),x51982))
% 11.41/11.18 [5215]E(f134(a859,f784(f304(a859,x52151),x52152)),f120(a859))+P85(f784(f784(f243(a859),x52151),x52152))
% 11.41/11.18 [5220]~E(f784(f50(x52201),f784(f164(x52201),x52202)),f784(f188(f860(x52201)),x52202))+P85(f784(f132(x52201),x52202))
% 11.41/11.18 [5224]~P85(f784(f132(x52241),x52242))+P85(f784(f132(x52241),f784(f161(x52241),x52242)))
% 11.41/11.18 [5225]~P85(f784(f132(x52251),x52252))+P85(f784(f132(x52251),f784(f163(x52251),x52252)))
% 11.41/11.18 [5226]~P85(f784(f132(x52261),x52262))+P85(f784(f132(x52261),f784(f162(x52261),x52262)))
% 11.41/11.18 [5234]P85(f784(x52341,x52342))+~P85(f784(x52341,f784(a114,f786(x52341))))
% 11.41/11.18 [5235]P85(f784(f784(f242(a859),x52352),x52351))+P85(f784(f784(f242(a859),x52351),x52352))
% 11.41/11.18 [5236]P85(f784(f784(f242(a1),x52362),x52361))+P85(f784(f784(f242(a1),x52361),x52362))
% 11.41/11.18 [5238]~P79(x52381)+P85(f784(f784(f242(x52381),x52382),f784(f84(x52381),x52382)))
% 11.41/11.18 [5241]P85(f784(x52411,f740(x52411)))+~P85(f784(x52411,f784(f109(a1),x52412)))
% 11.41/11.18 [5264]E(f784(f784(f51(a859),x52641),x52642),f2(a859))+~P85(f784(f784(f243(a859),x52641),x52642))
% 11.41/11.18 [5265]E(f784(f784(f3(a859),x52651),x52652),f2(a859))+~P85(f784(f784(f242(a859),x52651),x52652))
% 11.41/11.18 [5266]E(f784(f784(f3(a859),x52661),x52662),f2(a859))+~P85(f784(f784(f242(a859),x52661),x52662))
% 11.41/11.18 [5282]E(f60(a859,x52821,x52822),x52821)+~P85(f784(f784(f243(a859),x52821),x52822))
% 11.41/11.18 [5283]E(f60(a859,x52831,x52832),x52831)+~P85(f784(f784(f243(a859),x52831),x52832))
% 11.41/11.18 [5290]E(f60(a1,x52901,f784(f88(a1),x52902)),f294(x52901,x52902))+P85(f784(f784(f242(a1),f2(a1)),x52902))
% 11.41/11.18 [5302]E(f784(f784(f3(a1),x53021),x53022),f195(x53021,x53022))+~P85(f784(f784(f242(a1),x53022),x53021))
% 11.41/11.18 [5303]E(f784(f784(f3(a1),x53031),x53032),f195(x53031,x53032))+~P85(f784(f784(f242(a1),x53032),x53031))
% 11.41/11.18 [5321]P85(f784(f784(f242(a1),f2(a1)),f739(x53211)))+P85(f784(x53211,f784(f109(a1),x53212)))
% 11.41/11.18 [5334]~P120(x53341)+P85(f784(f784(f242(x53341),f2(x53341)),f784(f109(x53341),x53342)))
% 11.41/11.18 [5335]~P120(x53351)+P85(f784(f784(f242(x53351),f2(x53351)),f784(f109(x53351),x53352)))
% 11.41/11.18 [5336]~P79(x53361)+P85(f784(f784(f242(x53361),f2(x53361)),f784(f84(x53361),x53362)))
% 11.41/11.18 [5364]E(f784(f784(f89(a859),x53641),f693(x53642,x53641)),x53642)+~P85(f784(f784(f242(a859),x53641),x53642))
% 11.41/11.18 [5365]E(f784(f784(f89(a859),x53651),f612(x53652,x53651)),x53652)+~P85(f784(f784(f243(a859),x53651),x53652))
% 11.41/11.18 [5377]~E(f784(f113(a1),x53771),f784(f109(a1),x53772))+P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x53771)))
% 11.41/11.18 [5380]E(f305(a1,x53801,x53802),f187(f869(a1,a852)))+~P85(f784(f784(f243(a1),x53802),x53801))
% 11.41/11.18 [5383]~P113(x53831)+E(f784(f784(f90(x53831),f784(f84(x53831),x53832)),f784(f84(x53831),x53832)),f784(f784(f90(x53831),x53832),x53832))
% 11.41/11.18 [5388]E(f134(a859,f784(f304(a859,x53881),f784(a160,x53882))),f120(a859))+P85(f784(f784(f242(a859),x53881),x53882))
% 11.41/11.18 [5392]E(f784(f784(f51(a1),x53921),x53922),f295(x53921,x53922))+~P85(f784(f784(f242(a1),f2(a1)),x53922))
% 11.41/11.18 [5412]P85(f784(f132(x54121),x54122))+~P85(f784(f132(x54121),f784(f161(x54121),x54122)))
% 11.41/11.18 [5413]P85(f784(f132(x54131),x54132))+~P85(f784(f132(x54131),f784(f162(x54131),x54132)))
% 11.41/11.18 [5436]P85(f784(f71(a859),x54361))+P85(f784(f784(f347(a859),f388(x54361,x54362)),x54361))
% 11.41/11.18 [5437]P85(f784(f71(a859),x54371))+P85(f784(f784(f347(a859),f413(x54371,x54372)),x54371))
% 11.41/11.18 [5438]P85(f784(f784(f243(a859),x54382),f784(a160,x54381)))+P85(f784(f784(f243(a859),x54381),x54382))
% 11.41/11.18 [5439]E(f60(a1,x54391,x54392),f294(x54391,x54392))+~P85(f784(f784(f242(a1),f2(a1)),x54392))
% 11.41/11.18 [5441]E(f134(a859,f784(f304(a859,x54411),x54412)),f120(a859))+~P85(f784(f784(f242(a859),x54412),x54411))
% 11.41/11.18 [5442]E(f134(a859,f784(f304(a859,x54421),x54422)),f120(a859))+~P85(f784(f784(f242(a859),x54422),x54421))
% 11.41/11.18 [5443]~P77(x54431)+E(f784(f313(x54431,x54431,f88(x54431)),f784(f267(x54431),x54432)),f784(f306(x54431),f784(f88(x54431),x54432)))
% 11.41/11.18 [5444]~P77(x54441)+E(f784(f313(x54441,x54441,f88(x54441)),f784(f306(x54441),x54442)),f784(f267(x54441),f784(f88(x54441),x54442)))
% 11.41/11.18 [5445]~P77(x54451)+E(f784(f313(x54451,x54451,f88(x54451)),f784(f303(x54451),x54452)),f784(f268(x54451),f784(f88(x54451),x54452)))
% 11.41/11.18 [5446]~P77(x54461)+E(f784(f313(x54461,x54461,f88(x54461)),f784(f268(x54461),x54462)),f784(f303(x54461),f784(f88(x54461),x54462)))
% 11.41/11.18 [5457]E(x54571,f187(f869(x54572,a852)))+P85(f784(f784(f347(x54572),f415(x54571,x54572)),x54571))
% 11.41/11.18 [5458]E(x54581,f187(f869(x54582,a852)))+P85(f784(f784(f347(x54582),f426(x54581,x54582)),x54581))
% 11.41/11.18 [5465]~P85(f784(f784(f243(a859),x54651),x54652))+P85(f784(f784(f242(a859),x54651),x54652))
% 11.41/11.18 [5466]~P85(f784(f784(f243(a859),x54661),x54662))+P85(f784(f784(f242(a859),x54661),x54662))
% 11.41/11.18 [5467]~P85(f784(f784(f243(a859),x54671),x54672))+P85(f784(f784(f242(a859),x54671),x54672))
% 11.41/11.18 [5468]~P85(f784(f784(f243(a859),x54681),x54682))+P85(f784(f784(f242(a859),x54681),x54682))
% 11.41/11.18 [5469]~P85(f784(f784(f243(a859),x54691),x54692))+P85(f784(f784(f242(a859),x54691),x54692))
% 11.41/11.18 [5470]~P85(f784(f784(f243(a1),x54701),x54702))+P85(f784(f784(f242(a1),x54701),x54702))
% 11.41/11.18 [5482]E(f62(x54821,x54822),f784(f784(f251(a1,a1),f2(a1)),x54821))+~P85(f784(f784(f243(a1),x54821),x54822))
% 11.41/11.18 [5483]E(f220(f784(f88(a1),x54831),f784(f88(a1),x54832)),f220(x54831,x54832))+~P85(f784(f784(f243(a1),x54832),f2(a1)))
% 11.41/11.18 [5495]E(x54951,x54952)+~E(f784(a5,f784(a160,f784(a22,x54951))),f784(a5,f784(a160,f784(a22,x54952))))
% 11.41/11.18 [5500]E(f62(x55001,x55002),f784(f784(f251(a1,a1),f2(a1)),x55001))+~P85(f784(f784(f242(a1),x55002),f2(a1)))
% 11.41/11.18 [5527]E(f60(a859,f784(f113(a859),x55271),f784(f113(a859),x55272)),f2(a859))+~P85(f784(a193,f784(f113(a1),x55271)))
% 11.41/11.18 [5542]P85(f784(f784(f242(a1),f2(a1)),f740(x55421)))+~P85(f784(x55421,f784(f109(a1),x55422)))
% 11.41/11.18 [5573]P37(f305(a1,x55731,x55732))+~P85(f784(f784(f242(a1),f2(a1)),x55731))
% 11.41/11.18 [5577]~P85(f784(f71(x55771),x55772))+P85(f784(f71(f869(x55771,a852)),f784(f311(x55771),x55772)))
% 11.41/11.18 [5590]E(f784(f784(f89(a1),x55901),f784(f109(a1),f800(x55902,x55901))),x55902)+~P85(f784(f784(f242(a1),x55901),x55902))
% 11.41/11.18 [5598]P85(f784(f784(f242(a859),x55981),x55982))+P85(f784(f784(f242(a859),f784(a160,x55982)),x55981))
% 11.41/11.18 [5643]E(f784(f784(f51(a859),f784(f113(a859),x56431)),f784(f113(a859),x56432)),f2(a859))+~P85(f784(a193,f784(f113(a1),x56431)))
% 11.41/11.18 [5644]E(f784(f784(f90(a859),f784(f113(a859),x56441)),f784(f113(a859),x56442)),f2(a859))+~P85(f784(f784(f243(a1),x56441),a92))
% 11.41/11.18 [5645]P85(f784(f784(f243(a859),x56451),f784(a160,x56452)))+~P85(f784(f784(f243(a859),x56451),x56452))
% 11.41/11.18 [5646]P85(f784(f784(f243(a859),x56461),f784(a160,x56462)))+~P85(f784(f784(f243(a859),x56461),x56462))
% 11.41/11.18 [5647]P85(f784(f784(f243(a859),x56471),f784(a160,x56472)))+~P85(f784(f784(f242(a859),x56471),x56472))
% 11.41/11.18 [5648]P85(f784(f784(f243(a859),x56481),f784(a160,x56482)))+~P85(f784(f784(f242(a859),x56481),x56482))
% 11.41/11.18 [5649]P85(f784(f784(f242(a859),x56491),f784(a160,x56492)))+~P85(f784(f784(f242(a859),x56491),x56492))
% 11.41/11.18 [5650]P85(f784(f784(f242(a859),x56501),f784(a160,x56502)))+~P85(f784(f784(f242(a859),x56501),x56502))
% 11.41/11.18 [5651]~E(x56511,x56512)+P85(f784(f784(f243(a1),x56511),f784(f784(f89(a1),x56512),f87(a1))))
% 11.41/11.18 [5654]E(f60(a1,x56541,x56542),f2(a1))+E(f784(f784(f3(a1),x56542),f60(a1,x56541,x56542)),f60(a1,f784(f88(a1),x56541),x56542))
% 11.41/11.18 [5662]E(x56621,f120(x56622))+P85(f784(f784(f347(x56622),f138(x56622,x56621)),f784(f164(x56622),x56621)))
% 11.41/11.18 [5673]E(f94(f868(a859,a859),f63(x56731,x56732)),f784(f784(f251(a859,a859),f2(a859)),x56731))+~P85(f784(f784(f243(a859),x56731),x56732))
% 11.41/11.18 [5674]E(f94(f868(a859,a859),f63(x56741,x56742)),f784(f784(f251(a859,a859),f2(a859)),x56741))+~P85(f784(f784(f243(a859),x56741),x56742))
% 11.41/11.18 [5714]E(f784(f784(f89(a859),f784(f113(a859),x57141)),f784(f113(a859),x57142)),f784(f113(a859),x57142))+~P85(f784(f784(f243(a1),x57141),a92))
% 11.41/11.18 [5715]E(f784(f784(f3(a859),f784(f113(a859),x57151)),f784(f113(a859),x57152)),f784(f113(a859),x57151))+~P85(f784(f784(f243(a1),x57152),a92))
% 11.41/11.18 [5720]E(f784(a160,f784(f784(f89(a859),x57201),f600(x57202,x57201))),x57202)+~P85(f784(f784(f243(a859),x57201),x57202))
% 11.41/11.18 [5721]E(f784(a160,f784(f784(f89(a859),x57211),f613(x57212,x57211))),x57212)+~P85(f784(f784(f243(a859),x57211),x57212))
% 11.41/11.18 [5728]~P85(f784(f784(f289(a1),x57281),x57282))+P85(f784(f784(f289(a1),x57281),f784(f88(a1),x57282)))
% 11.41/11.18 [5729]P85(f784(f784(f243(a859),f2(a859)),f612(x57291,x57292)))+~P85(f784(f784(f243(a859),x57292),x57291))
% 11.41/11.18 [5748]P85(f784(x57481,x57482))+~P85(f784(x57481,f784(a98,f614(x57482,x57481))))
% 11.41/11.18 [5756]~P85(f784(f784(f243(a859),x57561),f784(a160,x57562)))+P85(f784(f784(f242(a859),x57561),x57562))
% 11.41/11.18 [5804]E(f784(f784(f312(a859),x58041),f784(f304(a859,x58042),x58041)),f784(f304(a859,x58042),f784(a160,x58041)))+~P85(f784(f784(f242(a859),x58042),x58041))
% 11.41/11.18 [5809]E(x58091,f120(x58092))+E(f784(f784(f130(x58092),f121(x58092,x58091)),f784(f784(f144(x58092),f138(x58092,x58091)),f120(x58092))),x58091)
% 11.41/11.18 [5819]P85(f784(f71(x58191),x58192))+~P85(f784(f784(f243(a859),f2(a859)),f784(f50(x58191),x58192)))
% 11.41/11.18 [5820]P85(f784(f71(x58201),x58202))+~P85(f784(f784(f243(a859),f2(a859)),f784(f50(x58201),x58202)))
% 11.41/11.18 [5824]~E(x58241,f187(f869(x58242,a852)))+~P85(f784(f784(f243(a859),f2(a859)),f784(f50(x58242),x58241)))
% 11.41/11.18 [5832]~P85(f784(f784(f243(a859),x58321),x58322))+P85(f784(f784(f242(a859),f784(a160,x58321)),x58322))
% 11.41/11.18 [5833]~P85(f784(f784(f243(a859),x58331),x58332))+P85(f784(f784(f242(a859),f784(a160,x58331)),x58332))
% 11.41/11.18 [5834]~P85(f784(f784(f243(a859),x58341),x58342))+P85(f784(f784(f242(a859),f784(a160,x58341)),x58342))
% 11.41/11.18 [5843]E(x58431,f120(x58432))+P85(f784(f784(f347(x58432),f784(f135(x58432),x58431)),f784(f164(x58432),x58431)))
% 11.41/11.18 [5849]~P120(x58491)+P85(f784(f784(f243(x58491),x58492),f784(f784(f89(x58491),x58492),f87(x58491))))
% 11.41/11.18 [5851]~P79(x58511)+P85(f784(f784(f242(x58511),f784(f88(x58511),x58512)),f784(f84(x58511),x58512)))
% 11.41/11.18 [5863]P85(f784(f784(f289(a1),x58631),x58632))+~P85(f784(f784(f289(a1),x58631),f784(f88(a1),x58632)))
% 11.41/11.18 [5864]~E(x58641,x58642)+E(f292(a859,f289(a859),x58641,x58642),f784(f784(f312(a859),x58641),f187(f869(a859,a852))))
% 11.41/11.18 [5882]P85(f784(f71(a859),x58821))+~P85(f784(f784(f243(a859),f413(x58821,x58822)),x58822))
% 11.41/11.18 [5883]P85(f784(f71(a859),x58831))+~P85(f784(f784(f242(a859),f388(x58831,x58832)),x58832))
% 11.41/11.18 [5887]~P85(f784(f71(f868(x58871,x58871)),x58872))+P85(f784(f71(x58871),f784(f286(x58871),x58872)))
% 11.41/11.18 [5936]E(f292(a859,f289(a859),x59361,x59362),f187(f869(a859,a852)))+P85(f784(f784(f289(a859),x59361),x59362))
% 11.41/11.18 [5937]E(f292(a859,f289(a859),x59371,x59372),f187(f869(a859,a852)))+P85(f784(f784(f289(a859),x59371),x59372))
% 11.41/11.18 [5938]E(f169(f784(f113(a1),x59381),f784(f113(a1),x59382)),f120(a1))+P85(f784(f784(f242(a1),f784(f113(a1),x59381)),f784(f113(a1),x59382)))
% 11.41/11.18 [5943]~P85(f784(f784(f243(a859),x59432),f784(a160,x59431)))+~P85(f784(f784(f243(a859),x59431),x59432))
% 11.41/11.18 [5944]~P100(x59441)+E(f784(f784(f111(f869(x59441,a852)),f784(f303(x59441),x59442)),f784(f268(x59441),x59442)),f784(f784(f312(x59441),x59442),f187(f869(x59441,a852))))
% 11.41/11.18 [5946]E(f784(f784(f252(a859),f784(f113(a859),x59461)),f784(f113(a859),x59462)),f784(f784(f252(a859),f2(a859)),f784(f113(a859),x59462)))+~P85(f784(a193,f784(f113(a1),x59461)))
% 11.41/11.18 [5957]P85(f784(f71(x59571),x59572))+~P85(f784(f71(f869(x59571,a852)),f784(f311(x59571),x59572)))
% 11.41/11.18 [5979]P85(f784(f784(f243(a859),f784(a160,x59791)),f784(a160,x59792)))+~P85(f784(f784(f243(a859),x59791),x59792))
% 11.41/11.18 [5980]P85(f784(f784(f243(a859),f784(a160,x59801)),f784(a160,x59802)))+~P85(f784(f784(f243(a859),x59801),x59802))
% 11.41/11.18 [5981]P85(f784(f784(f243(a859),f784(a22,x59811)),f784(a22,x59812)))+~P85(f784(f784(f243(a108),x59811),x59812))
% 11.41/11.18 [5982]P85(f784(f784(f243(a108),f784(a5,x59821)),f784(a5,x59822)))+~P85(f784(f784(f243(a859),x59821),x59822))
% 11.41/11.18 [5983]P85(f784(f784(f242(a859),f784(a160,x59831)),f784(a160,x59832)))+~P85(f784(f784(f242(a859),x59831),x59832))
% 11.41/11.18 [5984]P85(f784(f784(f242(a859),f784(a22,x59841)),f784(a22,x59842)))+~P85(f784(f784(f242(a108),x59841),x59842))
% 11.41/11.18 [5985]P85(f784(f784(f242(a108),f784(a5,x59851)),f784(a5,x59852)))+~P85(f784(f784(f242(a859),x59851),x59852))
% 11.41/11.18 [5988]E(x59881,x59882)+~E(f784(f313(a859,a1,f109(a1)),x59881),f784(f313(a859,a1,f109(a1)),x59882))
% 11.41/11.18 [6004]P85(f784(f784(f243(a859),x60041),x60042))+~P85(f784(f784(f243(a859),f784(a160,x60041)),x60042))
% 11.41/11.18 [6005]P85(f784(f784(f243(a859),x60051),x60052))+~P85(f784(f784(f242(a859),f784(a160,x60051)),x60052))
% 11.41/11.18 [6006]P85(f784(f784(f243(a859),x60061),x60062))+~P85(f784(f784(f242(a859),f784(a160,x60061)),x60062))
% 11.41/11.18 [6007]P85(f784(f784(f243(a859),x60071),x60072))+~P85(f784(f784(f242(a859),f784(a160,x60071)),x60072))
% 11.41/11.18 [6008]P85(f784(f784(f242(a859),x60081),x60082))+~P85(f784(f784(f242(a859),f784(a160,x60081)),x60082))
% 11.41/11.18 [6025]E(f60(a1,x60251,x60252),f2(a1))+E(f784(f784(f3(a1),f60(a1,x60251,x60252)),x60252),f60(a1,x60251,f784(f88(a1),x60252)))
% 11.41/11.18 [6095]E(f784(f50(f869(x60951,a852)),f784(f311(x60951),x60952)),f784(f784(f252(a859),f784(a160,f784(a160,f2(a859)))),f784(f50(x60951),x60952)))+~P85(f784(f71(x60951),x60952))
% 11.41/11.18 [6098]E(x60981,f120(x60982))+E(f784(f784(f155(x60982),x60981),f784(f784(f3(a859),f784(f188(f860(x60982)),x60981)),f87(a859))),f138(x60982,x60981))
% 11.41/11.18 [6122]E(x61221,f120(x61222))+E(f784(f784(f130(x61222),f784(f163(x61222),x61221)),f784(f784(f144(x61222),f784(f135(x61222),x61221)),f120(x61222))),f784(f161(x61222),x61221))
% 11.41/11.18 [6123]~P85(f784(f187(f869(x61231,a852)),x61232))+P85(f784(f784(f347(x61231),x61232),f187(f869(x61231,a852))))
% 11.41/11.18 [6153]~P85(f784(f71(x61531),f52(f869(x61531,a852),x61532)))+P85(f784(f71(f869(x61531,a852)),x61532))
% 11.41/11.18 [6174]P85(f784(f784(f242(a859),f784(f113(a859),x61741)),f784(f113(a859),x61742)))+~P85(f784(f784(f242(a1),x61741),a92))
% 11.41/11.18 [6194]~P85(f784(f784(f243(a1),x61941),x61942))+P85(f784(f784(f243(a1),x61941),f784(f784(f89(a1),x61942),f87(a1))))
% 11.41/11.18 [6195]~P85(f784(f784(f242(a1),x61951),x61952))+P85(f784(f784(f243(a1),x61951),f784(f784(f89(a1),x61952),f87(a1))))
% 11.41/11.18 [6196]~P85(f784(f784(f243(a1),x61961),x61962))+P85(f784(f784(f242(a1),x61961),f784(f784(f3(a1),x61962),f87(a1))))
% 11.41/11.18 [6198]~P85(f784(f784(f243(a859),x61981),x61982))+P85(f784(f784(f243(a1),f784(f109(a1),x61981)),f784(f109(a1),x61982)))
% 11.41/11.18 [6199]~P85(f784(f784(f243(a859),x61991),x61992))+P85(f784(f784(f243(a1),f784(f109(a1),x61991)),f784(f109(a1),x61992)))
% 11.41/11.18 [6200]~P85(f784(f784(f243(a1),x62001),x62002))+P85(f784(f784(f243(a1),f784(f113(a1),x62001)),f784(f113(a1),x62002)))
% 11.41/11.18 [6201]~P85(f784(f784(f242(a1),x62011),x62012))+P85(f784(f784(f242(a859),f784(f113(a859),x62011)),f784(f113(a859),x62012)))
% 11.41/11.18 [6202]~P85(f784(f784(f242(a859),x62021),x62022))+P85(f784(f784(f242(a1),f784(f109(a1),x62021)),f784(f109(a1),x62022)))
% 11.41/11.18 [6203]~P85(f784(f784(f242(a859),x62031),x62032))+P85(f784(f784(f242(a1),f784(f109(a1),x62031)),f784(f109(a1),x62032)))
% 11.41/11.18 [6204]~P85(f784(f784(f242(a1),x62041),x62042))+P85(f784(f784(f242(a1),f784(f113(a1),x62041)),f784(f113(a1),x62042)))
% 11.41/11.18 [6205]~P85(f784(f784(f289(a859),x62051),x62052))+P85(f784(f784(f289(a1),f784(f109(a1),x62051)),f784(f109(a1),x62052)))
% 11.41/11.18 [6206]~P85(f784(f784(f289(a859),x62061),x62062))+P85(f784(f784(f289(a1),f784(f109(a1),x62061)),f784(f109(a1),x62062)))
% 11.41/11.18 [6213]~E(x62132,f187(f869(x62131,a852)))+P85(f784(f784(f242(f869(x62131,a852)),x62132),f187(f869(x62131,a852))))
% 11.41/11.18 [6221]~P85(f784(f784(f242(a859),x62211),x62212))+~P85(f784(f784(f242(a859),f784(a160,x62212)),x62211))
% 11.41/11.18 [6267]~P85(f784(f784(f243(a859),f784(a160,x62671)),f784(a160,x62672)))+P85(f784(f784(f243(a859),x62671),x62672))
% 11.41/11.18 [6268]~P85(f784(f784(f243(a859),f784(a160,x62681)),f784(a160,x62682)))+P85(f784(f784(f243(a859),x62681),x62682))
% 11.41/11.18 [6269]~P85(f784(f784(f243(a108),f784(a5,x62691)),f784(a5,x62692)))+P85(f784(f784(f243(a859),x62691),x62692))
% 11.41/11.18 [6270]~P85(f784(f784(f243(a859),f784(a114,x62701)),f784(a114,x62702)))+P85(f784(f784(f243(a1),x62701),x62702))
% 11.41/11.18 [6271]~P85(f784(f784(f243(a859),f784(a22,x62711)),f784(a22,x62712)))+P85(f784(f784(f243(a108),x62711),x62712))
% 11.41/11.18 [6272]~P85(f784(f784(f242(a859),f784(a160,x62721)),f784(a160,x62722)))+P85(f784(f784(f242(a859),x62721),x62722))
% 11.41/11.18 [6273]~P85(f784(f784(f242(a108),f784(a5,x62731)),f784(a5,x62732)))+P85(f784(f784(f242(a859),x62731),x62732))
% 11.41/11.18 [6274]~P85(f784(f784(f242(a859),f784(a22,x62741)),f784(a22,x62742)))+P85(f784(f784(f242(a108),x62741),x62742))
% 11.41/11.18 [6291]~P85(f784(f784(f289(a859),x62912),x62911))+P85(f784(f784(f347(a859),x62911),f296(a859,f289(a859),x62912)))
% 11.41/11.18 [6292]~P85(f784(f784(f289(a859),x62921),x62922))+P85(f784(f784(f347(a859),x62921),f298(a859,f289(a859),x62922)))
% 11.41/11.18 [6297]~P85(f784(f784(f347(x62971),x62972),f187(f869(x62971,a852))))+P85(f784(f187(f869(x62971,a852)),x62972))
% 11.41/11.18 [6318]~P85(f784(f784(f243(a859),f784(a114,x63182)),f784(a114,x63181)))+P85(f784(f784(f243(a1),f2(a1)),x63181))
% 11.41/11.18 [6329]~E(f60(a1,f784(f113(a1),x63292),f784(f113(a1),x63291)),f2(a1))+P85(f784(f784(f289(a1),f784(f113(a1),x63291)),f784(f113(a1),x63292)))
% 11.41/11.18 [6347]P85(f784(f784(f242(a1),f2(a1)),f60(a1,x63471,x63472)))+~P85(f784(f784(f243(a1),f2(a1)),x63472))
% 11.41/11.18 [6348]P85(f784(f784(f242(a1),f2(a1)),f60(a1,x63481,x63482)))+~P85(f784(f784(f243(a1),f2(a1)),x63482))
% 11.41/11.18 [6516]P35(x65161,x65162)+~E(f784(f784(f291(x65161,x65161,x65161),x65162),x65162),f187(f869(f868(x65161,x65161),a852)))
% 11.41/11.18 [6532]~P35(x65321,x65322)+P35(x65321,f784(f784(f291(x65321,x65321,x65321),x65322),x65322))
% 11.41/11.18 [6544]P85(f784(f784(f243(a1),x65441),x65442))+~P85(f784(f784(f242(a1),x65441),f784(f784(f3(a1),x65442),f87(a1))))
% 11.41/11.18 [6545]P85(f784(f784(f242(a1),x65451),x65452))+~P85(f784(f784(f243(a1),x65451),f784(f784(f89(a1),x65452),f87(a1))))
% 11.41/11.18 [6547]P85(f784(f784(f243(a859),x65471),x65472))+~P85(f784(f784(f243(a1),f784(f109(a1),x65471)),f784(f109(a1),x65472)))
% 11.41/11.18 [6548]P85(f784(f784(f243(a859),x65481),x65482))+~P85(f784(f784(f243(a1),f784(f109(a1),x65481)),f784(f109(a1),x65482)))
% 11.41/11.18 [6549]P85(f784(f784(f243(a1),x65491),x65492))+~P85(f784(f784(f243(a859),f784(f113(a859),x65491)),f784(f113(a859),x65492)))
% 11.41/11.18 [6550]P85(f784(f784(f243(a1),x65501),x65502))+~P85(f784(f784(f243(a1),f784(f113(a1),x65501)),f784(f113(a1),x65502)))
% 11.41/11.18 [6551]P85(f784(f784(f242(a859),x65511),x65512))+~P85(f784(f784(f242(a1),f784(f109(a1),x65511)),f784(f109(a1),x65512)))
% 11.41/11.18 [6552]P85(f784(f784(f242(a859),x65521),x65522))+~P85(f784(f784(f242(a1),f784(f109(a1),x65521)),f784(f109(a1),x65522)))
% 11.41/11.18 [6553]P85(f784(f784(f242(a1),x65531),x65532))+~P85(f784(f784(f242(a1),f784(f113(a1),x65531)),f784(f113(a1),x65532)))
% 11.41/11.18 [6554]P85(f784(f784(f289(a859),x65541),x65542))+~P85(f784(f784(f289(a1),f784(f109(a1),x65541)),f784(f109(a1),x65542)))
% 11.41/11.18 [6555]P85(f784(f784(f289(a859),x65551),x65552))+~P85(f784(f784(f289(a1),f784(f109(a1),x65551)),f784(f109(a1),x65552)))
% 11.41/11.18 [6610]E(f60(a1,f784(f113(a1),x66101),f784(f113(a1),x66102)),f2(a1))+~P85(f784(f784(f289(a1),f784(f113(a1),x66102)),f784(f113(a1),x66101)))
% 11.41/11.18 [6624]~E(f292(a859,f289(a859),x66241,x66242),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x66241),x66242))
% 11.41/11.18 [6625]~E(f292(a859,f289(a859),x66251,x66252),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x66251),x66252))
% 11.41/11.18 [6651]P85(f784(f784(f289(a859),x66511),x66512))+~P85(f784(f784(f347(a859),x66512),f296(a859,f289(a859),x66511)))
% 11.41/11.18 [6652]P85(f784(f784(f289(a859),x66521),x66522))+~P85(f784(f784(f347(a859),x66521),f298(a859,f289(a859),x66522)))
% 11.41/11.18 [6653]~E(f778(x66532,x66531),f120(x66531))+E(f784(f136(f860(x66531),f860(x66531),f130(x66531),f120(x66531)),x66532),f120(x66531))
% 11.41/11.18 [6654]~E(f780(x66542,x66541),f120(x66541))+E(f784(f136(f860(x66541),f860(x66541),f130(x66541),f120(x66541)),x66542),f120(x66541))
% 11.41/11.18 [6660]~P6(x66601)+E(f784(f136(x66601,x66601,f111(x66601),f249(x66601)),x66602),f53(x66601,f784(f164(x66601),x66602)))
% 11.41/11.18 [6661]~P6(x66611)+E(f784(f136(x66611,x66611,f110(x66611),f187(x66611)),x66612),f52(x66611,f784(f164(x66611),x66612)))
% 11.41/11.18 [6673]E(x66731,f2(a108))+E(f784(f784(f89(a859),f784(a22,f784(f784(f3(a108),x66731),f87(a108)))),f784(a160,x66732)),f784(f784(f89(a859),f784(a22,x66731)),x66732))
% 11.41/11.18 [6725]P85(f784(f784(f243(a1),f784(f784(f3(a1),x67251),x67252)),f2(a1)))+~P85(f784(f784(f243(a1),x67251),x67252))
% 11.41/11.18 [6752]~P101(x67521)+E(f784(f784(f110(f869(x67521,a852)),f784(f784(f312(x67521),x67522),f187(f869(x67521,a852)))),f784(f306(x67521),x67522)),f784(f268(x67521),x67522))
% 11.41/11.18 [6834]~P57(x68341,x68342)+P35(x68341,f784(f266(f868(x68341,x68341)),f784(f261(x68341,x68341,a852),x68342)))
% 11.41/11.18 [6835]~P57(x68351,x68352)+P55(x68351,f784(f266(f868(x68351,x68351)),f784(f261(x68351,x68351,a852),x68352)))
% 11.41/11.18 [6836]E(x68361,f187(f869(x68362,a852)))+~P85(f784(f784(f242(f869(x68362,a852)),x68361),f187(f869(x68362,a852))))
% 11.41/11.18 [6920]~P85(f784(f784(f243(a859),f2(a859)),x69202))+P85(f784(f784(f243(a859),f60(a859,x69201,x69202)),x69202))
% 11.41/11.18 [6921]~P85(f784(f784(f243(a1),f2(a1)),x69212))+P85(f784(f784(f243(a1),f60(a1,x69211,x69212)),x69212))
% 11.41/11.18 [6922]~P85(f784(f784(f243(a1),f2(a1)),x69222))+P85(f784(f784(f243(a1),f60(a1,x69221,x69222)),x69222))
% 11.41/11.18 [6923]~P85(f784(f784(f243(a859),f2(a859)),x69232))+P85(f784(f784(f242(a859),f60(a859,x69231,x69232)),x69232))
% 11.41/11.18 [6924]~P85(f784(f784(f242(a1),f2(a1)),x69241))+P85(f784(f784(f242(a1),f60(a1,x69241,x69242)),x69241))
% 11.41/11.18 [6995]~P100(x69951)+E(f784(f784(f3(f869(x69951,a852)),f784(f784(f312(x69951),x69952),f187(f869(x69951,a852)))),f784(f267(x69951),x69952)),f784(f784(f312(x69951),x69952),f187(f869(x69951,a852))))
% 11.41/11.18 [7073]~P48(x70731,x70732)+P46(x70731,f249(f869(x70731,a852)),f784(f266(f868(x70731,x70731)),f784(f261(x70731,x70731,a852),x70732)))
% 11.41/11.18 [7074]P85(f784(x70741,x70742))+P85(f784(f784(f347(f869(f868(a859,a859),a852)),f614(x70742,x70741)),a107))
% 11.41/11.18 [7115]E(f784(f784(f130(a859),f134(a859,f784(f304(a859,x71151),x71152))),f784(f784(f144(a859),x71152),f120(a859))),f134(a859,f784(f304(a859,x71151),f784(a160,x71152))))+~P85(f784(f784(f242(a859),x71151),x71152))
% 11.41/11.18 [7116]E(f784(f784(f130(a859),f134(a859,f784(f304(a859,x71161),x71162))),f784(f784(f144(a859),x71162),f120(a859))),f134(a859,f784(f304(a859,x71161),f784(a160,x71162))))+~P85(f784(f784(f242(a859),x71161),x71162))
% 11.41/11.18 [7273]E(x72731,f2(a859))+~E(f784(f136(a859,a859,f89(a859),x72731),x72732),f2(a859))
% 11.41/11.18 [7302]~P85(f784(f784(f243(a1),f784(f784(f3(a1),x73021),x73022)),f2(a1)))+P85(f784(f784(f243(a1),x73021),x73022))
% 11.41/11.18 [7332]P35(x73321,x73322)+~P35(x73321,f784(f784(f291(x73321,x73321,x73321),x73322),x73322))
% 11.41/11.18 [7364]~P85(f784(f784(f242(a859),f784(a160,x73641)),x73642))+P85(f182(a852,a185,f784(f242(a859),x73641),x73642))
% 11.41/11.18 [7523]P26(a859,a859,f784(f784(f9(a859,a859,a859),f3(a859)),x75231),x75232)+P85(f784(f784(f347(a859),f619(x75231,x75232)),x75232))
% 11.41/11.18 [7581]E(f784(f784(f784(f75(a859,x75811,f89(a859)),f784(f18(a859,x75811),f87(a859))),f2(a859)),x75812),f784(f50(x75811),x75812))+~P85(f784(f71(x75811),x75812))
% 11.41/11.18 [7582]E(f784(f784(f784(f75(a859,x75821,f89(a859)),f784(f18(a859,x75821),f87(a859))),f2(a859)),x75822),f784(f50(x75821),x75822))+~P85(f784(f71(x75821),x75822))
% 11.41/11.18 [7625]P26(a859,a859,f784(f784(f9(a859,a859,a859),f3(a859)),x76251),x76252)+~P85(f784(f784(f242(a859),x76251),f619(x76251,x76252)))
% 11.41/11.18 [7681]P35(x76811,x76812)+P85(f784(f784(f242(f869(x76811,a852)),f610(x76812,x76811)),f784(f287(x76811,x76811,x76812),f610(x76812,x76811))))
% 11.41/11.18 [7685]P57(x76851,x76852)+~P35(x76851,f784(f266(f868(x76851,x76851)),f784(f261(x76851,x76851,a852),x76852)))
% 11.41/11.18 [7757]P85(f784(f784(f242(a859),f784(a160,x77571)),x77572))+~P85(f182(a852,a185,f784(f242(a859),x77571),x77572))
% 11.41/11.18 [7813]P85(f784(f784(f347(f868(a859,a859)),f784(f784(f251(a859,a859),x78131),x78132)),f310(a859,a336)))+~P85(f784(f784(f242(a859),x78131),x78132))
% 11.41/11.18 [7907]P48(x79071,x79072)+~P46(x79071,f249(f869(x79071,a852)),f784(f266(f868(x79071,x79071)),f784(f261(x79071,x79071,a852),x79072)))
% 11.41/11.18 [8159]~P35(x81591,f784(f288(x81591,x81591),x81592))+P35(x81591,f784(f288(x81591,x81591),f784(f784(f291(x81591,x81591,x81591),x81592),f310(x81591,x81592))))
% 11.41/11.18 [8277]P85(f784(f71(f868(x82771,x82771)),f784(f784(f291(x82771,x82771,x82771),x82772),f310(x82771,x82772))))+~P85(f784(f71(f868(x82771,x82771)),x82772))
% 11.41/11.18 [8307]E(x83071,f2(a1))+P85(f784(f64(x83072,x83071),f784(f784(f251(a1,a1),f784(f784(f51(a1),x83072),x83071)),f60(a1,x83072,x83071))))
% 11.41/11.18 [8321]~P85(f784(f784(f347(f868(a859,a859)),f784(f784(f251(a859,a859),x83211),x83212)),f310(a859,a336)))+P85(f784(f784(f242(a859),x83211),x83212))
% 11.41/11.18 [8342]~P67(x83421)+E(f784(f136(x83421,x83421,f784(f9(x83421,x83421,x83421),f89(x83421)),f2(x83421)),f784(f162(x83421),x83422)),f784(f136(x83421,x83421,f89(x83421),f2(x83421)),x83422))
% 11.41/11.18 [8616]P85(f784(f784(f347(f868(a859,a859)),f784(f784(f251(a859,a859),x86161),x86162)),f784(f784(f291(a859,a859,a859),a336),f310(a859,a336))))+~P85(f784(f784(f243(a859),x86161),x86162))
% 11.41/11.18 [8658]~P85(f784(f71(f868(x86581,x86581)),f784(f784(f291(x86581,x86581,x86581),x86582),f310(x86581,x86582))))+P85(f784(f71(f868(x86581,x86581)),x86582))
% 11.41/11.18 [8880]P55(x88801,x88802)+P85(f784(f784(f347(f868(x88801,x88801)),f784(f784(f251(x88801,x88801),f645(x88802,x88801)),f645(x88802,x88801))),f784(f784(f291(x88801,x88801,x88801),x88802),f310(x88801,x88802))))
% 11.41/11.18 [8881]P55(x88811,x88812)+P85(f784(f784(f347(f868(x88811,x88811)),f784(f784(f251(x88811,x88811),f653(x88812,x88811)),f653(x88812,x88811))),f784(f784(f291(x88811,x88811,x88811),x88812),f310(x88811,x88812))))
% 11.41/11.18 [8989]~P85(f784(f784(f347(f868(a859,a859)),f784(f784(f251(a859,a859),x89891),x89892)),f784(f784(f291(a859,a859,a859),a336),f310(a859,a336))))+P85(f784(f784(f243(a859),x89891),x89892))
% 11.41/11.18 [4990]~P89(x49901)+E(f784(f784(f89(x49901),f784(f113(x49901),a92)),x49902),x49902)
% 11.41/11.18 [5020]~P70(x50201)+E(f784(f784(f89(x50201),f784(f88(x50201),x50202)),x50202),f2(x50201))
% 11.41/11.18 [5021]~P3(x50211)+E(f784(f784(f89(x50211),f784(f88(x50211),x50212)),x50212),f2(x50211))
% 11.41/11.18 [5022]~P91(x50221)+E(f784(f784(f110(x50221),f784(f88(x50221),x50222)),x50222),f249(x50221))
% 11.41/11.18 [5023]~P91(x50231)+E(f784(f784(f111(x50231),f784(f88(x50231),x50232)),x50232),f187(x50231))
% 11.41/11.18 [5053]~P89(x50531)+E(f784(f784(f90(x50531),f784(f113(x50531),a106)),x50532),f784(f88(x50531),x50532))
% 11.41/11.18 [5209]~P105(x52091)+E(f784(f784(f90(x52091),f784(f88(x52091),f87(x52091))),x52092),f784(f88(x52091),x52092))
% 11.41/11.18 [5250]E(f784(f84(a1),x52501),f87(a1))+~E(f784(f84(a1),f784(f784(f90(a1),x52501),x52502)),f87(a1))
% 11.41/11.18 [5338]~P89(x53381)+E(f784(f784(f89(x53381),f87(x53381)),f784(f113(x53381),x53382)),f784(f113(x53381),f784(f784(f3(a1),x53382),a106)))
% 11.41/11.18 [5393]~P93(x53931)+E(f15(x53931,f784(f784(f312(x53931),x53932),f187(f869(x53931,a852)))),x53932)
% 11.41/11.18 [5394]~P101(x53941)+E(f16(x53941,f784(f784(f312(x53941),x53942),f187(f869(x53941,a852)))),x53942)
% 11.41/11.18 [5395]~P101(x53951)+E(f17(x53951,f784(f784(f312(x53951),x53952),f187(f869(x53951,a852)))),x53952)
% 11.41/11.18 [5396]~P93(x53961)+E(f12(x53961,f784(f784(f312(x53961),x53962),f187(f869(x53961,a852)))),x53962)
% 11.41/11.18 [5397]~P6(x53971)+E(f53(x53971,f784(f784(f312(x53971),x53972),f187(f869(x53971,a852)))),x53972)
% 11.41/11.18 [5398]~P6(x53981)+E(f52(x53981,f784(f784(f312(x53981),x53982),f187(f869(x53981,a852)))),x53982)
% 11.41/11.18 [5420]E(f784(f784(f89(a859),x54201),f784(f784(f3(a859),x54202),x54201)),x54202)+P85(f784(f784(f243(a859),x54202),x54201))
% 11.41/11.18 [5452]E(x54521,f120(x54522))+P85(f784(f784(f243(a859),f2(a859)),f784(f188(f860(x54522)),x54521)))
% 11.41/11.18 [5570]~P101(x55701)+E(f13(x55701,f186(x55701),f784(f784(f312(x55701),x55702),f187(f869(x55701,a852)))),x55702)
% 11.41/11.18 [5571]~P101(x55711)+E(f14(x55711,f246(x55711),f784(f784(f312(x55711),x55712),f187(f869(x55711,a852)))),x55712)
% 11.41/11.18 [5632]E(f784(f784(f89(a859),x56321),f784(f784(f3(a859),x56322),x56321)),x56322)+~P85(f784(f784(f242(a859),x56321),x56322))
% 11.41/11.18 [5633]E(f784(f784(f90(a1),x56331),f784(f784(f51(a1),x56332),x56331)),x56332)+~P85(f784(f784(f289(a1),x56331),x56332))
% 11.41/11.18 [5634]E(f784(f784(f3(a859),x56341),f784(f784(f3(a859),x56341),x56342)),x56342)+~P85(f784(f784(f242(a859),x56342),x56341))
% 11.41/11.18 [5652]E(f60(a859,f784(f784(f3(a859),x56521),x56522),x56522),f60(a859,x56521,x56522))+P85(f784(f784(f243(a859),x56521),x56522))
% 11.41/11.18 [5653]E(f60(a859,f784(f784(f3(a859),x56531),x56532),x56532),f60(a859,x56531,x56532))+P85(f784(f784(f243(a859),x56531),x56532))
% 11.41/11.18 [5663]E(f784(f88(a1),f784(f784(f51(a1),x56631),f784(f88(a1),x56632))),f295(x56631,x56632))+P85(f784(f784(f242(a1),f2(a1)),x56632))
% 11.41/11.18 [5665]~E(x56652,f2(a859))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f252(a859),x56651),x56652)))
% 11.41/11.18 [5725]~P89(x57251)+E(f784(f784(f89(x57251),f784(f88(x57251),f87(x57251))),f784(f113(x57251),x57252)),f784(f113(x57251),f784(f784(f89(a1),x57252),a106)))
% 11.41/11.18 [5726]E(f784(f784(f252(a859),f784(f113(a859),x57261)),x57262),f784(f784(f252(a859),f2(a859)),x57262))+~P85(f784(a193,f784(f113(a1),x57261)))
% 11.41/11.18 [5826]E(f784(f135(a859),f134(a859,f784(f304(a859,x58261),x58262))),x58261)+~P85(f784(f784(f243(a859),x58261),x58262))
% 11.41/11.18 [5844]E(f784(f784(f90(a859),f784(f113(a859),x58441)),f784(f113(a859),x58442)),f784(f113(a859),f784(f784(f90(a1),x58441),x58442)))+P85(f784(f784(f243(a1),x58441),a92))
% 11.41/11.18 [5850]~P121(x58501)+P85(f784(f784(f242(x58501),f2(x58501)),f784(f784(f90(x58501),x58502),x58502)))
% 11.41/11.18 [5862]E(f784(f784(f3(a859),f784(a160,x58621)),x58622),f784(a160,f784(f784(f3(a859),x58621),x58622)))+~P85(f784(f784(f242(a859),x58622),x58621))
% 11.41/11.18 [5865]E(f60(a859,f784(f784(f3(a859),x58651),x58652),x58652),f60(a859,x58651,x58652))+~P85(f784(f784(f242(a859),x58652),x58651))
% 11.41/11.18 [5916]E(f784(f784(f252(a859),f784(a114,x59161)),x59162),f784(a114,f784(f784(f252(a1),x59161),x59162)))+~P85(f784(f784(f242(a1),f2(a1)),x59161))
% 11.41/11.18 [5917]E(f784(f784(f252(a859),f784(a114,x59171)),x59172),f784(a114,f784(f784(f252(a1),x59171),x59172)))+~P85(f784(f784(f242(a1),f2(a1)),x59171))
% 11.41/11.18 [5932]P85(f784(f132(x59321),x59322))+P85(f784(f784(f243(a859),f734(x59322,x59321)),f784(f188(f860(x59321)),x59322)))
% 11.41/11.18 [5933]P85(f784(f132(x59331),x59332))+P85(f784(f784(f243(a859),f738(x59332,x59331)),f784(f188(f860(x59331)),x59332)))
% 11.41/11.18 [5948]~P85(f784(f784(f289(a1),x59481),x59482))+P85(f784(f784(f289(a1),f784(f88(a1),x59481)),x59482))
% 11.41/11.18 [5951]~E(x59511,f120(x59512))+~P85(f784(f784(f243(a859),f2(a859)),f784(f188(f860(x59512)),x59511)))
% 11.41/11.18 [5964]E(f138(a859,f134(a859,f784(f304(a859,x59641),x59642))),f784(f784(f3(a859),x59642),f87(a859)))+~P85(f784(f784(f243(a859),x59641),x59642))
% 11.41/11.18 [5967]E(f784(f784(f89(a1),x59671),f784(f109(a1),f784(a160,f650(x59672,x59671)))),x59672)+~P85(f784(f784(f243(a1),x59671),x59672))
% 11.41/11.18 [5973]E(x59731,f2(a859))+E(f784(f784(f90(a859),x59732),f784(f784(f252(a859),x59732),f784(f784(f3(a859),x59731),f87(a859)))),f784(f784(f252(a859),x59732),x59731))
% 11.41/11.18 [5998]E(f784(f784(f90(a859),f784(a114,x59981)),f784(a114,x59982)),f784(a114,f784(f784(f90(a1),x59981),x59982)))+~P85(f784(f784(f242(a1),f2(a1)),x59981))
% 11.41/11.18 [5999]E(f784(f784(f51(a859),f784(a114,x59991)),f784(a114,x59992)),f784(a114,f784(f784(f51(a1),x59991),x59992)))+~P85(f784(f784(f242(a1),f2(a1)),x59991))
% 11.41/11.18 [6013]~P86(x60131)+E(f784(f784(f89(x60131),x60132),x60132),f784(f784(f90(x60131),f784(f784(f89(x60131),f87(x60131)),f87(x60131))),x60132))
% 11.41/11.18 [6032]E(f784(f784(f51(a1),f784(f84(a1),x60321)),f784(f84(a1),x60322)),f784(f84(a1),f784(f784(f51(a1),x60321),x60322)))+~P85(f784(f784(f289(a1),x60322),x60321))
% 11.41/11.18 [6033]E(f784(f784(f3(a1),f784(f109(a1),x60331)),f784(f109(a1),x60332)),f784(f109(a1),f784(f784(f3(a859),x60331),x60332)))+~P85(f784(f784(f242(a859),x60332),x60331))
% 11.41/11.18 [6035]E(f784(f784(f251(a1,a1),f784(f113(a1),a106)),f784(f784(f89(a1),x60351),x60352)),f65(x60351,x60352))+~P85(f784(f784(f242(a1),x60352),f2(a1)))
% 11.41/11.18 [6073]E(f170(x60731,x60732),f120(f860(x60731)))+P85(f784(f784(f347(f860(x60731)),f733(x60732,x60731)),f784(f164(f860(x60731)),x60732)))
% 11.41/11.18 [6137]~P85(f784(f784(f289(a859),x61371),x61372))+P85(f784(f784(f289(a859),x61371),f784(f784(f89(a859),x61372),x61371)))
% 11.41/11.18 [6159]E(f784(f784(f144(a1),x61591),f169(f784(f784(f89(a1),x61591),f87(a1)),x61592)),f169(x61591,x61592))+~P85(f784(f784(f242(a1),x61591),x61592))
% 11.41/11.18 [6197]~P85(f784(f784(f243(a859),x61972),x61971))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f3(a859),x61971),x61972)))
% 11.41/11.18 [6228]~P85(f784(f784(f243(a859),x62281),f784(a114,x62282)))+P85(f784(f784(f243(a1),f784(f109(a1),x62281)),x62282))
% 11.41/11.18 [6229]P85(f784(f784(f289(a1),x62291),x62292))+~P85(f784(f784(f289(a1),f784(f88(a1),x62291)),x62292))
% 11.41/11.18 [6258]~P101(x62581)+E(f784(f784(f110(f869(x62581,a852)),f784(f267(x62581),x62582)),f784(f784(f312(x62581),x62582),f187(f869(x62581,a852)))),f784(f303(x62581),x62582))
% 11.41/11.18 [6259]~P85(f784(f784(f243(a859),f2(a859)),x62592))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f89(a859),x62591),x62592)))
% 11.41/11.18 [6260]~P85(f784(f784(f243(a859),f2(a859)),x62601))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f89(a859),x62601),x62602)))
% 11.41/11.18 [6261]~P85(f784(f784(f243(a859),f2(a859)),x62611))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f252(a859),x62611),x62612)))
% 11.41/11.18 [6262]~P85(f784(f784(f242(a1),f2(a1)),x62621))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f252(a1),x62621),x62622)))
% 11.41/11.18 [6290]~E(f784(x62901,f2(a859)),f2(a859))+E(f784(f784(f8(a859,a859),x62901),f305(a859,f784(a160,f2(a859)),x62902)),f784(f784(f8(a859,a859),x62901),f305(a859,f2(a859),x62902)))
% 11.41/11.18 [6356]~P89(x63561)+E(f784(f784(f90(x63561),f784(f784(f89(x63561),f87(x63561)),f87(x63561))),f784(f113(x63561),x63562)),f784(f113(x63561),f784(f784(f89(a1),x63562),x63562)))
% 11.41/11.18 [6378]E(f784(f784(f312(a1),x63781),f305(a1,f784(f784(f89(a1),x63781),f87(a1)),x63782)),f305(a1,x63781,x63782))+P85(f784(f784(f243(a1),x63782),x63781))
% 11.41/11.18 [6379]P85(f784(f784(f243(a859),x63791),f784(a114,x63792)))+~P85(f784(f784(f243(a1),f784(f109(a1),x63791)),x63792))
% 11.41/11.18 [6481]P85(f784(f784(f289(a859),x64811),x64812))+~P85(f784(f784(f289(a859),x64811),f784(f784(f89(a859),x64812),x64811)))
% 11.41/11.18 [6487]E(f784(a114,f784(f784(f51(a1),f784(f113(a1),x64871)),f784(f113(a1),x64872))),f784(f784(f51(a859),f784(f113(a859),x64871)),f784(f113(a859),x64872)))+P85(f784(a193,f784(f113(a1),x64871)))
% 11.41/11.18 [6488]E(f784(a114,f784(f784(f252(a1),f784(f113(a1),x64881)),f784(f113(a859),x64882))),f784(f784(f252(a859),f784(f113(a859),x64881)),f784(f113(a859),x64882)))+P85(f784(a193,f784(f113(a1),x64881)))
% 11.41/11.18 [6546]P85(f784(f784(f243(a859),x65461),x65462))+~P85(f784(f784(f243(a859),f2(a859)),f784(f784(f3(a859),x65462),x65461)))
% 11.41/11.18 [6589]P85(f784(f784(f243(a859),f2(a859)),x65891))+~P85(f784(f784(f243(a859),f2(a859)),f784(f784(f90(a859),x65892),x65891)))
% 11.41/11.18 [6590]P85(f784(f784(f243(a859),f2(a859)),x65901))+~P85(f784(f784(f243(a859),f2(a859)),f784(f784(f90(a859),x65901),x65902)))
% 11.41/11.18 [6604]E(f134(a859,f784(f304(a859,f784(f113(a859),x66041)),f784(f113(a859),x66042))),f120(a859))+P85(f784(f784(f243(a859),f784(f113(a859),x66041)),f784(f113(a859),x66042)))
% 11.41/11.18 [6606]~P85(f784(f784(f242(a1),x66061),f2(a1)))+E(f784(f784(f90(a859),f784(a114,f784(f88(a1),x66061))),f784(a114,f784(f88(a1),x66062))),f784(a114,f784(f784(f90(a1),x66061),x66062)))
% 11.41/11.18 [6671]~E(x66712,f187(f869(x66711,a852)))+P85(f784(f784(f242(f869(x66711,a852)),x66712),f784(f88(f869(x66711,a852)),x66712)))
% 11.41/11.18 [6734]~P89(x67341)+E(f784(f784(f89(x67341),f784(f784(f89(x67341),f2(x67341)),f784(f113(x67341),x67342))),f784(f113(x67341),x67342)),f784(f113(x67341),f784(f784(f89(a1),x67342),x67342)))
% 11.41/11.18 [6743]~P85(f784(f784(f289(a1),f784(f109(a1),x67431)),x67432))+P85(f784(f784(f289(a859),x67431),f784(a114,f784(f84(a1),x67432))))
% 11.41/11.18 [6793]~P85(f784(f784(f243(a1),x67931),x67932))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x67931),f87(a1))),x67932))
% 11.41/11.18 [6794]~P85(f784(f784(f243(a1),x67941),x67942))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x67941),f87(a1))),x67942))
% 11.41/11.18 [6833]P85(f784(f784(f289(a1),f784(f109(a1),x68331)),x68332))+~P85(f784(f784(f289(a859),x68331),f784(a114,f784(f84(a1),x68332))))
% 11.41/11.18 [6867]E(x68671,f2(a859))+~P85(f784(f784(f242(a1),f784(f109(a1),x68672)),f784(f88(a1),f784(f109(a1),x68671))))
% 11.41/11.18 [6868]E(x68681,f2(a859))+~P85(f784(f784(f242(a1),f784(f109(a1),x68681)),f784(f88(a1),f784(f109(a1),x68682))))
% 11.41/11.18 [6971]E(f784(f784(f251(a1,a1),f784(f113(a1),a106)),f784(f784(f89(a1),x69711),x69712)),f65(x69711,x69712))+~P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),x69711),x69712)))
% 11.41/11.18 [7008]~P27(x70081,x70082)+P35(x70081,f784(f250(f869(f868(x70081,x70081),a852),f869(f868(x70081,x70081),a852)),x70082))
% 11.41/11.18 [7029]~P85(f784(f784(f242(a859),f784(a160,f2(a859))),x70291))+P85(f784(f784(f242(a859),f784(a160,f2(a859))),f784(f784(f252(a859),x70291),x70292)))
% 11.41/11.18 [7197]~P85(f784(f784(f243(a1),x71971),x71972))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x71971),x71971)),f784(f784(f89(a1),x71972),x71972)))
% 11.41/11.18 [7198]~P85(f784(f784(f243(a1),x71981),x71982))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x71981),x71981)),f784(f784(f89(a1),x71982),x71982)))
% 11.41/11.18 [7209]~P85(f784(f784(f242(a1),x72091),x72092))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x72091),x72091)),f784(f784(f89(a1),x72092),x72092)))
% 11.41/11.18 [7210]~P85(f784(f784(f242(a1),x72101),x72102))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x72101),x72101)),f784(f784(f89(a1),x72102),x72102)))
% 11.41/11.18 [7277]~P85(f784(f784(f243(a859),f2(a859)),x72771))+P85(f784(f784(f243(a859),f784(f784(f3(a859),x72771),f784(a160,x72772))),x72771))
% 11.41/11.18 [7314]P85(f784(f784(f242(a859),f784(a160,f2(a859))),x73141))+~P85(f784(f784(f242(a859),f784(a160,f2(a859))),f784(f784(f90(a859),x73142),x73141)))
% 11.41/11.18 [7315]P85(f784(f784(f242(a859),f784(a160,f2(a859))),x73151))+~P85(f784(f784(f242(a859),f784(a160,f2(a859))),f784(f784(f90(a859),x73151),x73152)))
% 11.41/11.18 [7319]P85(f784(f784(f242(a859),f784(f784(f155(a859),x73191),x73192)),f784(f157(a859),x73191)))+~P85(f784(f784(f243(a859),x73192),f784(f188(f860(a859)),x73191)))
% 11.41/11.18 [7363]P85(f784(f784(f243(a1),x73631),x73632))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),x73631),f87(a1))),x73632))
% 11.41/11.18 [7372]~P85(f784(f784(f347(a859),x73721),x73722))+P85(f784(f784(f347(a1),f784(f109(a1),x73721)),f784(f313(a859,a1,f109(a1)),x73722)))
% 11.41/11.18 [7409]P85(f784(f71(x74091),f249(f869(x74091,a852))))+~P85(f784(f71(f869(x74092,x74091)),f249(f869(f869(x74092,x74091),a852))))
% 11.41/11.18 [7410]P85(f784(f71(x74101),f249(f869(x74101,a852))))+~P85(f784(f71(f870(x74102,x74101)),f249(f869(f870(x74102,x74101),a852))))
% 11.41/11.18 [7411]P85(f784(f71(x74111),f249(f869(x74111,a852))))+~P85(f784(f71(f870(x74111,x74112)),f249(f869(f870(x74111,x74112),a852))))
% 11.41/11.18 [7449]E(x74491,f187(f869(x74492,a852)))+~P85(f784(f784(f242(f869(x74492,a852)),x74491),f784(f88(f869(x74492,a852)),x74491)))
% 11.41/11.18 [7592]E(f784(f136(f860(x75921),f860(x75921),f130(x75921),f120(x75921)),x75922),f120(x75921))+P85(f784(f784(f347(f860(x75921)),f778(x75922,x75921)),f784(f164(f860(x75921)),x75922)))
% 11.41/11.18 [7593]E(f784(f136(f860(x75931),f860(x75931),f130(x75931),f120(x75931)),x75932),f120(x75931))+P85(f784(f784(f347(f860(x75931)),f780(x75932,x75931)),f784(f164(f860(x75931)),x75932)))
% 11.41/11.18 [7728]E(f170(x77281,f784(f784(f144(f860(x77281)),f120(x77281)),x77282)),f170(x77281,x77282))+~P85(f784(f334(f860(f860(x77281)),f171(x77281)),f784(f784(f144(f860(x77281)),f120(x77281)),x77282)))
% 11.41/11.18 [7832]P85(f784(f784(f243(a1),x78321),x78322))+~P85(f784(f784(f243(a1),f784(f784(f89(a1),x78321),x78321)),f784(f784(f89(a1),x78322),x78322)))
% 11.41/11.18 [7833]P85(f784(f784(f243(a1),x78331),x78332))+~P85(f784(f784(f243(a1),f784(f784(f89(a1),x78331),x78331)),f784(f784(f89(a1),x78332),x78332)))
% 11.41/11.18 [7835]P85(f784(f784(f242(a1),x78351),x78352))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),x78351),x78351)),f784(f784(f89(a1),x78352),x78352)))
% 11.41/11.18 [7836]P85(f784(f784(f242(a1),x78361),x78362))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),x78361),x78361)),f784(f784(f89(a1),x78362),x78362)))
% 11.41/11.18 [7927]~P86(x79271)+E(f784(f784(f90(x79271),f784(f784(f89(x79271),f87(x79271)),f87(x79271))),f784(f784(f8(a859,x79271),f109(x79271)),f305(a859,f87(a859),x79272))),f784(f784(f90(x79271),f784(f109(x79271),x79272)),f784(f784(f89(x79271),f784(f109(x79271),x79272)),f87(x79271))))
% 11.41/11.18 [7968]E(f784(f784(f144(a1),f784(f113(a1),x79681)),f169(f784(f784(f89(a1),f784(f113(a1),x79681)),f87(a1)),f784(f113(a1),x79682))),f169(f784(f113(a1),x79681),f784(f113(a1),x79682)))+~P85(f784(f784(f242(a1),f784(f113(a1),x79681)),f784(f113(a1),x79682)))
% 11.41/11.18 [7983]P85(f784(f784(f347(a859),x79831),x79832))+~P85(f784(f784(f347(a1),f784(f109(a1),x79831)),f784(f313(a859,a1,f109(a1)),x79832)))
% 11.41/11.18 [8131]~P85(f784(f71(x81311),x81312))+E(f784(f313(a859,x81311,f587(x81312,x81311)),f784(f266(a859),f784(f784(f9(a859,a859,a852),f243(a859)),f588(x81312,x81311)))),x81312)
% 11.41/11.18 [8415]P47(x84151,x84152)+P85(f784(f784(f347(f868(x84151,x84151)),f784(f784(f251(x84151,x84151),f486(x84152,x84151)),f486(x84152,x84151))),x84152))
% 11.41/11.18 [8549]~P89(x85491)+E(f784(f784(f3(x85491),f87(x85491)),f784(f113(x85491),x85492)),f784(f113(x85491),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f88(a1),x85492))))
% 11.41/11.18 [8654]~P85(f784(f784(f243(f869(a859,a852)),x86541),x86542))+P85(f784(f784(f243(f869(a1,a852)),f784(f313(a859,a1,f109(a1)),x86541)),f784(f313(a859,a1,f109(a1)),x86542)))
% 11.41/11.18 [8655]~P85(f784(f784(f242(f869(a859,a852)),x86551),x86552))+P85(f784(f784(f242(f869(a1,a852)),f784(f313(a859,a1,f109(a1)),x86551)),f784(f313(a859,a1,f109(a1)),x86552)))
% 11.41/11.18 [8680]~P85(f784(f784(f243(a1),x86801),x86802))+P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x86801),x86801)),a106)),f784(f784(f89(a1),x86802),x86802)))
% 11.41/11.18 [8681]~P85(f784(f784(f243(a1),x86811),x86812))+P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x86811),x86811)),a106)),f784(f784(f89(a1),x86812),x86812)))
% 11.41/11.18 [8682]~P85(f784(f784(f243(a1),x86821),x86822))+P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x86821),x86821)),a106)),f784(f784(f89(a1),x86822),x86822)))
% 11.41/11.18 [8683]~P85(f784(f784(f243(a1),x86831),x86832))+P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x86831),x86831)),a106)),f784(f784(f89(a1),x86832),x86832)))
% 11.41/11.18 [8750]~P85(f784(f784(f347(a859),x87501),f784(f164(a859),x87502)))+P85(f784(f784(f242(a859),x87501),f784(f136(a859,a859,f89(a859),f2(a859)),x87502)))
% 11.41/11.18 [8825]P43(x88251,x88252)+~P85(f784(f784(f347(f868(x88251,x88251)),f784(f784(f251(x88251,x88251),f435(x88252,x88251)),f435(x88252,x88251))),x88252))
% 11.41/11.18 [8956]~P85(f784(f784(f243(f869(a1,a852)),f784(f313(a859,a1,f109(a1)),x89561)),f784(f313(a859,a1,f109(a1)),x89562)))+P85(f784(f784(f243(f869(a859,a852)),x89561),x89562))
% 11.41/11.18 [8957]~P85(f784(f784(f242(f869(a1,a852)),f784(f313(a859,a1,f109(a1)),x89571)),f784(f313(a859,a1,f109(a1)),x89572)))+P85(f784(f784(f242(f869(a859,a852)),x89571),x89572))
% 11.41/11.18 [9039]P85(f784(f784(f243(a1),x90391),x90392))+~P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x90391),x90391)),a106)),f784(f784(f89(a1),x90392),x90392)))
% 11.41/11.18 [9040]P85(f784(f784(f243(a1),x90401),x90402))+~P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x90401),x90401)),a106)),f784(f784(f89(a1),x90402),x90402)))
% 11.41/11.18 [9041]P85(f784(f784(f243(a1),x90411),x90412))+~P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x90411),x90411)),a106)),f784(f784(f89(a1),x90412),x90412)))
% 11.41/11.18 [9042]P85(f784(f784(f243(a1),x90421),x90422))+~P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x90421),x90421)),a106)),f784(f784(f89(a1),x90422),x90422)))
% 11.41/11.18 [9905]~P85(f784(f71(x99051),x99052))+E(f784(f188(f860(x99051)),f99(f860(x99051),f784(f784(f20(f860(x99051),a852,a852),f784(f784(f10(a852,f869(a852,a852),f860(x99051)),a344),f784(f784(f9(f860(x99051),f869(x99051,a852),a852),f784(f784(f10(f869(x99051,a852),f869(f869(x99051,a852),a852),f860(x99051)),a343),f164(x99051))),x99052))),f132(x99051)))),f219(x99051,x99052))
% 11.41/11.18 [5963]E(f784(f784(f89(a859),f784(f784(f3(a859),x59631),x59632)),x59632),x59631)+~P85(f784(f784(f242(a859),x59632),x59631))
% 11.41/11.18 [6028]E(f784(f784(f51(a859),f784(f784(f90(a859),x60281),x60282)),x60282),x60281)+~P85(f784(f784(f243(a859),f2(a859)),x60282))
% 11.41/11.18 [6029]E(f784(f784(f51(a859),f784(f784(f90(a859),x60291),x60292)),x60291),x60292)+~P85(f784(f784(f243(a859),f2(a859)),x60291))
% 11.41/11.18 [6034]~P68(x60341)+E(f784(f784(f8(a859,x60341),f784(f155(x60341),x60342)),f784(f304(a859,f2(a859)),f784(f188(f860(x60341)),x60342))),f784(f157(x60341),x60342))
% 11.41/11.18 [6151]E(f60(a859,f784(a160,f784(f784(f90(a859),x61511),x61512)),x61511),f87(a859))+~P85(f784(f784(f243(a859),f87(a859)),x61511))
% 11.41/11.18 [6157]E(f784(a160,f784(f784(f89(a859),f784(f113(a859),x61571)),x61572)),f784(f784(f89(a859),f87(a859)),x61572))+~P85(f784(a193,f784(f113(a1),x61571)))
% 11.41/11.18 [6183]E(f784(a114,f784(f784(f252(a1),f784(f113(a1),x61831)),x61832)),f784(f784(f252(a859),f784(f113(a859),x61831)),x61832))+P85(f784(a193,f784(f113(a1),x61831)))
% 11.41/11.18 [6434]E(f784(f784(f3(a859),x64341),f784(f113(a859),f784(f784(f89(a1),x64342),a106))),f784(f784(f3(a859),f784(a160,x64341)),f784(f113(a859),x64342)))+~P85(f784(f784(f243(a1),a92),x64342))
% 11.41/11.18 [6515]E(x65151,f2(a859))+E(f784(a160,f784(f784(f89(a859),f784(f784(f3(a859),x65151),f87(a859))),x65152)),f784(f784(f89(a859),x65151),x65152))
% 11.41/11.18 [6560]E(x65601,f2(a1))+P85(f784(f784(f243(a1),f2(a1)),f784(f784(f252(a1),f784(f84(a1),x65601)),x65602)))
% 11.41/11.18 [6575]~E(x65752,f2(a859))+P85(f784(f784(f243(a1),f2(a1)),f784(f784(f252(a1),f784(f84(a1),x65751)),x65752)))
% 11.41/11.18 [6611]E(x66111,f2(a859))+E(f784(f784(f89(a859),x66112),f784(f784(f90(a859),f784(f784(f3(a859),x66111),f87(a859))),x66112)),f784(f784(f90(a859),x66111),x66112))
% 11.41/11.18 [6665]~P85(f784(f784(f242(a1),x66651),x66652))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x66651),a106)),x66652))
% 11.41/11.18 [6797]E(f784(f784(f144(a859),x67971),f134(a859,f784(f304(a859,f784(a160,x67971)),x67972))),f134(a859,f784(f304(a859,x67971),x67972)))+~P85(f784(f784(f243(a859),x67971),x67972))
% 11.41/11.18 [6798]E(f784(f784(f144(a859),x67981),f134(a859,f784(f304(a859,f784(a160,x67981)),x67982))),f134(a859,f784(f304(a859,x67981),x67982)))+~P85(f784(f784(f243(a859),x67981),x67982))
% 11.41/11.18 [6965]~P85(f784(f784(f289(a1),x69651),f784(f109(a1),x69652)))+P85(f784(f784(f289(a859),f784(a114,f784(f84(a1),x69651))),x69652))
% 11.41/11.18 [6999]E(x69991,x69992)+~E(f784(f784(f3(a1),f784(f784(f89(a1),x69991),x69991)),a106),f784(f784(f3(a1),f784(f784(f89(a1),x69992),x69992)),a106))
% 11.41/11.18 [7002]E(x70021,f120(x70022))+E(f273(x70022,f784(f784(f146(x70022,f868(a108,x70022)),f784(f251(a108,x70022),f87(a108))),x70021)),f280(x70022,x70021))
% 11.41/11.18 [7240]P85(f784(f784(f242(a1),x72401),x72402))+~P85(f784(f784(f243(a1),f784(f784(f89(a1),x72401),a106)),x72402))
% 11.41/11.18 [7382]P85(f784(f784(f289(a1),x73821),f784(f109(a1),x73822)))+~P85(f784(f784(f289(a859),f784(a114,f784(f84(a1),x73821))),x73822))
% 11.41/11.18 [7730]~P85(f784(f784(f243(a859),x77301),x77302))+P85(f784(f784(f347(f868(a859,a859)),f784(f784(f251(a859,a859),x77301),x77302)),a247))
% 11.41/11.18 [7957]~P85(f784(f784(f243(a108),f2(a108)),x79571))+P85(f784(f784(f243(a108),f784(f250(a108,f868(a108,a108)),f784(f274(x79571),x79572))),x79571))
% 11.41/11.18 [8256]~P79(x82561)+P85(f784(f784(f242(x82561),f784(f84(x82561),f784(f157(x82561),x82562))),f784(f157(x82561),f784(f784(f146(x82561,x82561),f84(x82561)),x82562))))
% 11.41/11.18 [8279]P85(f784(f784(f243(a859),x82791),x82792))+~P85(f784(f784(f347(f868(a859,a859)),f784(f784(f251(a859,a859),x82791),x82792)),a247))
% 11.41/11.18 [8438]E(f784(f784(f251(x84381,x84381),f666(x84382,x84381)),f666(x84382,x84381)),x84382)+~P85(f784(f784(f347(f868(x84381,x84381)),x84382),f310(x84381,f187(f869(f868(x84381,x84381),a852)))))
% 11.41/11.18 [8482]E(f784(f304(a859,x84821),f784(f784(f89(a859),x84821),f784(f50(a859),x84822))),x84822)+~P85(f784(f784(f242(f869(a859,a852)),x84822),f784(f304(a859,x84821),f784(f784(f89(a859),x84821),f784(f50(a859),x84822)))))
% 11.41/11.18 [8503]E(f784(f784(f144(a859),f784(f113(a859),x85031)),f134(a859,f784(f304(a859,f784(a160,f784(f113(a859),x85031))),f784(f113(a859),x85032)))),f134(a859,f784(f304(a859,f784(f113(a859),x85031)),f784(f113(a859),x85032))))+~P85(f784(f784(f243(a859),f784(f113(a859),x85031)),f784(f113(a859),x85032)))
% 11.41/11.18 [8783]E(f784(f784(f51(a1),f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),x87831),x87831)),a106))),f784(f113(a1),f784(f784(f89(a1),x87832),x87832))),f784(f784(f51(a1),f784(f113(a1),x87831)),f784(f113(a1),x87832)))+~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x87832)))
% 11.41/11.18 [8890]E(f168(f860(x88901),f784(f784(f10(a852,a852,f860(x88901)),a341),f784(f784(f9(f860(x88901),f860(x88901),a852),a343),f120(x88901))),x88902),f170(x88901,f170(x88901,x88902)))+~P15(a859,f784(f162(a859),f784(f784(f146(f860(x88901),a859),f188(f860(x88901))),x88902)))
% 11.41/11.18 [8893]E(f784(f784(f51(a1),f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),x88931),x88931)),a106))),f784(f113(a1),f784(f784(f89(a1),x88932),x88932))),f784(f784(f51(a1),f784(f784(f89(a1),f784(f113(a1),x88931)),f87(a1))),f784(f113(a1),x88932)))+P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x88932)))
% 11.41/11.18 [9673]P85(f784(a193,x96732))+E(f784(f784(f95(a1,a859),f784(f784(f3(a1),x96731),x96732)),f784(f784(f20(a1,a859,a859),f784(f784(f9(a1,a859,f869(a859,a859)),f784(f784(f10(a852,f869(a859,f869(a859,a859)),a1),f105(a859)),a193)),f2(a859))),a114)),f784(f784(f3(a859),f784(a114,x96731)),f784(a114,x96732)))
% 11.41/11.18 [9677]E(f784(f784(f95(a1,a859),f784(f113(a1),f784(f784(f89(a1),x96771),f784(f88(a1),x96772)))),f784(f784(f20(a1,a859,a859),f784(f784(f9(a1,a859,f869(a859,a859)),f784(f784(f10(a852,f869(a859,f869(a859,a859)),a1),f105(a859)),a193)),f2(a859))),a114)),f784(f784(f3(a859),f784(f113(a859),x96771)),f784(f113(a859),x96772)))+P85(f784(f784(f243(a1),x96772),a92))
% 11.41/11.18 [9678]~P27(x96781,x96782)+P85(f784(f784(f242(f869(f868(x96781,x96781),a852)),f784(f784(f291(x96781,x96781,x96781),f784(f250(f869(f868(x96781,x96781),a852),f869(f868(x96781,x96781),a852)),x96782)),f784(f260(f869(f868(x96781,x96781),a852),f869(f868(x96781,x96781),a852)),x96782))),f784(f250(f869(f868(x96781,x96781),a852),f869(f868(x96781,x96781),a852)),x96782)))
% 11.41/11.18 [9734]~E(f784(f50(a859),f784(f266(a859),f784(f784(f20(a859,a852,a852),f784(f784(f10(a852,f869(a852,a852),a859),a344),f784(f784(f9(a859,f869(a859,a852),a852),f347(a859)),x97341))),f784(f784(f9(a859,a859,a852),f243(a859)),f784(a160,x97342))))),f2(a859))+~P85(f784(f784(f347(a859),f2(a859)),x97341))
% 11.41/11.18 [9747]E(f301(a859,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97471,x97472),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x97472),x97471))
% 11.41/11.18 [9753]E(f302(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97531,x97532),f187(f869(a859,a852)))+P85(f784(f784(f289(a859),x97531),x97532))
% 11.41/11.18 [9754]E(f299(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97541,x97542),f187(f869(a859,a852)))+P85(f784(f784(f289(a859),x97541),x97542))
% 11.41/11.18 [9755]E(f302(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97551,x97552),f187(f869(a859,a852)))+P85(f784(f784(f289(a859),x97551),x97552))
% 11.41/11.18 [9756]E(f299(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97561,x97562),f187(f869(a859,a852)))+P85(f784(f784(f289(a859),x97561),x97562))
% 11.41/11.18 [9757]E(f302(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97571,x97572),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x97572),x97571))
% 11.41/11.18 [9758]E(f299(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97581,x97582),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x97582),x97581))
% 11.41/11.18 [9759]E(f302(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97591,x97592),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x97592),x97591))
% 11.41/11.18 [9760]E(f302(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97601,x97602),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x97602),x97601))
% 11.41/11.18 [9761]E(f299(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97611,x97612),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x97612),x97611))
% 11.41/11.18 [9762]E(f299(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97621,x97622),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x97622),x97621))
% 11.41/11.18 [9805]E(f60(a1,f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),x98051),x98051)),a106)),f784(f113(a1),f784(f784(f89(a1),x98052),x98052))),f784(f784(f89(a1),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f60(a1,f784(f113(a1),x98051),f784(f113(a1),x98052)))),f87(a1)))+~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x98052)))
% 11.41/11.18 [9814]E(f60(a1,f784(f113(a1),f784(f784(f3(a1),f784(f784(f89(a1),x98141),x98141)),a106)),f784(f113(a1),f784(f784(f89(a1),x98142),x98142))),f784(f784(f3(a1),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f60(a1,f784(f784(f89(a1),f784(f113(a1),x98141)),f87(a1)),f784(f113(a1),x98142)))),f87(a1)))+P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x98142)))
% 11.41/11.18 [9876]~P6(x98761)+E(f52(x98761,f784(f266(x98761),f784(f784(f10(f869(x98761,a852),a852,x98761),f97(x98761)),f784(f784(f10(f869(x98761,a852),f869(x98761,a852),x98761),f784(f20(x98761,a852,a852),f784(f784(f10(a852,f869(a852,a852),x98761),a348),f784(f784(f9(x98761,f869(x98761,a852),a852),f347(x98761)),x98762)))),f242(x98761))))),f53(x98761,x98762))
% 11.41/11.18 [9898]~P35(x98981,x98982)+P57(x98981,f784(f784(f9(x98981,f869(f868(x98981,x98981),a852),f869(x98981,a852)),f784(f784(f10(f869(x98981,f869(f869(f868(x98981,x98981),a852),a852)),f869(f869(f868(x98981,x98981),a852),f869(x98981,a852)),x98981),f9(x98981,f869(f868(x98981,x98981),a852),a852)),f784(f784(f10(f869(x98981,f868(x98981,x98981)),f869(x98981,f869(f869(f868(x98981,x98981),a852),a852)),x98981),f784(f10(f868(x98981,x98981),f869(f869(f868(x98981,x98981),a852),a852),x98981),f347(f868(x98981,x98981)))),f251(x98981,x98981)))),x98982))
% 11.41/11.18 [9899]~P9(x98991,f249(f869(x98991,a852)),x98992)+P8(x98991,f784(f784(f9(x98991,f869(f868(x98991,x98991),a852),f869(x98991,a852)),f784(f784(f10(f869(x98991,f869(f869(f868(x98991,x98991),a852),a852)),f869(f869(f868(x98991,x98991),a852),f869(x98991,a852)),x98991),f9(x98991,f869(f868(x98991,x98991),a852),a852)),f784(f784(f10(f869(x98991,f868(x98991,x98991)),f869(x98991,f869(f869(f868(x98991,x98991),a852),a852)),x98991),f784(f10(f868(x98991,x98991),f869(f869(f868(x98991,x98991),a852),a852),x98991),f347(f868(x98991,x98991)))),f251(x98991,x98991)))),x98992))
% 11.41/11.18 [9934]P35(x99341,x99342)+~P57(x99341,f784(f784(f9(x99341,f869(f868(x99341,x99341),a852),f869(x99341,a852)),f784(f784(f10(f869(x99341,f869(f869(f868(x99341,x99341),a852),a852)),f869(f869(f868(x99341,x99341),a852),f869(x99341,a852)),x99341),f9(x99341,f869(f868(x99341,x99341),a852),a852)),f784(f784(f10(f869(x99341,f868(x99341,x99341)),f869(x99341,f869(f869(f868(x99341,x99341),a852),a852)),x99341),f784(f10(f868(x99341,x99341),f869(f869(f868(x99341,x99341),a852),a852),x99341),f347(f868(x99341,x99341)))),f251(x99341,x99341)))),x99342))
% 11.41/11.18 [9935]P9(x99351,f249(f869(x99351,a852)),x99352)+~P8(x99351,f784(f784(f9(x99351,f869(f868(x99351,x99351),a852),f869(x99351,a852)),f784(f784(f10(f869(x99351,f869(f869(f868(x99351,x99351),a852),a852)),f869(f869(f868(x99351,x99351),a852),f869(x99351,a852)),x99351),f9(x99351,f869(f868(x99351,x99351),a852),a852)),f784(f784(f10(f869(x99351,f868(x99351,x99351)),f869(x99351,f869(f869(f868(x99351,x99351),a852),a852)),x99351),f784(f10(f868(x99351,x99351),f869(f869(f868(x99351,x99351),a852),a852),x99351),f347(f868(x99351,x99351)))),f251(x99351,x99351)))),x99352))
% 11.41/11.18 [7186]E(f784(f784(f89(a859),f784(f113(a859),f784(f784(f3(a1),x71861),a106))),x71862),f784(a160,f784(f784(f89(a859),f784(f113(a859),x71861)),x71862)))+P85(f784(a193,f784(f113(a1),x71861)))
% 11.41/11.18 [7650]~P89(x76501)+E(f784(f784(f89(x76501),f784(f784(f89(x76501),f87(x76501)),f784(f113(x76501),x76502))),f784(f113(x76501),x76502)),f784(f113(x76501),f784(f784(f3(a1),f784(f784(f89(a1),x76502),x76502)),a106)))
% 11.41/11.18 [8280]~P85(f784(f784(f242(a1),x82801),x82802))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x82801),x82801)),f784(f784(f3(a1),f784(f784(f89(a1),x82802),x82802)),a106)))
% 11.41/11.18 [8281]~P85(f784(f784(f242(a1),x82811),x82812))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x82811),x82811)),f784(f784(f3(a1),f784(f784(f89(a1),x82812),x82812)),a106)))
% 11.41/11.18 [8282]~P85(f784(f784(f242(a1),x82821),x82822))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x82821),x82821)),f784(f784(f3(a1),f784(f784(f89(a1),x82822),x82822)),a106)))
% 11.41/11.18 [8283]~P85(f784(f784(f242(a1),x82831),x82832))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x82831),x82831)),f784(f784(f3(a1),f784(f784(f89(a1),x82832),x82832)),a106)))
% 11.41/11.18 [8684]P85(f784(f784(f242(a1),x86841),x86842))+~P85(f784(f784(f243(a1),f784(f784(f89(a1),x86841),x86841)),f784(f784(f3(a1),f784(f784(f89(a1),x86842),x86842)),a106)))
% 11.41/11.18 [8685]P85(f784(f784(f242(a1),x86851),x86852))+~P85(f784(f784(f243(a1),f784(f784(f89(a1),x86851),x86851)),f784(f784(f3(a1),f784(f784(f89(a1),x86852),x86852)),a106)))
% 11.41/11.18 [8686]P85(f784(f784(f242(a1),x86861),x86862))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),x86861),x86861)),f784(f784(f3(a1),f784(f784(f89(a1),x86862),x86862)),a106)))
% 11.41/11.18 [8687]P85(f784(f784(f242(a1),x86871),x86872))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),x86871),x86871)),f784(f784(f3(a1),f784(f784(f89(a1),x86872),x86872)),a106)))
% 11.41/11.18 [8947]~P85(f784(f784(f243(a1),x89471),x89472))+P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x89471),x89471)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),x89472),x89472)),a106)))
% 11.41/11.18 [8948]~P85(f784(f784(f243(a1),x89481),x89482))+P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x89481),x89481)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),x89482),x89482)),a106)))
% 11.41/11.18 [8949]~P85(f784(f784(f242(a1),x89491),x89492))+P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x89491),x89491)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),x89492),x89492)),a106)))
% 11.41/11.18 [8950]~P85(f784(f784(f242(a1),x89501),x89502))+P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x89501),x89501)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),x89502),x89502)),a106)))
% 11.41/11.18 [9184]P85(f784(f784(f243(a1),x91841),x91842))+~P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x91841),x91841)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),x91842),x91842)),a106)))
% 11.41/11.18 [9185]P85(f784(f784(f243(a1),x91851),x91852))+~P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),x91851),x91851)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),x91852),x91852)),a106)))
% 11.41/11.18 [9186]P85(f784(f784(f242(a1),x91861),x91862))+~P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x91861),x91861)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),x91862),x91862)),a106)))
% 11.41/11.18 [9187]P85(f784(f784(f242(a1),x91871),x91872))+~P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),x91871),x91871)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),x91872),x91872)),a106)))
% 11.41/11.18 [9217]~P85(f784(f71(x92171),x92172))+P85(f784(f71(f869(x92171,a852)),f784(f266(f869(x92171,a852)),f784(f784(f9(f869(x92171,a852),f869(x92171,a852),a852),f242(f869(x92171,a852))),x92172))))
% 11.41/11.18 [9263]~E(f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),x92631),f187(f869(f868(a859,a859),a852)))),f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),x92632),f187(f869(f868(a859,a859),a852)))))+P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),x92631),x92632)),a118))
% 11.41/11.18 [9350]E(f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),x93501),f187(f869(f868(a859,a859),a852)))),f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),x93502),f187(f869(f868(a859,a859),a852)))))+~P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),x93501),x93502)),a118))
% 11.41/11.18 [9383]P85(f784(f784(f242(a1),f2(a1)),f710(x93831,x93832)))+E(f784(f266(a1),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),f2(a1)))),x93831)),f784(f266(a1),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),f2(a1)))),x93832)))
% 11.41/11.18 [9884]~P6(x98841)+E(f53(x98841,f784(f266(x98841),f784(f784(f10(f869(x98841,a852),a852,x98841),f97(x98841)),f784(f784(f10(f869(x98841,a852),f869(x98841,a852),x98841),f784(f20(x98841,a852,a852),f784(f784(f10(a852,f869(a852,a852),x98841),a348),f784(f784(f9(x98841,f869(x98841,a852),a852),f347(x98841)),x98842)))),f784(f9(x98841,x98841,a852),f242(x98841)))))),f52(x98841,x98842))
% 11.41/11.18 [9904]P85(f784(f784(f347(a859),f2(a859)),x99041))+E(f784(f50(a859),f784(f266(a859),f784(f784(f20(a859,a852,a852),f784(f784(f10(a852,f869(a852,a852),a859),a344),f784(f784(f9(a859,f869(a859,a852),a852),f784(f784(f10(a859,f869(f869(a859,a852),a852),a859),f347(a859)),a160)),x99041))),f784(f784(f9(a859,a859,a852),f243(a859)),x99042)))),f784(f50(a859),f784(f266(a859),f784(f784(f20(a859,a852,a852),f784(f784(f10(a852,f869(a852,a852),a859),a344),f784(f784(f9(a859,f869(a859,a852),a852),f347(a859)),x99041))),f784(f784(f9(a859,a859,a852),f243(a859)),f784(a160,x99042))))))
% 11.41/11.18 [9949]P85(f784(f784(f289(a859),x99491),x99492))+~P85(f784(f784(f347(a859),x99492),f297(a859,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x99491)))
% 11.41/11.18 [9950]P85(f784(f784(f289(a859),x99501),x99502))+~P85(f784(f784(f347(a859),x99501),f300(a859,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x99502)))
% 11.41/11.18 [9951]~P85(f784(f784(f289(a859),x99511),x99512))+~P85(f784(f784(f347(a859),x99512),f300(a859,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x99511)))
% 11.41/11.18 [9952]~P85(f784(f784(f289(a859),x99521),x99522))+~P85(f784(f784(f347(a859),x99521),f297(a859,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x99522)))
% 11.41/11.18 [7517]~P89(x75171)+E(f784(f784(f90(x75171),x75172),f784(f113(x75171),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),x75172)
% 11.41/11.18 [7783]~P89(x77831)+E(f784(f784(f89(x77831),f784(f113(x77831),x77832)),f87(x77831)),f784(f113(x77831),f784(f784(f89(a1),x77832),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))
% 11.41/11.18 [7926]P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x79262)))+E(f784(f784(f252(a1),x79261),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),x79262),x79262)),a106))),f87(a1))
% 11.41/11.18 [9241]~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x92412)))+E(f784(f784(f252(a1),x92411),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),x92412),x92412)),a106))),f784(f784(f95(a1,a1),f784(f784(f252(a1),x92411),f784(f113(a859),x92412))),f784(f784(f20(a1,a1,a1),f784(f784(f10(a1,f869(a1,a1),a1),f90(a1)),f784(f90(a1),x92411))),f7(a1))))
% 11.41/11.18 [9724]~P85(f784(f784(f243(a859),f784(f113(a859),x97241)),f784(a160,x97242)))+P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x97241),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f9(a1,a859,a852),f784(f784(f10(a859,f869(a859,a852),a1),f243(a859)),a114)),x97242))))
% 11.41/11.18 [9725]~P85(f784(f784(f242(a859),f784(f113(a859),x97251)),f784(a160,x97252)))+P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x97251),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f9(a1,a859,a852),f784(f784(f10(a859,f869(a859,a852),a1),f242(a859)),a114)),x97252))))
% 11.41/11.18 [9789]P85(f784(f784(f243(a859),f784(f113(a859),x97891)),f784(a160,x97892)))+~P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x97891),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f9(a1,a859,a852),f784(f784(f10(a859,f869(a859,a852),a1),f243(a859)),a114)),x97892))))
% 11.41/11.18 [9790]P85(f784(f784(f242(a859),f784(f113(a859),x97901)),f784(a160,x97902)))+~P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x97901),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f9(a1,a859,a852),f784(f784(f10(a859,f869(a859,a852),a1),f242(a859)),a114)),x97902))))
% 11.41/11.18 [9820]~P85(f784(f784(f243(a859),f784(a160,x98202)),f784(f113(a859),x98201)))+P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x98201),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f10(a859,a852,a1),f784(f243(a859),x98202)),a114)))))
% 11.41/11.18 [9821]~P85(f784(f784(f242(a859),f784(a160,x98212)),f784(f113(a859),x98211)))+P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x98211),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f10(a859,a852,a1),f784(f242(a859),x98212)),a114)))))
% 11.41/11.18 [9874]P85(f784(f784(f243(a859),f784(a160,x98741)),f784(f113(a859),x98742)))+~P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x98742),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f10(a859,a852,a1),f784(f243(a859),x98741)),a114)))))
% 11.41/11.18 [9875]P85(f784(f784(f242(a859),f784(a160,x98751)),f784(f113(a859),x98752)))+~P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x98752),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f10(a859,a852,a1),f784(f242(a859),x98751)),a114)))))
% 11.41/11.18 [9942]~P85(f784(f784(f347(a859),f2(a859)),x99421))+E(f784(a160,f784(f50(a859),f784(f266(a859),f784(f784(f20(a859,a852,a852),f784(f784(f10(a852,f869(a852,a852),a859),a344),f784(f784(f9(a859,f869(a859,a852),a852),f784(f784(f10(a859,f869(f869(a859,a852),a852),a859),f347(a859)),a160)),x99421))),f784(f784(f9(a859,a859,a852),f243(a859)),x99422))))),f784(f50(a859),f784(f266(a859),f784(f784(f20(a859,a852,a852),f784(f784(f10(a852,f869(a852,a852),a859),a344),f784(f784(f9(a859,f869(a859,a852),a852),f347(a859)),x99421))),f784(f784(f9(a859,a859,a852),f243(a859)),f784(a160,x99422))))))
% 11.41/11.18 [8464]~P89(x84641)+E(f784(f784(f90(x84641),f784(f113(x84641),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),x84642),x84642)
% 11.41/11.18 [8523]~P89(x85231)+E(f784(f784(f89(x85231),f87(x85231)),f784(f113(x85231),x85232)),f784(f113(x85231),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),x85232)))
% 11.41/11.18 [8569]~P89(x85691)+E(f784(f784(f3(x85691),f784(f113(x85691),x85692)),f87(x85691)),f784(f113(x85691),f784(f784(f89(a1),x85692),f784(f88(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.18 [8703]~P85(f784(f784(f243(a859),f784(f113(a859),a92)),x87032))+E(f784(f784(f3(a859),x87031),f784(f784(f3(a859),x87032),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f784(f3(a859),f784(a160,x87031)),x87032))
% 11.41/11.18 [9280]~P86(x92801)+E(f784(f784(f90(x92801),x92802),x92802),f784(f784(f252(x92801),x92802),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.18 [9281]~P75(x92811)+E(f784(f784(f252(x92811),x92812),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f784(f90(x92811),x92812),x92812))
% 11.41/11.18 [9283]~P89(x92831)+E(f784(f784(f90(x92831),x92832),f784(f113(x92831),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f784(f89(x92831),x92832),x92832))
% 11.41/11.18 [9517]~P136(x95171)+E(f784(f784(f252(x95171),f784(f88(x95171),x95172)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f784(f252(x95171),x95172),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.18 [9518]~P113(x95181)+E(f784(f784(f252(x95181),f784(f84(x95181),x95182)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f784(f252(x95181),x95182),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.18 [9514]~P89(x95141)+E(f784(f784(f90(x95141),f784(f113(x95141),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x95142),f784(f784(f89(x95141),x95142),x95142))
% 11.41/11.18 [9637]~P113(x96371)+E(f784(f84(x96371),f784(f784(f252(x96371),x96372),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x96371),x96372),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.18 [9685]~P113(x96851)+P85(f784(f784(f242(x96851),f2(x96851)),f784(f784(f252(x96851),x96852),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.18 [9865]~E(f784(a160,x98652),f784(f113(a859),x98651))+P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x98651),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f9(a1,a859,a852),f784(f784(f10(a859,f869(a859,a852),a1),a343),a114)),x98652)))))
% 11.41/11.18 [9866]~E(f784(f113(a859),x98661),f784(a160,x98662))+P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x98661),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f9(a1,a859,a852),f784(f784(f10(a859,f869(a859,a852),a1),a343),a114)),x98662)))))
% 11.41/11.18 [9907]E(f784(a160,x99071),f784(f113(a859),x99072))+~P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x99072),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f9(a1,a859,a852),f784(f784(f10(a859,f869(a859,a852),a1),a343),a114)),x99071)))))
% 11.41/11.18 [9908]E(f784(f113(a859),x99081),f784(a160,x99082))+~P85(f784(f784(f95(a1,a852),f784(f113(a1),f784(f784(f89(a1),x99081),a106))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a348),f784(f784(f10(a852,a852,a1),a341),a193))),f784(f784(f9(a1,a859,a852),f784(f784(f10(a859,f869(a859,a852),a1),a343),a114)),x99082)))))
% 11.41/11.18 [9683]~P89(x96831)+E(f784(f784(f252(x96831),f784(f113(x96831),a106)),f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x96832)),f87(x96831))
% 11.41/11.18 [9684]~P136(x96841)+E(f784(f784(f252(x96841),f784(f88(x96841),f87(x96841))),f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x96842)),f87(x96841))
% 11.41/11.18 [9687]~P75(x96871)+E(f784(f784(f252(x96871),x96872),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),a106))),f784(f784(f90(x96871),f784(f784(f90(x96871),x96872),x96872)),x96872))
% 11.41/11.18 [9887]~P85(f784(f784(f242(a1),f2(a1)),x98872))+E(f60(a1,f784(f784(f89(a1),f87(a1)),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x98871)),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x98872)),f784(f784(f89(a1),f87(a1)),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f60(a1,x98871,x98872))))
% 11.41/11.18 [9910]~P85(f784(f784(f242(a1),f2(a1)),x99102))+E(f784(f784(f51(a1),f784(f784(f89(a1),f87(a1)),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x99101))),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x99102)),f784(f784(f51(a1),x99101),x99102))
% 11.41/11.18 [9912]~P85(f784(f784(f242(a1),x99122),f2(a1)))+E(f784(f784(f51(a1),f784(f784(f89(a1),f87(a1)),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x99121))),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x99122)),f784(f784(f51(a1),f784(f784(f89(a1),x99121),f87(a1))),x99122))
% 11.41/11.18 [9913]~P85(f784(f784(f242(a1),x99132),f2(a1)))+E(f60(a1,f784(f784(f89(a1),f87(a1)),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x99131)),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x99132)),f784(f784(f3(a1),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f60(a1,f784(f784(f89(a1),x99131),f87(a1)),x99132))),f87(a1)))
% 11.41/11.18 [9780]~P89(x97801)+E(f784(f784(f252(x97801),f784(f113(x97801),a106)),f784(a160,f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97802))),f784(f113(x97801),a106))
% 11.41/11.18 [9782]~P136(x97821)+E(f784(f784(f252(x97821),f784(f88(x97821),f87(x97821))),f784(a160,f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97822))),f784(f88(x97821),f87(x97821)))
% 11.41/11.18 [6014]E(x60141,x60142)+~P38(a25,x60141,x60143,x60142)
% 11.41/11.18 [5031]~P35(x50311,x50313)+P35(x50311,f340(x50311,x50312,x50313))
% 11.41/11.18 [5274]~P9(x52741,x52742,x52743)+P9(f860(x52741),f152(x52741,x52742),f150(x52741,x52743))
% 11.41/11.18 [5275]~P46(x52751,x52752,x52753)+P46(f860(x52751),f152(x52751,x52752),f150(x52751,x52753))
% 11.41/11.18 [5385]P53(x53851,x53852,x53853)+~E(f639(x53853,x53852,x53851),f640(x53853,x53852,x53851))
% 11.41/11.18 [5386]P52(x53861,x53862,x53863)+~E(f651(x53863,x53862,x53861),f652(x53863,x53862,x53861))
% 11.41/11.18 [6333]P31(x63331,x63332,x63333)+~P32(x63331,f615(x63333,x63332,x63331),f617(x63333,x63332,x63331))
% 11.41/11.18 [4585]~E(x45851,f190(x45852))+~E(x45851,f784(f237(x45852),x45853))
% 11.41/11.18 [4586]~E(x45861,f190(x45862))+~E(x45861,f784(f237(x45862),x45863))
% 11.41/11.18 [4634]~E(f784(f162(x46342),x46341),x46343)+E(x46341,f784(f162(x46342),x46343))
% 11.41/11.18 [4635]~E(x46352,f784(f162(x46351),x46353))+E(f784(f162(x46351),x46352),x46353)
% 11.41/11.18 [4679]E(x46791,x46792)+~E(f784(f237(x46793),x46791),f784(f237(x46793),x46792))
% 11.41/11.18 [4680]E(x46801,x46802)+~E(f784(f162(x46803),x46801),f784(f162(x46803),x46802))
% 11.41/11.18 [4878]~P8(x48783,x48781)+P85(f784(f784(x48781,x48782),x48782))
% 11.41/11.18 [4879]~P48(x48793,x48791)+P85(f784(f784(x48791,x48792),x48792))
% 11.41/11.18 [4880]~P57(x48801,x48802)+P85(f784(f334(x48801,x48802),x48803))
% 11.41/11.18 [4881]~P57(x48811,x48812)+P85(f784(f334(x48811,x48812),x48813))
% 11.41/11.18 [4945]~P35(x49451,x49452)+P35(f860(x49451),f784(f137(x49451,x49452),x49453))
% 11.41/11.18 [4949]~P85(f784(x49492,x49493))+~E(f784(f266(x49491),x49492),f187(f869(x49491,a852)))
% 11.41/11.18 [4950]~P85(f784(x49502,x49503))+~E(f187(f869(x49501,a852)),f784(f266(x49501),x49502))
% 11.41/11.18 [4984]~P85(f784(x49841,x49843))+P85(f784(x49841,f99(x49842,x49841)))
% 11.41/11.18 [4985]~P85(f784(x49851,x49853))+P85(f784(x49851,f99(x49852,x49851)))
% 11.41/11.18 [4986]~P85(f784(x49861,x49863))+P85(f784(x49861,f99(x49862,x49861)))
% 11.41/11.18 [4987]~P85(f784(x49871,x49873))+P85(f784(x49871,f99(x49872,x49871)))
% 11.41/11.18 [5110]~E(x51102,x51103)+P85(f784(f784(f347(x51101),x51102),f784(a343,x51103)))
% 11.41/11.18 [5162]E(f784(f162(x51621),x51622),f784(f784(f144(x51621),x51623),f120(x51621)))+~E(x51622,f784(f784(f144(x51621),x51623),f120(x51621)))
% 11.41/11.18 [5163]~E(x51633,f784(f784(f144(x51631),x51632),f120(x51631)))+E(f784(f784(f144(x51631),x51632),f120(x51631)),f784(f162(x51631),x51633))
% 11.41/11.18 [5188]~E(x51883,f784(f18(f864(x51882),x51881),f190(x51882)))+E(f175(x51881,x51882,x51883),f187(f869(x51881,a852)))
% 11.41/11.18 [5208]E(f784(f50(x52081),f386(x52082,x52083,x52081)),x52082)+~E(f784(f50(x52081),x52083),f784(a160,x52082))
% 11.41/11.18 [5213]~P35(x52131,x52133)+P85(f784(f784(f347(x52131),x52132),f335(x52131,x52133)))
% 11.41/11.18 [5214]~P35(x52141,x52143)+P85(f784(f784(f347(x52141),x52142),f335(x52141,x52143)))
% 11.41/11.18 [5217]~E(f784(f162(x52172),x52171),f784(f784(f144(x52172),x52173),f120(x52172)))+E(x52171,f784(f784(f144(x52172),x52173),f120(x52172)))
% 11.41/11.18 [5218]~E(f784(f784(f144(x52182),x52183),f120(x52182)),f784(f162(x52182),x52181))+E(x52181,f784(f784(f144(x52182),x52183),f120(x52182)))
% 11.41/11.18 [5233]E(x52331,f784(f18(f864(x52332),x52333),f190(x52332)))+~E(f175(x52333,x52332,x52331),f187(f869(x52333,a852)))
% 11.41/11.18 [5239]E(f94(f868(a859,a859),f63(x52391,x52392)),x52393)+~P85(f784(f63(x52391,x52392),x52393))
% 11.41/11.18 [5246]~E(x52463,f784(f237(x52461),x52462))+P85(f784(f784(f347(x52461),x52462),f236(x52461,x52463)))
% 11.41/11.18 [5337]~E(x53372,f120(x53371))+P85(f784(f784(f347(f860(x53371)),x53372),f152(x53371,x53373)))
% 11.41/11.18 [5345]~P46(x53451,x53452,x53453)+P46(x53451,x53452,f784(f288(x53451,x53451),x53453))
% 11.41/11.18 [5346]~P53(x53461,x53462,x53463)+P53(x53461,x53462,f784(f288(x53461,x53461),x53463))
% 11.41/11.18 [5366]~P4(x53661)+E(f60(x53661,f60(x53661,x53662,x53663),x53663),f60(x53661,x53662,x53663))
% 11.41/11.18 [5463]E(x54631,x54632)+~P85(f784(f784(f347(x54633),x54631),f784(a343,x54632)))
% 11.41/11.18 [5505]~P112(x55051)+E(f189(x55051,x55052,f2(a859),x55053),x55053)
% 11.41/11.18 [5525]P46(x55251,x55252,x55253)+~P46(x55251,x55252,f784(f288(x55251,x55251),x55253))
% 11.41/11.18 [5526]P53(x55261,x55262,x55263)+~P53(x55261,x55262,f784(f288(x55261,x55261),x55263))
% 11.41/11.18 [5548]E(x55481,f784(f237(x55482),x55483))+~P85(f784(f784(f347(x55482),x55483),f236(x55482,x55481)))
% 11.41/11.18 [5629]~P85(f784(a26,x56293))+P85(f784(a26,f34(x56291,x56292,x56293)))
% 11.41/11.18 [5630]~P85(f784(a26,x56303))+P85(f784(a26,f34(x56301,x56302,x56303)))
% 11.41/11.18 [5642]E(f784(f131(x56421,x56422),x56423),f120(x56421))+P85(f784(x56422,f759(x56423,x56422,x56421)))
% 11.41/11.18 [5798]~P85(f784(f132(x57981),x57983))+P85(f784(f132(x57981),f154(x57981,x57982,x57983)))
% 11.41/11.18 [5799]~P85(f784(f132(x57991),x57992))+P85(f784(f132(x57991),f166(x57991,x57992,x57993)))
% 11.41/11.18 [5800]~P142(x58001,x58002,x58003)+P85(f784(x58001,f60(a1,x58002,x58003)))
% 11.41/11.18 [5899]P85(f784(a26,f33(x58991,x58992,x58993)))+~P85(f784(a26,f784(a29,x58992)))
% 11.41/11.18 [5900]P85(f784(a26,f33(x59001,x59002,x59003)))+~P85(f784(a26,f784(a29,x59002)))
% 11.41/11.18 [5912]~P100(x59121)+E(f784(f784(f111(f869(x59121,a852)),f784(f267(x59121),x59122)),f305(x59121,x59122,x59123)),f187(f869(x59121,a852)))
% 11.41/11.18 [5913]~P100(x59131)+E(f784(f784(f111(f869(x59131,a852)),f784(f303(x59131),x59132)),f307(x59131,x59132,x59133)),f187(f869(x59131,a852)))
% 11.41/11.18 [5914]~P100(x59141)+E(f784(f784(f111(f869(x59141,a852)),f784(f303(x59141),x59142)),f308(x59141,x59142,x59143)),f187(f869(x59141,a852)))
% 11.41/11.18 [6061]P85(f784(a26,x60611))+~P85(f784(a26,f34(x60612,x60613,x60611)))
% 11.41/11.18 [6062]P85(f784(a26,x60621))+~P85(f784(a26,f34(x60622,x60623,x60621)))
% 11.41/11.18 [6063]P85(f784(a26,x60631))+~P85(f784(a26,f35(x60632,x60633,x60631)))
% 11.41/11.18 [6064]P85(f784(a26,x60641))+~P85(f784(a26,f35(x60642,x60643,x60641)))
% 11.41/11.18 [6065]P85(f784(a26,x60651))+~P85(f784(a26,f35(x60652,x60651,x60653)))
% 11.41/11.18 [6066]P85(f784(a26,x60661))+~P85(f784(a26,f35(x60662,x60661,x60663)))
% 11.41/11.18 [6146]E(f784(f131(x61461,x61462),x61463),x61463)+~P85(f784(x61462,f761(x61463,x61462,x61461)))
% 11.41/11.18 [6148]E(f784(f784(f312(x61481),f430(x61482,x61483,x61481)),f386(x61482,x61483,x61481)),x61483)+~E(f784(f50(x61481),x61483),f784(a160,x61482))
% 11.41/11.18 [6163]P142(x61631,x61632,x61633)+~P85(f784(x61631,f60(a1,x61632,x61633)))
% 11.41/11.18 [6253]~P85(f784(a26,f33(x62532,x62531,x62533)))+P85(f784(a26,f784(a29,x62531)))
% 11.41/11.18 [6254]~P85(f784(a26,f33(x62542,x62541,x62543)))+P85(f784(a26,f784(a29,x62541)))
% 11.41/11.18 [6302]~P85(f784(x63022,f604(x63023,x63022,x63021)))+P85(f784(f255(x63021,x63022),x63023))
% 11.41/11.18 [6561]~P85(f784(f334(x65611,x65612),f829(x65613,x65612,x65611)))+P85(f784(f334(x65611,x65612),x65613))
% 11.41/11.18 [6562]~P85(f784(f334(x65621,x65622),f830(x65623,x65622,x65621)))+P85(f784(f334(x65621,x65622),x65623))
% 11.41/11.18 [7187]~P4(x71871)+E(f784(f784(f89(x71871),f784(f784(f90(x71871),x71872),f784(f784(f51(x71871),x71873),x71872))),f60(x71871,x71873,x71872)),x71873)
% 11.41/11.18 [7674]E(f784(f784(f251(x76741,x76741),f485(x76742,x76743,x76741)),f485(x76742,x76743,x76741)),x76743)+~P85(f784(f784(f347(f868(x76741,x76741)),x76743),f270(x76741,x76742)))
% 11.41/11.18 [7792]~P85(f784(f784(f347(x77921),f537(x77923,x77922,x77921)),f335(x77921,x77923)))+P85(f784(f784(f347(x77921),x77922),f335(x77921,x77923)))
% 11.41/11.18 [7793]~P85(f784(f784(f347(x77931),f631(x77933,x77932,x77931)),f335(x77931,x77933)))+P85(f784(f784(f347(x77931),x77932),f335(x77931,x77933)))
% 11.41/11.18 [7794]~P85(f784(f784(f347(x77941),f633(x77943,x77942,x77941)),f335(x77941,x77943)))+P85(f784(f784(f347(x77941),x77942),f335(x77941,x77943)))
% 11.41/11.18 [7978]~P4(x79781)+E(f784(f784(f89(x79781),f784(f784(f90(x79781),f784(f784(f51(x79781),x79782),x79783)),x79783)),f60(x79781,x79782,x79783)),x79782)
% 11.41/11.18 [7979]~P4(x79791)+E(f784(f784(f89(x79791),f784(f784(f90(x79791),f784(f784(f51(x79791),x79792),x79793)),x79793)),f60(x79791,x79792,x79793)),x79792)
% 11.41/11.18 [8019]~E(f784(f50(x80191),x80192),f784(a160,x80193))+~P85(f784(f784(f347(x80191),f430(x80193,x80192,x80191)),f386(x80193,x80192,x80191)))
% 11.41/11.18 [8618]P85(f784(f784(f242(f869(f868(x86181,x86181),a852)),f310(x86181,x86182)),f310(x86181,x86183)))+~P85(f784(f784(f242(f869(f868(x86181,x86181),a852)),x86182),f310(x86181,x86183)))
% 11.41/11.18 [8858]E(x88581,f120(x88582))+~P85(f784(f784(f347(f868(f860(x88582),f860(x88582))),f784(f784(f251(f860(x88582),f860(x88582)),x88581),f120(x88582))),f150(x88582,x88583)))
% 11.41/11.18 [8884]E(x88841,f120(x88842))+~P85(f784(f784(f347(f868(f860(x88842),f860(x88842))),f784(f784(f251(f860(x88842),f860(x88842)),f120(x88842)),x88841)),f150(x88842,x88843)))
% 11.41/11.18 [9010]E(f784(f784(f144(x90101),f758(x90102,x90103,x90101)),f763(x90102,x90103,x90101)),x90103)+~P85(f784(f784(f347(f868(f860(x90101),f860(x90101))),f784(f784(f251(f860(x90101),f860(x90101)),f120(x90101)),x90103)),f141(x90101,x90102)))
% 11.41/11.18 [9210]~P121(x92101)+~P85(f784(f784(f243(x92101),f784(f784(f89(x92101),f784(f784(f90(x92101),x92102),x92102)),f784(f784(f90(x92101),x92103),x92103))),f2(x92101)))
% 11.41/11.18 [9258]P85(f784(f71(x92581),x92582))+~P85(f784(f784(f347(f868(f869(x92581,a852),f869(x92581,a852))),f784(f784(f251(f869(x92581,a852),f869(x92581,a852)),x92583),x92582)),f309(x92581)))
% 11.41/11.18 [9539]~P44(x95391,x95392,x95393)+P85(f784(f784(f243(a1),f784(f784(f82(f868(a1,a1),a1,x95391,f250(a1,a1)),f217(x95391)),f234(x95391,x95392,f231(x95391,x95393)))),f2(a1)))
% 11.41/11.18 [9540]~P45(x95401,x95402,x95403)+P85(f784(f784(f242(a1),f784(f784(f82(f868(a1,a1),a1,x95401,f250(a1,a1)),f217(x95401)),f234(x95401,x95402,f231(x95401,x95403)))),f2(a1)))
% 11.41/11.18 [9661]P44(x96611,x96612,x96613)+~P85(f784(f784(f243(a1),f784(f784(f82(f868(a1,a1),a1,x96611,f250(a1,a1)),f217(x96611)),f234(x96611,x96612,f231(x96611,x96613)))),f2(a1)))
% 11.41/11.18 [9662]P45(x96621,x96622,x96623)+~P85(f784(f784(f242(a1),f784(f784(f82(f868(a1,a1),a1,x96621,f250(a1,a1)),f217(x96621)),f234(x96621,x96622,f231(x96621,x96623)))),f2(a1)))
% 11.41/11.18 [9993]~P113(x99931)+~P85(f784(f784(f243(x99931),f784(f784(f89(x99931),f784(f784(f252(x99931),x99932),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99931),x99933),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))),f2(x99931)))
% 11.41/11.18 [4661]~E(x46613,f120(x46611))+E(f784(f784(f130(x46611),x46612),x46613),x46612)
% 11.41/11.18 [4662]~E(x46622,f120(x46621))+E(f784(f784(f130(x46621),x46622),x46623),x46623)
% 11.41/11.18 [4663]~E(x46633,f120(x46631))+E(f784(f784(f130(x46631),x46632),x46633),x46632)
% 11.41/11.18 [4664]~E(x46642,f120(x46641))+E(f784(f784(f130(x46641),x46642),x46643),x46643)
% 11.41/11.18 [4670]~E(x46702,f2(a859))+E(f784(f784(f165(x46701),x46702),x46703),f120(x46701))
% 11.41/11.18 [4674]~E(x46743,f120(x46741))+E(f784(f784(f165(x46741),x46742),x46743),f120(x46741))
% 11.41/11.18 [4713]~E(x47131,x47133)+E(x47131,f784(f784(f130(x47132),f120(x47132)),x47133))
% 11.41/11.18 [4794]~P107(x47942)+E(f784(f249(f869(x47941,x47942)),x47943),f249(x47942))
% 11.41/11.18 [4795]~P102(x47952)+E(f784(f187(f869(x47951,x47952)),x47953),f187(x47952))
% 11.41/11.18 [4796]~P102(x47962)+E(f784(f187(f869(x47961,x47962)),x47963),f187(x47962))
% 11.41/11.18 [4813]E(x48131,f120(x48132))+~E(f784(f784(f130(x48132),x48131),x48133),x48133)
% 11.41/11.18 [4814]E(x48141,f120(x48142))+~E(f784(f784(f130(x48142),x48143),x48141),x48143)
% 11.41/11.18 [4815]E(x48151,f120(x48152))+~E(f784(f784(f130(x48152),x48153),x48151),x48153)
% 11.41/11.18 [4816]E(x48161,f120(x48162))+~E(f784(f784(f130(x48162),x48161),x48163),x48163)
% 11.41/11.18 [4822]E(x48221,f120(x48222))+~E(f784(f784(f130(x48222),x48223),x48221),f120(x48222))
% 11.41/11.18 [4823]E(x48231,f120(x48232))+~E(f784(f784(f130(x48232),x48231),x48233),f120(x48232))
% 11.41/11.18 [4824]E(x48241,f120(x48242))+~E(f784(f784(f130(x48242),x48243),x48241),f120(x48242))
% 11.41/11.18 [4825]E(x48251,f120(x48252))+~E(f784(f784(f130(x48252),x48251),x48253),f120(x48252))
% 11.41/11.18 [4850]~E(x48502,f2(a859))+E(f784(f784(f90(a859),x48501),x48502),f784(f784(f90(a859),x48503),x48502))
% 11.41/11.18 [4851]~E(x48511,f2(a859))+E(f784(f784(f90(a859),x48511),x48512),f784(f784(f90(a859),x48511),x48513))
% 11.41/11.18 [4852]~E(x48521,f2(a859))+E(f784(f784(f90(a859),x48521),x48522),f784(f784(f90(a859),x48521),x48523))
% 11.41/11.18 [4905]~P86(x49051)+E(f784(f784(f89(x49051),x49052),x49053),f784(f784(f89(x49051),x49053),x49052))
% 11.41/11.18 [4906]~P86(x49061)+E(f784(f784(f90(x49061),x49062),x49063),f784(f784(f90(x49061),x49063),x49062))
% 11.41/11.18 [4907]~P101(x49071)+E(f784(f784(f246(x49071),x49072),x49073),f784(f784(f246(x49071),x49073),x49072))
% 11.41/11.18 [4908]~P101(x49081)+E(f784(f784(f246(x49081),x49082),x49083),f784(f784(f246(x49081),x49083),x49082))
% 11.41/11.18 [4909]~P101(x49091)+E(f784(f784(f186(x49091),x49092),x49093),f784(f784(f186(x49091),x49093),x49092))
% 11.41/11.18 [4910]~P101(x49101)+E(f784(f784(f186(x49101),x49102),x49103),f784(f784(f186(x49101),x49103),x49102))
% 11.41/11.18 [4911]~P93(x49111)+E(f784(f784(f110(x49111),x49112),x49113),f784(f784(f110(x49111),x49113),x49112))
% 11.41/11.18 [4912]~P98(x49121)+E(f784(f784(f110(x49121),x49122),x49123),f784(f784(f110(x49121),x49123),x49122))
% 11.41/11.18 [4913]~P98(x49131)+E(f784(f784(f110(x49131),x49132),x49133),f784(f784(f110(x49131),x49133),x49132))
% 11.41/11.18 [4914]~P93(x49141)+E(f784(f784(f111(x49141),x49142),x49143),f784(f784(f111(x49141),x49143),x49142))
% 11.41/11.18 [4915]~P99(x49151)+E(f784(f784(f111(x49151),x49152),x49153),f784(f784(f111(x49151),x49153),x49152))
% 11.41/11.18 [4916]~P99(x49161)+E(f784(f784(f111(x49161),x49162),x49163),f784(f784(f111(x49161),x49163),x49162))
% 11.41/11.18 [4982]E(f60(a859,x49821,x49822),f2(a859))+~E(x49821,f784(f784(f90(a859),x49822),x49823))
% 11.41/11.18 [4983]E(f60(a1,x49831,x49832),f2(a1))+~E(x49831,f784(f784(f90(a1),x49832),x49833))
% 11.41/11.18 [5043]E(x50431,x50432)+~E(f784(f784(f89(a859),x50433),x50431),f784(f784(f89(a859),x50433),x50432))
% 11.41/11.18 [5044]E(x50441,x50442)+~E(f784(f784(f89(a859),x50441),x50443),f784(f784(f89(a859),x50442),x50443))
% 11.41/11.18 [5054]~P105(x50541)+E(f784(f784(f89(x50541),x50542),f784(f88(x50541),x50543)),f784(f784(f3(x50541),x50542),x50543))
% 11.41/11.18 [5055]~P70(x50551)+E(f784(f784(f89(x50551),x50552),f784(f88(x50551),x50553)),f784(f784(f3(x50551),x50552),x50553))
% 11.41/11.18 [5056]~P3(x50561)+E(f784(f784(f89(x50561),x50562),f784(f88(x50561),x50563)),f784(f784(f3(x50561),x50562),x50563))
% 11.41/11.18 [5057]~P91(x50571)+E(f784(f784(f111(x50571),x50572),f784(f88(x50571),x50573)),f784(f784(f3(x50571),x50572),x50573))
% 11.41/11.18 [5058]~P70(x50581)+E(f784(f784(f3(x50581),x50582),f784(f88(x50581),x50583)),f784(f784(f89(x50581),x50582),x50583))
% 11.41/11.18 [5104]~P85(f784(x51043,x51042))+P85(f784(f784(f347(x51041),x51042),x51043))
% 11.41/11.18 [5105]~P68(x51052)+E(f784(f784(f8(x51051,x51052),x51053),f187(f869(x51051,a852))),f2(x51052))
% 11.41/11.18 [5106]~P68(x51062)+E(f784(f784(f8(x51061,x51062),x51063),f187(f869(x51061,a852))),f2(x51062))
% 11.41/11.18 [5107]~P71(x51072)+E(f784(f784(f11(x51071,x51072),x51073),f187(f869(x51071,a852))),f87(x51072))
% 11.41/11.18 [5108]~P71(x51082)+E(f784(f784(f11(x51081,x51082),x51083),f187(f869(x51081,a852))),f87(x51082))
% 11.41/11.18 [5152]~E(x51522,f784(f784(f89(a859),x51521),x51523))+P85(f784(f784(f242(a859),x51521),x51522))
% 11.41/11.18 [5154]~E(x51542,f187(f869(x51541,a852)))+E(f784(f784(f69(x51541),x51542),x51543),f187(f869(f869(x51541,a852),a852)))
% 11.41/11.18 [5155]~E(x51552,f187(f869(x51551,a852)))+E(f187(f869(f869(x51551,a852),a852)),f784(f784(f69(x51551),x51552),x51553))
% 11.41/11.18 [5221]~E(f784(f269(x52212,x52213),x52211),f187(f869(x52213,a852)))+E(x52211,f187(f869(f868(x52212,x52213),a852)))
% 11.41/11.18 [5222]~E(f784(f271(x52222,x52223),x52221),f187(f869(x52222,a852)))+E(x52221,f187(f869(f868(x52222,x52223),a852)))
% 11.41/11.18 [5252]E(f784(f269(x52521,x52522),x52523),f187(f869(x52522,a852)))+~E(x52523,f187(f869(f868(x52521,x52522),a852)))
% 11.41/11.18 [5253]E(f784(f271(x52531,x52532),x52533),f187(f869(x52531,a852)))+~E(x52533,f187(f869(f868(x52531,x52532),a852)))
% 11.41/11.18 [5256]E(f279(x52561,x52562,x52563),f784(f784(f3(a108),x52562),x52563))+P85(f784(f784(f243(a108),x52562),x52563))
% 11.41/11.18 [5272]P85(f784(x52721,x52722))+~P85(f784(f784(f347(x52723),x52722),x52721))
% 11.41/11.18 [5308]E(x53081,x53082)+~E(f784(f88(f869(x53083,a852)),x53081),f784(f88(f869(x53083,a852)),x53082))
% 11.41/11.18 [5313]E(f317(x53131,x53132,x53133),f190(f860(a851)))+~P85(f784(f784(f243(a1),x53132),x53133))
% 11.41/11.18 [5316]~E(x53161,f187(f869(x53162,a852)))+~P85(f784(f784(f347(x53162),x53163),x53161))
% 11.41/11.18 [5317]~E(x53171,f187(f869(x53172,a852)))+~P85(f784(f784(f347(x53172),x53173),x53171))
% 11.41/11.18 [5318]~E(x53181,f187(f869(x53182,a852)))+~P85(f784(f784(f347(x53182),x53183),x53181))
% 11.41/11.18 [5347]~E(x53472,f784(f784(f89(a1),x53471),f784(f109(a1),x53473)))+P85(f784(f784(f242(a1),x53471),x53472))
% 11.41/11.18 [5363]E(f784(f784(f312(x53631),x53632),x53633),x53633)+~P85(f784(f784(f347(x53631),x53632),x53633))
% 11.41/11.18 [5375]E(x53751,f187(f869(x53752,a852)))+~E(f784(f784(f69(x53752),x53751),x53753),f187(f869(f869(x53752,a852),a852)))
% 11.41/11.18 [5376]E(x53761,f187(f869(x53762,a852)))+~E(f187(f869(f869(x53762,a852),a852)),f784(f784(f69(x53762),x53761),x53763))
% 11.41/11.18 [5382]~P123(x53821)+E(f784(f784(f90(x53821),f784(f88(x53821),x53822)),f784(f88(x53821),x53823)),f784(f784(f90(x53821),x53822),x53823))
% 11.41/11.18 [5384]~P59(x53841)+E(f784(f784(f293(x53841),f784(f88(x53841),x53842)),f784(f88(x53841),x53843)),f784(f784(f293(x53841),x53842),x53843))
% 11.41/11.18 [5415]~P85(f784(x54153,x54152))+P85(f784(f784(f347(x54151),x54152),f784(f266(x54151),x54153)))
% 11.41/11.18 [5416]~P85(f784(x54163,x54162))+P85(f784(f784(f347(x54161),x54162),f784(f266(x54161),x54163)))
% 11.41/11.18 [5456]E(f154(x54561,x54562,x54563),x54563)+P85(f784(f784(f347(x54561),x54562),f784(f164(x54561),x54563)))
% 11.41/11.18 [5534]~P85(f784(f132(x55341),x55343))+P85(f784(f132(x55341),f784(f131(x55341,x55342),x55343)))
% 11.41/11.18 [5576]~P4(x55761)+E(f784(f784(f51(x55761),f60(x55761,x55762,x55763)),x55763),f2(x55761))
% 11.41/11.18 [5594]E(f166(x55941,f784(f784(f144(x55941),x55942),f120(x55941)),x55943),f120(x55941))+P85(f784(f784(f347(a859),f2(a859)),x55943))
% 11.41/11.18 [5659]E(x56591,x56592)+~E(f784(f784(f90(a859),f784(a160,x56593)),x56591),f784(f784(f90(a859),f784(a160,x56593)),x56592))
% 11.41/11.18 [5660]~E(x56602,f784(f784(f89(a1),x56601),f784(f109(a1),f784(a160,x56603))))+P85(f784(f784(f243(a1),x56601),x56602))
% 11.41/11.18 [5778]~E(x57783,f120(x57781))+E(f784(f784(f784(f180(f860(x57781),f860(x57781)),x57782),f161(x57781)),x57783),f120(x57781))
% 11.41/11.18 [5780]P85(f784(x57801,x57802))+~P85(f784(f784(f347(x57803),x57802),f784(f266(x57803),x57801)))
% 11.41/11.18 [5781]P85(f784(x57811,x57812))+~P85(f784(f784(f347(x57813),x57812),f784(f266(x57813),x57811)))
% 11.41/11.18 [5782]P85(f784(x57821,x57822))+~P85(f784(f784(f347(x57823),x57822),f784(f266(x57823),x57821)))
% 11.41/11.18 [5815]E(x58151,x58152)+~E(f784(f784(f312(x58153),x58151),f187(f869(x58153,a852))),f784(f784(f312(x58153),x58152),f187(f869(x58153,a852))))
% 11.41/11.18 [5825]~P100(x58251)+E(f784(f784(f111(f869(x58251,a852)),f784(f267(x58251),x58252)),f784(f304(x58251,x58252),x58253)),f187(f869(x58251,a852)))
% 11.41/11.18 [5886]~P77(x58861)+E(f784(f313(x58861,x58861,f88(x58861)),f784(f304(x58861,x58862),x58863)),f307(x58861,f784(f88(x58861),x58863),f784(f88(x58861),x58862)))
% 11.41/11.18 [5894]E(f784(f188(f860(x58941)),f154(x58941,x58942,x58943)),f784(f188(f860(x58941)),x58943))+P85(f784(f784(f347(x58941),x58942),f784(f164(x58941),x58943)))
% 11.41/11.18 [5915]P85(f784(x59151,x59152))+~P85(f784(f784(f347(x59153),x59152),f187(f869(x59153,a852))))
% 11.41/11.18 [5950]~P100(x59501)+E(f784(f784(f111(f869(x59501,a852)),f784(f304(x59501,x59502),x59503)),f784(f268(x59501),x59503)),f187(f869(x59501,a852)))
% 11.41/11.18 [5971]~P77(x59711)+E(f784(f313(x59711,x59711,f88(x59711)),f305(x59711,x59712,x59713)),f305(x59711,f784(f88(x59711),x59713),f784(f88(x59711),x59712)))
% 11.41/11.18 [5972]~P77(x59721)+E(f784(f313(x59721,x59721,f88(x59721)),f308(x59721,x59722,x59723)),f308(x59721,f784(f88(x59721),x59723),f784(f88(x59721),x59722)))
% 11.41/11.18 [6030]E(f166(x60301,f784(f784(f144(x60301),x60302),f120(x60301)),x60303),f784(f784(f144(x60301),x60302),f120(x60301)))+~P85(f784(f784(f347(a859),f2(a859)),x60303))
% 11.41/11.18 [6038]~P77(x60381)+E(f784(f313(x60381,x60381,f88(x60381)),f307(x60381,x60382,x60383)),f784(f304(x60381,f784(f88(x60381),x60383)),f784(f88(x60381),x60382)))
% 11.41/11.18 [6057]~P5(x60571)+E(f60(x60571,f784(f88(x60571),f60(x60571,x60572,x60573)),x60573),f60(x60571,f784(f88(x60571),x60572),x60573))
% 11.41/11.18 [6161]~P85(f784(f71(f868(x61612,x61611)),x61613))+P85(f784(f71(x61611),f784(f269(x61612,x61611),x61613)))
% 11.41/11.18 [6162]~P85(f784(f71(f868(x61621,x61622)),x61623))+P85(f784(f71(x61621),f784(f271(x61621,x61622),x61623)))
% 11.41/11.18 [6167]~P100(x61671)+E(f784(f784(f111(f869(x61671,a852)),f305(x61671,x61672,x61673)),f784(f306(x61671),x61673)),f187(f869(x61671,a852)))
% 11.41/11.18 [6168]~P100(x61681)+E(f784(f784(f111(f869(x61681,a852)),f307(x61681,x61682,x61683)),f784(f306(x61681),x61683)),f187(f869(x61681,a852)))
% 11.41/11.18 [6169]~P100(x61691)+E(f784(f784(f111(f869(x61691,a852)),f308(x61691,x61692,x61693)),f784(f268(x61691),x61693)),f187(f869(x61691,a852)))
% 11.41/11.18 [6236]E(f784(f784(f155(x62361),x62362),f741(x62362,x62363,x62361)),x62363)+~P85(f784(f784(f347(x62361),x62363),f784(f164(x62361),x62362)))
% 11.41/11.18 [6388]E(x63881,f120(x63882))+~E(f784(f784(f784(f180(f860(x63882),f860(x63882)),x63883),f161(x63882)),x63881),f120(x63882))
% 11.41/11.18 [6467]P38(x64671,x64672,f682(x64673,x64672,x64671),x64673)+~P85(f784(f784(f194(x64671),x64672),x64673))
% 11.41/11.18 [6468]P38(x64681,x64682,f828(x64683,x64682,x64681),x64683)+~P85(f784(f784(f194(x64681),x64682),x64683))
% 11.41/11.18 [6497]~P85(f784(f71(f868(x64972,x64971)),x64973))+P85(f784(f71(f868(x64971,x64972)),f784(f288(x64972,x64971),x64973)))
% 11.41/11.18 [6519]E(x65191,x65192)+~E(f292(a859,f289(a859),x65193,x65191),f784(f784(f312(a859),x65192),f187(f869(a859,a852))))
% 11.41/11.18 [6520]E(x65201,x65202)+~E(f292(a859,f289(a859),x65201,x65202),f784(f784(f312(a859),x65203),f187(f869(a859,a852))))
% 11.41/11.18 [6655]P53(x66551,x66552,x66553)+P85(f784(f784(f347(x66551),f640(x66553,x66552,x66551)),x66552))
% 11.41/11.18 [6656]P53(x66561,x66562,x66563)+P85(f784(f784(f347(x66561),f639(x66563,x66562,x66561)),x66562))
% 11.41/11.18 [6667]P85(f784(f334(x66671,x66672),x66673))+P85(f784(f784(x66672,f829(x66673,x66672,x66671)),x66673))
% 11.41/11.18 [6668]P85(f784(f334(x66681,x66682),x66683))+P85(f784(f784(x66682,f830(x66683,x66682,x66681)),x66683))
% 11.41/11.18 [6699]E(f784(f188(f860(x66991)),f154(x66991,x66992,x66993)),f784(f784(f3(a859),f784(f188(f860(x66991)),x66993)),f87(a859)))+~P85(f784(f784(f347(x66991),x66992),f784(f164(x66991),x66993)))
% 11.41/11.18 [6739]P85(f784(f255(x67391,x67392),x67393))+P85(f784(f784(f347(x67391),f604(x67393,x67392,x67391)),x67393))
% 11.41/11.18 [6751]~P85(f784(f71(f868(x67512,x67511)),f784(f288(x67511,x67512),x67513)))+P85(f784(f71(f868(x67511,x67512)),x67513))
% 11.41/11.18 [6812]~P85(f784(f784(f347(x68121),x68122),f784(f164(x68121),f121(x68121,x68123))))+P85(f784(f784(f347(x68121),x68122),f784(f164(x68121),x68123)))
% 11.41/11.18 [6819]P31(x68191,x68192,x68193)+P85(f784(f784(f347(f858(x68191)),f617(x68193,x68192,x68191)),x68193))
% 11.41/11.18 [6848]E(f784(f131(x68481,x68482),x68483),x68483)+P85(f784(f784(f347(x68481),f761(x68483,x68482,x68481)),f784(f164(x68481),x68483)))
% 11.41/11.18 [6865]E(f784(f131(x68651,x68652),x68653),f120(x68651))+P85(f784(f784(f347(x68651),f759(x68653,x68652,x68651)),f784(f164(x68651),x68653)))
% 11.41/11.18 [7012]P85(f784(f784(f347(x70121),x70122),f708(x70123,x70122,x70121)))+~P85(f784(f784(f347(x70121),x70122),f52(f869(x70121,a852),x70123)))
% 11.41/11.18 [7014]~P68(x70141)+E(f784(f784(f89(x70141),f784(f784(f8(a859,x70141),x70142),f784(f267(a859),x70143))),f784(x70142,x70143)),f784(f784(f8(a859,x70141),x70142),f784(f267(a859),f784(a160,x70143))))
% 11.41/11.18 [7117]~P85(f784(f784(f347(x71171),x71172),f698(x71172,x71173,x71171)))+P85(f784(f784(f347(x71171),x71172),f53(f869(x71171,a852),x71173)))
% 11.41/11.18 [7146]~P68(x71461)+E(f784(f784(f89(x71461),f784(f784(f8(a859,x71461),x71462),f784(f303(a859),x71463))),f784(x71462,f784(a160,x71463))),f784(f784(f8(a859,x71461),x71462),f784(f303(a859),f784(a160,x71463))))
% 11.41/11.18 [7300]P85(f784(f784(f347(f860(x73001)),x73002),f152(x73001,x73003)))+P85(f784(f784(f347(x73001),f757(x73003,x73002,x73001)),f784(f164(x73001),x73002)))
% 11.41/11.18 [7317]~P85(f784(f784(f347(f860(x73171)),x73172),f152(x73171,f335(x73171,x73173))))+P85(f784(f784(f347(f860(x73171)),x73172),f335(f860(x73171),f149(x73171,x73173))))
% 11.41/11.18 [7345]~P85(f784(f784(f347(f860(x73451)),x73452),f335(f860(x73451),f149(x73451,x73453))))+P85(f784(f784(f347(f860(x73451)),x73452),f152(x73451,f335(x73451,x73453))))
% 11.41/11.18 [7385]E(f784(f784(f784(f180(f860(x73851),f860(x73851)),x73852),f161(x73851)),x73853),x73853)+~P85(f784(f784(f242(a859),f784(f188(f860(x73851)),x73853)),f87(a859)))
% 11.41/11.18 [7437]~P26(x74371,x74372,x74373,f249(f869(x74371,a852)))+P26(f860(x74371),f860(x74372),f784(f146(x74371,x74372),x74373),f249(f869(f860(x74371),a852)))
% 11.41/11.18 [7438]~P26(x74381,x74382,x74383,f249(f869(x74381,a852)))+P26(f860(x74381),f860(x74382),f784(f146(x74381,x74382),x74383),f249(f869(f860(x74381),a852)))
% 11.41/11.18 [7595]E(x75951,f784(f784(f89(a859),f784(f784(f90(a859),f784(f250(a859,a859),x75952)),x75953)),f784(f260(a859,a859),x75952)))+~P85(f784(f63(x75951,x75953),x75952))
% 11.41/11.18 [7602]P26(x76021,x76022,x76023,f249(f869(x76021,a852)))+~P26(f860(x76021),f860(x76022),f784(f146(x76021,x76022),x76023),f249(f869(f860(x76021),a852)))
% 11.41/11.18 [7603]P26(x76031,x76032,x76033,f249(f869(x76031,a852)))+~P26(f860(x76031),f860(x76032),f784(f146(x76031,x76032),x76033),f249(f869(f860(x76031),a852)))
% 11.41/11.18 [7646]P85(f784(f784(f347(f869(x76461,a852)),f698(x76462,x76463,x76461)),x76463))+P85(f784(f784(f347(x76461),x76462),f53(f869(x76461,a852),x76463)))
% 11.41/11.18 [7734]P85(f784(f784(f347(f860(x77341)),x77342),f152(x77341,x77343)))+~P85(f784(f784(f347(x77341),f757(x77343,x77342,x77341)),x77343))
% 11.41/11.18 [7865]E(x78651,x78652)+~E(f784(f784(f9(x78653,f869(x78653,a852),a852),f347(x78653)),x78651),f784(f784(f9(x78653,f869(x78653,a852),a852),f347(x78653)),x78652))
% 11.41/11.18 [7871]~P85(f784(f784(f347(f868(x78711,x78711)),x78713),f270(x78711,x78712)))+P85(f784(f784(f347(x78711),f485(x78712,x78713,x78711)),x78712))
% 11.41/11.18 [7873]~P85(f784(f784(f347(x78731),x78733),f52(f869(x78731,a852),x78732)))+P85(f784(f784(f347(f869(x78731,a852)),f708(x78732,x78733,x78731)),x78732))
% 11.41/11.18 [8130]E(f784(f239(f864(f860(a851)),f860(a851),f317(x81301,x81302,f784(f784(f89(a1),x81303),f87(a1))),f237(f860(a851))),f784(x81301,x81303)),f317(x81301,x81302,x81303))+P85(f784(f784(f243(a1),x81302),x81303))
% 11.41/11.18 [8228]E(x82281,f120(x82282))+P85(f784(f784(f347(x82282),f784(f250(x82282,f868(a108,a108)),f784(f280(x82282,x82281),x82283))),f784(f164(x82282),x82281)))
% 11.41/11.18 [8327]~P2(x83271)+E(f784(f136(x83271,x83271,f784(f9(x83271,x83271,x83271),f89(x83271)),x83272),f784(f162(x83271),x83273)),f784(f136(x83271,x83271,f89(x83271),x83272),x83273))
% 11.41/11.18 [8787]~P101(x87871)+E(f784(f164(x87871),f143(x87871,x87871,f7(x87871),x87872,x87873)),f784(f784(f312(x87871),x87872),f784(f164(x87871),x87873)))
% 11.41/11.18 [8796]P85(f784(f784(f243(a859),f2(a859)),f649(x87961,x87962,x87963)))+~P85(f784(f784(f347(f868(x87963,x87963)),x87962),f784(f784(f291(x87963,x87963,x87963),x87961),f310(x87963,x87961))))
% 11.41/11.18 [9062]~P55(x90621,x90622)+~P85(f784(f784(f347(f868(x90621,x90621)),f784(f784(f251(x90621,x90621),x90623),x90623)),f784(f784(f291(x90621,x90621,x90621),x90622),f310(x90621,x90622))))
% 11.41/11.18 [9173]~E(f784(f784(f111(f869(f868(x91731,x91731),a852)),f784(f288(x91731,x91731),x91732)),f310(x91731,x91732)),f187(f869(f868(x91731,x91731),a852)))+~P85(f784(f784(f347(f868(x91731,x91731)),f784(f784(f251(x91731,x91731),x91733),x91733)),f784(f784(f291(x91731,x91731,x91731),x91732),f310(x91731,x91732))))
% 11.41/11.18 [9346]~P85(f784(f71(x93461),x93462))+P85(f784(f784(f242(a859),f784(f50(x93461),f784(f784(f3(f869(x93461,a852)),x93462),f784(f784(f312(x93461),x93463),f187(f869(x93461,a852)))))),f784(f50(x93461),x93462)))
% 11.41/11.18 [4964]~E(x49643,f120(x49641))+E(f138(x49641,f784(f784(f144(x49641),x49642),x49643)),x49642)
% 11.41/11.18 [4965]~E(x49653,f120(x49651))+E(f138(x49651,f784(f784(f144(x49651),x49652),x49653)),x49652)
% 11.41/11.18 [4979]~E(x49793,f120(x49791))+E(f121(x49791,f784(f784(f144(x49791),x49792),x49793)),f120(x49791))
% 11.41/11.18 [5007]E(x50071,f120(x50072))+E(f138(x50072,f784(f784(f144(x50072),x50073),x50071)),f138(x50072,x50071))
% 11.41/11.18 [5008]E(x50081,f120(x50082))+E(f138(x50082,f784(f784(f144(x50082),x50083),x50081)),f138(x50082,x50081))
% 11.41/11.18 [5009]E(x50091,f120(x50092))+E(f138(x50092,f784(f784(f130(x50092),x50093),x50091)),f138(x50092,x50091))
% 11.41/11.18 [5010]E(x50101,f120(x50102))+E(f138(x50102,f784(f784(f130(x50102),x50103),x50101)),f138(x50102,x50101))
% 11.41/11.18 [5016]~E(x50163,f120(x50161))+E(f138(x50161,f784(f784(f130(x50161),x50162),x50163)),f138(x50161,x50162))
% 11.41/11.18 [5017]~E(x50173,f120(x50171))+E(f138(x50171,f784(f784(f130(x50171),x50172),x50173)),f138(x50171,x50172))
% 11.41/11.18 [5018]~E(x50183,f120(x50181))+E(f121(x50181,f784(f784(f130(x50181),x50182),x50183)),f121(x50181,x50182))
% 11.41/11.18 [5047]E(x50471,f120(x50472))+E(f784(f135(x50472),f784(f784(f130(x50472),x50471),x50473)),f784(f135(x50472),x50471))
% 11.41/11.18 [5048]E(x50481,f120(x50482))+E(f784(f135(x50482),f784(f784(f130(x50482),x50481),x50483)),f784(f135(x50482),x50481))
% 11.41/11.18 [5079]~E(x50792,f120(x50791))+E(f784(f135(x50791),f784(f784(f130(x50791),x50792),x50793)),f784(f135(x50791),x50793))
% 11.41/11.18 [5129]~P101(x51291)+E(f784(f784(f246(x51291),x51292),f784(f784(f186(x51291),x51292),x51293)),x51292)
% 11.41/11.18 [5130]~P101(x51301)+E(f784(f784(f186(x51301),x51302),f784(f784(f246(x51301),x51302),x51303)),x51302)
% 11.41/11.18 [5131]~P93(x51311)+E(f784(f784(f110(x51311),x51312),f784(f784(f111(x51311),x51312),x51313)),x51312)
% 11.41/11.18 [5132]~P93(x51321)+E(f784(f784(f111(x51321),x51322),f784(f784(f110(x51321),x51322),x51323)),x51322)
% 11.41/11.18 [5150]~P4(x51501)+E(f60(x51501,f784(f784(f90(x51501),x51502),x51503),x51503),f2(x51501))
% 11.41/11.18 [5151]~P4(x51511)+E(f60(x51511,f784(f784(f90(x51511),x51512),x51513),x51512),f2(x51511))
% 11.41/11.18 [5216]~P3(x52161)+E(f784(f88(x52161),f784(f784(f3(x52161),x52162),x52163)),f784(f784(f3(x52161),x52163),x52162))
% 11.41/11.18 [5276]E(x52761,f120(x52762))+E(f121(x52762,f784(f784(f144(x52762),x52763),x52761)),f784(f784(f144(x52762),x52763),f121(x52762,x52761)))
% 11.41/11.18 [5277]E(x52771,f120(x52772))+E(f121(x52772,f784(f784(f130(x52772),x52773),x52771)),f784(f784(f130(x52772),x52773),f121(x52772,x52771)))
% 11.41/11.18 [5278]~P6(x52781)+E(f53(x52781,f784(f784(f312(x52781),x52782),x52783)),f784(f784(f111(x52781),x52782),f53(x52781,x52783)))
% 11.41/11.18 [5279]~P6(x52791)+E(f52(x52791,f784(f784(f312(x52791),x52792),x52793)),f784(f784(f110(x52791),x52792),f52(x52791,x52793)))
% 11.41/11.18 [5322]~P92(x53221)+E(f784(f784(f90(x53221),x53222),f784(f784(f90(x53221),x53222),x53223)),f784(f784(f90(x53221),x53222),x53223))
% 11.41/11.18 [5323]~P101(x53231)+E(f784(f784(f246(x53231),x53232),f784(f784(f246(x53231),x53232),x53233)),f784(f784(f246(x53231),x53232),x53233))
% 11.41/11.18 [5324]~P101(x53241)+E(f784(f784(f246(x53241),x53242),f784(f784(f246(x53241),x53242),x53243)),f784(f784(f246(x53241),x53242),x53243))
% 11.41/11.18 [5325]~P101(x53251)+E(f784(f784(f186(x53251),x53252),f784(f784(f186(x53251),x53252),x53253)),f784(f784(f186(x53251),x53252),x53253))
% 11.41/11.18 [5326]~P101(x53261)+E(f784(f784(f186(x53261),x53262),f784(f784(f186(x53261),x53262),x53263)),f784(f784(f186(x53261),x53262),x53263))
% 11.41/11.18 [5327]~P93(x53271)+E(f784(f784(f110(x53271),x53272),f784(f784(f110(x53271),x53272),x53273)),f784(f784(f110(x53271),x53272),x53273))
% 11.41/11.18 [5328]~P98(x53281)+E(f784(f784(f110(x53281),x53282),f784(f784(f110(x53281),x53282),x53283)),f784(f784(f110(x53281),x53282),x53283))
% 11.41/11.18 [5329]~P98(x53291)+E(f784(f784(f110(x53291),x53292),f784(f784(f110(x53291),x53292),x53293)),f784(f784(f110(x53291),x53292),x53293))
% 11.41/11.18 [5330]~P93(x53301)+E(f784(f784(f111(x53301),x53302),f784(f784(f111(x53301),x53302),x53303)),f784(f784(f111(x53301),x53302),x53303))
% 11.41/11.18 [5331]~P99(x53311)+E(f784(f784(f111(x53311),x53312),f784(f784(f111(x53311),x53312),x53313)),f784(f784(f111(x53311),x53312),x53313))
% 11.41/11.18 [5332]~P99(x53321)+E(f784(f784(f111(x53321),x53322),f784(f784(f111(x53321),x53322),x53323)),f784(f784(f111(x53321),x53322),x53323))
% 11.41/11.18 [5340]~P4(x53401)+E(f60(x53401,f784(f784(f89(x53401),x53402),x53403),x53403),f60(x53401,x53402,x53403))
% 11.41/11.18 [5341]~P4(x53411)+E(f60(x53411,f784(f784(f89(x53411),x53412),x53413),x53412),f60(x53411,x53413,x53412))
% 11.41/11.18 [5348]~P123(x53481)+E(f784(f784(f90(x53481),x53482),f784(f88(x53481),x53483)),f784(f88(x53481),f784(f784(f90(x53481),x53482),x53483)))
% 11.41/11.18 [5349]~P59(x53491)+E(f784(f784(f293(x53491),x53492),f784(f88(x53491),x53493)),f784(f88(x53491),f784(f784(f293(x53491),x53492),x53493)))
% 11.41/11.18 [5350]~P67(x53501)+E(f784(f784(f89(x53501),x53502),f784(f157(x53501),x53503)),f784(f157(x53501),f784(f784(f144(x53501),x53502),x53503)))
% 11.41/11.18 [5381]~P123(x53811)+E(f784(f784(f90(x53811),f784(f88(x53811),x53812)),x53813),f784(f784(f90(x53811),x53812),f784(f88(x53811),x53813)))
% 11.41/11.18 [5387]~P9(x53871,x53872,x53873)+E(f52(f869(x53871,a852),f784(f784(f69(x53871),x53872),x53873)),x53872)
% 11.41/11.18 [5447]~P86(x54471)+E(f784(f784(f90(x54471),x54472),f784(f784(f252(x54471),x54472),x54473)),f784(f784(f252(x54471),x54472),f784(a160,x54473)))
% 11.41/11.18 [5448]~P106(x54481)+E(f784(f784(f90(x54481),x54482),f784(f784(f252(x54481),x54482),x54483)),f784(f784(f252(x54481),x54482),f784(a160,x54483)))
% 11.41/11.18 [5449]~P86(x54491)+E(f784(f784(f90(x54491),x54492),f784(f784(f252(x54491),x54492),x54493)),f784(f784(f252(x54491),x54492),f784(a160,x54493)))
% 11.41/11.18 [5459]~P70(x54591)+E(f784(f784(f89(x54591),f784(f88(x54591),x54592)),f784(f784(f89(x54591),x54592),x54593)),x54593)
% 11.41/11.18 [5478]~P112(x54781)+E(f784(f784(f252(x54781),f784(f109(x54781),x54782)),x54783),f784(f109(x54781),f784(f784(f252(a859),x54782),x54783)))
% 11.41/11.18 [5479]~P136(x54791)+E(f784(f784(f252(x54791),f784(f112(x54791),x54792)),x54793),f784(f112(x54791),f784(f784(f252(a1),x54792),x54793)))
% 11.41/11.18 [5484]~P79(x54841)+E(f784(f84(x54841),f784(f784(f3(x54841),x54842),x54843)),f784(f84(x54841),f784(f784(f3(x54841),x54843),x54842)))
% 11.41/11.18 [5486]~P113(x54861)+E(f784(f784(f90(x54861),f91(x54861,x54862)),f91(x54861,x54863)),f91(x54861,f784(f784(f90(x54861),x54862),x54863)))
% 11.41/11.18 [5490]E(x54901,f120(x54902))+E(f784(f784(f130(x54902),f784(f163(x54902),x54901)),x54903),f784(f163(x54902),f784(f784(f130(x54902),x54901),x54903)))
% 11.41/11.18 [5496]~E(x54962,f784(a160,f784(f784(f89(a859),x54961),x54963)))+P85(f784(f784(f243(a859),x54961),x54962))
% 11.41/11.18 [5497]~P123(x54971)+E(f784(f784(f90(x54971),f784(f88(x54971),x54972)),x54973),f784(f88(x54971),f784(f784(f90(x54971),x54972),x54973)))
% 11.41/11.18 [5498]~P116(x54981)+E(f784(f784(f293(x54981),f784(f88(x54981),x54982)),x54983),f784(f88(x54981),f784(f784(f293(x54981),x54982),x54983)))
% 11.41/11.18 [5499]~P113(x54991)+E(f784(f784(f252(x54991),f784(f84(x54991),x54992)),x54993),f784(f84(x54991),f784(f784(f252(x54991),x54992),x54993)))
% 11.41/11.18 [5593]E(f506(x55931,x55932,x55933),f510(x55931,x55932,x55933))+E(f784(f784(f111(f869(x55933,a852)),x55932),x55931),f187(f869(x55933,a852)))
% 11.41/11.18 [5607]~P68(x56072)+E(f784(f784(f8(x56071,x56072),f784(f18(x56072,x56071),f2(x56072))),x56073),f2(x56072))
% 11.41/11.18 [5608]~P71(x56082)+E(f784(f784(f11(x56081,x56082),f784(f18(x56082,x56081),f87(x56082))),x56083),f87(x56082))
% 11.41/11.18 [5610]~P112(x56101)+E(f784(f784(f89(x56101),f784(f109(x56101),x56102)),f784(f109(x56101),x56103)),f784(f109(x56101),f784(f784(f89(a859),x56102),x56103)))
% 11.41/11.18 [5611]~P112(x56111)+E(f784(f784(f90(x56111),f784(f109(x56111),x56112)),f784(f109(x56111),x56113)),f784(f109(x56111),f784(f784(f90(a859),x56112),x56113)))
% 11.41/11.18 [5612]~P136(x56121)+E(f784(f784(f89(x56121),f784(f112(x56121),x56122)),f784(f112(x56121),x56123)),f784(f112(x56121),f784(f784(f89(a1),x56122),x56123)))
% 11.41/11.18 [5613]~P136(x56131)+E(f784(f784(f90(x56131),f784(f112(x56131),x56132)),f784(f112(x56131),x56133)),f784(f112(x56131),f784(f784(f90(a1),x56132),x56133)))
% 11.41/11.18 [5614]~P136(x56141)+E(f784(f784(f3(x56141),f784(f112(x56141),x56142)),f784(f112(x56141),x56143)),f784(f112(x56141),f784(f784(f3(a1),x56142),x56143)))
% 11.41/11.18 [5615]~P89(x56151)+E(f784(f784(f89(x56151),f784(f113(x56151),x56152)),f784(f113(x56151),x56153)),f784(f113(x56151),f784(f784(f89(a1),x56152),x56153)))
% 11.41/11.18 [5616]~P89(x56161)+E(f784(f784(f90(x56161),f784(f113(x56161),x56162)),f784(f113(x56161),x56163)),f784(f113(x56161),f784(f784(f90(a1),x56162),x56163)))
% 11.41/11.18 [5617]~P89(x56171)+E(f784(f784(f3(x56171),f784(f113(x56171),x56172)),f784(f113(x56171),x56173)),f784(f113(x56171),f784(f784(f3(a1),x56172),x56173)))
% 11.41/11.18 [5618]~P89(x56181)+E(f784(f784(f89(x56181),f784(f113(x56181),x56182)),f784(f113(x56181),x56183)),f784(f113(x56181),f784(f784(f89(a1),x56182),x56183)))
% 11.41/11.18 [5619]~P89(x56191)+E(f784(f784(f90(x56191),f784(f113(x56191),x56192)),f784(f113(x56191),x56193)),f784(f113(x56191),f784(f784(f90(a1),x56192),x56193)))
% 11.41/11.18 [5666]~E(x56663,x56662)+P85(f784(f784(f242(f869(x56661,a852)),x56662),x56663))
% 11.41/11.18 [5667]~E(x56672,x56673)+P85(f784(f784(f242(f869(x56671,a852)),x56672),x56673))
% 11.41/11.18 [5668]~E(x56682,x56683)+P85(f784(f784(f242(f869(x56681,a852)),x56682),x56683))
% 11.41/11.18 [5669]~E(x56692,x56693)+P85(f784(f784(f242(f869(x56691,a852)),x56692),x56693))
% 11.41/11.18 [5670]~E(x56702,x56703)+P85(f784(f784(f242(f869(x56701,a852)),x56702),x56703))
% 11.41/11.18 [5671]~E(x56712,x56713)+P85(f784(f784(f242(f869(x56711,a852)),x56712),x56713))
% 11.41/11.18 [5672]~E(x56722,x56723)+P85(f784(f784(f242(f869(x56721,a852)),x56722),x56723))
% 11.41/11.18 [5677]~P70(x56771)+E(f784(f784(f89(x56771),f784(f88(x56771),x56772)),f784(f88(x56771),x56773)),f784(f88(x56771),f784(f784(f89(x56771),x56773),x56772)))
% 11.41/11.18 [5678]~P3(x56781)+E(f784(f784(f89(x56781),f784(f88(x56781),x56782)),f784(f88(x56781),x56783)),f784(f88(x56781),f784(f784(f89(x56781),x56782),x56783)))
% 11.41/11.18 [5679]~P69(x56791)+E(f784(f784(f186(x56791),f784(f88(x56791),x56792)),f784(f88(x56791),x56793)),f784(f88(x56791),f784(f784(f246(x56791),x56792),x56793)))
% 11.41/11.18 [5680]~P69(x56801)+E(f784(f784(f246(x56801),f784(f88(x56801),x56802)),f784(f88(x56801),x56803)),f784(f88(x56801),f784(f784(f186(x56801),x56802),x56803)))
% 11.41/11.18 [5681]~P91(x56811)+E(f784(f784(f111(x56811),f784(f88(x56811),x56812)),f784(f88(x56811),x56813)),f784(f88(x56811),f784(f784(f110(x56811),x56812),x56813)))
% 11.41/11.18 [5682]~P91(x56821)+E(f784(f784(f110(x56821),f784(f88(x56821),x56822)),f784(f88(x56821),x56823)),f784(f88(x56821),f784(f784(f111(x56821),x56822),x56823)))
% 11.41/11.18 [5683]~P113(x56831)+E(f784(f784(f90(x56831),f784(f84(x56831),x56832)),f784(f84(x56831),x56833)),f784(f84(x56831),f784(f784(f90(x56831),x56832),x56833)))
% 11.41/11.18 [5684]~P61(x56841)+E(f784(f784(f293(x56841),f784(f84(x56841),x56842)),f784(f84(x56841),x56843)),f784(f84(x56841),f784(f784(f293(x56841),x56842),x56843)))
% 11.41/11.18 [5685]~P67(x56851)+E(f784(f784(f89(x56851),f784(f157(x56851),x56852)),f784(f157(x56851),x56853)),f784(f157(x56851),f784(f784(f130(x56851),x56852),x56853)))
% 11.41/11.18 [5686]E(x56861,f187(f869(x56862,a852)))+~E(f784(f784(f110(f869(x56862,a852)),x56863),x56861),f187(f869(x56862,a852)))
% 11.41/11.18 [5687]E(x56871,f187(f869(x56872,a852)))+~E(f784(f784(f110(f869(x56872,a852)),x56871),x56873),f187(f869(x56872,a852)))
% 11.41/11.18 [5688]~P143(x56881,x56882,x56883)+P85(f784(x56881,f784(f784(f51(a1),x56882),x56883)))
% 11.41/11.18 [5749]~P85(f784(f71(x57491),x57493))+P85(f784(f71(x57491),f784(f784(f312(x57491),x57492),x57493)))
% 11.41/11.18 [5750]~P85(f784(f71(x57501),x57503))+P85(f784(f71(x57501),f784(f784(f312(x57501),x57502),x57503)))
% 11.41/11.18 [5751]~P85(f784(f132(x57511),x57513))+P85(f784(f132(x57511),f784(f784(f165(x57511),x57512),x57513)))
% 11.41/11.18 [5752]~P85(f784(f132(x57521),x57523))+P85(f784(f132(x57521),f784(f784(f133(x57521),x57522),x57523)))
% 11.41/11.18 [5783]~P101(x57831)+P85(f784(f784(f242(x57831),x57832),f784(f784(f186(x57831),x57833),x57832)))
% 11.41/11.18 [5784]~P101(x57841)+P85(f784(f784(f242(x57841),x57842),f784(f784(f186(x57841),x57842),x57843)))
% 11.41/11.18 [5785]~P93(x57851)+P85(f784(f784(f242(x57851),x57852),f784(f784(f110(x57851),x57853),x57852)))
% 11.41/11.18 [5786]~P98(x57861)+P85(f784(f784(f242(x57861),x57862),f784(f784(f110(x57861),x57863),x57862)))
% 11.41/11.18 [5787]~P93(x57871)+P85(f784(f784(f242(x57871),x57872),f784(f784(f110(x57871),x57872),x57873)))
% 11.41/11.18 [5788]~P98(x57881)+P85(f784(f784(f242(x57881),x57882),f784(f784(f110(x57881),x57882),x57883)))
% 11.41/11.18 [5789]~P86(x57891)+P85(f784(f784(f289(x57891),x57892),f784(f784(f90(x57891),x57893),x57892)))
% 11.41/11.18 [5790]~P86(x57901)+P85(f784(f784(f289(x57901),x57902),f784(f784(f90(x57901),x57902),x57903)))
% 11.41/11.18 [5802]~E(x58021,f2(a859))+E(f784(f784(f51(a859),f784(f784(f90(a859),x58021),x58022)),f784(f784(f90(a859),x58021),x58023)),f2(a859))
% 11.41/11.18 [5866]P85(f784(x58661,x58662))+P85(f784(f784(f194(f37(x58661,x58663)),x58662),x58662))
% 11.41/11.18 [5867]P85(f784(x58671,x58672))+P85(f784(f784(f194(f37(x58671,x58673)),x58672),x58672))
% 11.41/11.18 [5879]~P89(x58791)+E(f784(f784(f3(x58791),f784(f113(x58791),x58792)),f784(f113(x58791),x58793)),f784(f113(x58791),f784(f784(f89(a1),x58792),f784(f88(a1),x58793))))
% 11.41/11.18 [5934]E(x59341,f2(a859))+E(f784(f784(f51(a859),f784(f784(f90(a859),x59341),x59342)),f784(f784(f90(a859),x59341),x59343)),f784(f784(f51(a859),x59342),x59343))
% 11.41/11.18 [6002]P143(x60021,x60022,x60023)+~P85(f784(x60021,f784(f784(f51(a1),x60022),x60023)))
% 11.41/11.18 [6078]E(x60781,f120(x60782))+E(f784(f784(f144(x60782),f784(f135(x60782),x60781)),f784(f784(f165(x60782),x60783),f784(f163(x60782),x60781))),f784(f784(f165(x60782),f784(a160,x60783)),x60781))
% 11.41/11.18 [6086]E(f784(f784(f3(f869(x60861,a852)),x60862),x60863),x60862)+~E(f784(f784(f111(f869(x60861,a852)),x60862),x60863),f187(f869(x60861,a852)))
% 11.41/11.18 [6129]~P85(f784(f784(f243(a859),x61291),x61293))+P85(f784(f784(f243(a859),x61291),f784(f784(f89(a859),x61292),x61293)))
% 11.41/11.18 [6130]~P85(f784(f784(f243(a859),x61301),x61303))+P85(f784(f784(f243(a859),x61301),f784(f784(f89(a859),x61302),x61303)))
% 11.41/11.18 [6131]~P85(f784(f784(f243(a859),x61311),x61312))+P85(f784(f784(f243(a859),x61311),f784(f784(f89(a859),x61312),x61313)))
% 11.41/11.18 [6132]~P85(f784(f784(f243(a859),x61321),x61322))+P85(f784(f784(f243(a859),x61321),f784(f784(f89(a859),x61322),x61323)))
% 11.41/11.18 [6133]~P85(f784(f784(f242(a859),x61331),x61333))+P85(f784(f784(f242(a859),x61331),f784(f784(f89(a859),x61332),x61333)))
% 11.41/11.18 [6134]~P85(f784(f784(f242(a859),x61341),x61343))+P85(f784(f784(f242(a859),x61341),f784(f784(f89(a859),x61342),x61343)))
% 11.41/11.18 [6135]~P85(f784(f784(f242(a859),x61351),x61352))+P85(f784(f784(f242(a859),x61351),f784(f784(f89(a859),x61352),x61353)))
% 11.41/11.18 [6136]~P85(f784(f784(f242(a859),x61361),x61362))+P85(f784(f784(f242(a859),x61361),f784(f784(f89(a859),x61362),x61363)))
% 11.41/11.18 [6175]P85(f784(f71(x61751),x61752))+~P85(f784(f71(x61751),f784(f784(f312(x61751),x61753),x61752)))
% 11.41/11.18 [6176]P85(f784(f132(x61761),x61762))+~P85(f784(f132(x61761),f784(f784(f144(x61761),x61763),x61762)))
% 11.41/11.18 [6177]P85(f784(f132(x61771),x61772))+~P85(f784(f132(x61771),f784(f784(f130(x61771),x61773),x61772)))
% 11.41/11.18 [6178]P85(f784(f132(x61781),x61782))+~P85(f784(f132(x61781),f784(f784(f130(x61781),x61782),x61783)))
% 11.41/11.18 [6222]~E(f60(a1,x62222,x62221),f60(a1,x62223,x62221))+P85(f784(f784(f289(a1),x62221),f784(f784(f3(a1),x62222),x62223)))
% 11.41/11.18 [6227]~P86(x62271)+E(f784(f784(f89(x62271),x62272),f784(f784(f90(x62271),x62273),x62272)),f784(f784(f90(x62271),f784(f784(f89(x62271),x62273),f87(x62271))),x62272))
% 11.41/11.18 [6275]~E(x62751,x62752)+~P85(f784(f784(f243(f869(x62753,a852)),x62751),x62752))
% 11.41/11.18 [6322]P85(f784(f784(f347(x63221),x63222),x63223))+P85(f784(f784(f347(x63221),x63222),f784(f88(f869(x63221,a852)),x63223)))
% 11.41/11.18 [6323]P85(f784(f784(f347(x63231),x63232),x63233))+P85(f784(f784(f347(x63231),x63232),f784(f88(f869(x63231,a852)),x63233)))
% 11.41/11.18 [6330]E(f138(x63301,f784(f784(f133(x63301),x63302),x63303)),f138(x63301,x63303))+~P85(f784(f784(f243(a859),x63302),f784(f188(f860(x63301)),x63303)))
% 11.41/11.18 [6331]E(f784(f784(f165(x63311),x63312),f121(x63311,x63313)),f784(f784(f165(x63311),x63312),x63313))+~P85(f784(f784(f243(a859),x63312),f784(f188(f860(x63311)),x63313)))
% 11.41/11.18 [6390]E(f784(f784(f784(f180(f860(x63901),f860(x63901)),x63902),f161(x63901)),x63903),x63903)+~E(f60(a859,x63902,f784(f188(f860(x63901)),x63903)),f2(a859))
% 11.41/11.18 [6399]~P9(x63991,x63993,x63992)+E(f784(f784(f291(x63991,x63991,x63991),f784(f288(x63991,x63991),x63992)),x63992),x63992)
% 11.41/11.18 [6442]~E(f784(f784(f110(f869(x64421,a852)),x64422),x64423),x64423)+P85(f784(f784(f242(f869(x64421,a852)),x64422),x64423))
% 11.41/11.18 [6447]~P52(x64471,x64471,x64473)+P52(x64471,x64471,f784(f784(f180(f868(x64471,x64471),a852),x64472),x64473))
% 11.41/11.18 [6449]~P85(f784(f784(f347(x64491),x64493),f784(f164(x64491),x64492)))+P85(f784(f784(f243(a859),f2(a859)),f784(f188(f860(x64491)),x64492)))
% 11.41/11.18 [6466]~E(x64662,x64663)+P85(f784(f784(f347(x64661),x64662),f784(f784(f312(x64661),x64663),f187(f869(x64661,a852)))))
% 11.41/11.18 [6479]~P79(x64791)+E(f784(f84(x64791),f784(f784(f89(x64791),f784(f84(x64791),x64792)),f784(f84(x64791),x64793))),f784(f784(f89(x64791),f784(f84(x64791),x64792)),f784(f84(x64791),x64793)))
% 11.41/11.18 [6490]E(f784(f784(f51(a859),f784(f784(f90(a859),x64901),x64902)),f784(f784(f90(a859),x64901),x64903)),f784(f784(f51(a859),x64902),x64903))+~P85(f784(f784(f243(a859),f2(a859)),x64901))
% 11.41/11.18 [6517]E(f60(a1,x65171,x65172),f60(a1,x65173,x65172))+~P85(f784(f784(f289(a1),x65172),f784(f784(f3(a1),x65171),x65173)))
% 11.41/11.18 [6630]~P85(f784(f71(x66301),x66303))+E(f784(f784(f74(x66301,f869(x66301,a852),f312(x66301)),x66302),x66303),f784(f784(f110(f869(x66301,a852)),x66303),x66302))
% 11.41/11.18 [6692]E(f784(f784(f110(f869(x66921,a852)),x66922),x66923),x66922)+~P85(f784(f784(f242(f869(x66921,a852)),x66923),x66922))
% 11.41/11.18 [6693]E(f784(f784(f110(f869(x66931,a852)),x66932),x66933),x66933)+~P85(f784(f784(f242(f869(x66931,a852)),x66932),x66933))
% 11.41/11.18 [6694]E(f784(f784(f110(f869(x66941,a852)),x66942),x66943),x66943)+~P85(f784(f784(f242(f869(x66941,a852)),x66942),x66943))
% 11.41/11.18 [6695]E(f784(f784(f111(f869(x66951,a852)),x66952),x66953),x66953)+~P85(f784(f784(f242(f869(x66951,a852)),x66953),x66952))
% 11.41/11.18 [6696]E(f784(f784(f111(f869(x66961,a852)),x66962),x66963),x66962)+~P85(f784(f784(f242(f869(x66961,a852)),x66962),x66963))
% 11.41/11.18 [6749]~P85(f784(f132(x67491),x67492))+E(f784(f784(f3(f869(x67491,a852)),f784(f164(x67491),x67492)),f784(f784(f312(x67491),x67493),f187(f869(x67491,a852)))),f784(f164(x67491),f154(x67491,x67493,x67492)))
% 11.41/11.18 [6807]P35(x68071,x68072)+~P35(x68071,f784(f784(f180(f868(x68071,x68071),a852),x68073),x68072))
% 11.41/11.18 [6823]~E(x68231,f2(a859))+P85(f784(f784(f289(a859),f784(f784(f90(a859),x68231),x68232)),f784(f784(f90(a859),x68231),x68233)))
% 11.41/11.18 [6877]P85(f784(f64(x68771,x68772),f784(a66,x68773)))+~P85(f784(f64(f784(f88(a1),x68771),f784(f88(a1),x68772)),x68773))
% 11.41/11.18 [6882]E(f784(f784(f3(f869(x68821,a852)),f784(f784(f312(x68821),x68822),x68823)),f784(f784(f312(x68821),x68822),f187(f869(x68821,a852)))),x68823)+P85(f784(f784(f347(x68821),x68822),x68823))
% 11.41/11.18 [6900]E(f784(f784(f111(f869(x69001,a852)),f784(f164(x69001),x69002)),f784(f164(x69001),x69003)),f187(f869(x69001,a852)))+~P85(f784(f132(x69001),f784(f784(f130(x69001),x69002),x69003)))
% 11.41/11.18 [6917]~P85(f784(f784(f347(x69171),x69172),f784(f164(x69171),x69173)))+~P85(f784(f132(x69171),f784(f784(f144(x69171),x69172),x69173)))
% 11.41/11.18 [6993]E(f784(f784(f111(f869(x69931,a852)),x69932),x69933),f187(f869(x69931,a852)))+P85(f784(f784(f347(x69931),f506(x69933,x69932,x69931)),x69932))
% 11.41/11.18 [6994]E(f784(f784(f111(f869(x69941,a852)),x69942),x69943),f187(f869(x69941,a852)))+P85(f784(f784(f347(x69941),f510(x69943,x69942,x69941)),x69943))
% 11.41/11.18 [6998]E(f121(x69981,f784(f784(f165(x69981),x69982),x69983)),f784(f784(f165(x69981),f784(f784(f3(a859),x69982),f87(a859))),x69983))+~P85(f784(f784(f242(a859),x69982),f784(f188(f860(x69981)),x69983)))
% 11.41/11.18 [7080]P85(f784(f784(f243(a859),f2(a859)),x70801))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x70802),x70801)),f784(f784(f90(a859),x70803),x70801)))
% 11.41/11.18 [7081]P85(f784(f784(f243(a859),f2(a859)),x70811))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x70811),x70812)),f784(f784(f90(a859),x70811),x70813)))
% 11.41/11.18 [7082]~P85(f784(f784(f347(x70821),x70822),x70823))+~P85(f784(f784(f347(x70821),x70822),f784(f88(f869(x70821,a852)),x70823)))
% 11.41/11.18 [7083]~P85(f784(f784(f347(x70831),x70832),x70833))+~P85(f784(f784(f347(x70831),x70832),f784(f88(f869(x70831,a852)),x70833)))
% 11.41/11.18 [7084]~P85(f784(f784(f347(x70841),x70842),x70843))+~P85(f784(f784(f347(x70841),x70842),f784(f88(f869(x70841,a852)),x70843)))
% 11.41/11.18 [7088]~P85(f784(f784(f243(f869(x70881,a852)),x70882),x70883))+P85(f784(f784(f242(f869(x70881,a852)),x70882),x70883))
% 11.41/11.18 [7089]~P85(f784(f784(f243(f869(x70891,a852)),x70892),x70893))+P85(f784(f784(f242(f869(x70891,a852)),x70892),x70893))
% 11.41/11.18 [7090]~P85(f784(f784(f243(f869(x70901,a852)),x70902),x70903))+P85(f784(f784(f242(f869(x70901,a852)),x70902),x70903))
% 11.41/11.18 [7194]~P85(f784(f784(f243(a859),x71942),x71943))+P85(f784(f784(f243(a859),f784(f784(f89(a859),x71941),x71942)),f784(f784(f89(a859),x71941),x71943)))
% 11.41/11.18 [7195]~P85(f784(f784(f243(a859),x71951),x71953))+P85(f784(f784(f243(a859),f784(f784(f89(a859),x71951),x71952)),f784(f784(f89(a859),x71953),x71952)))
% 11.41/11.18 [7196]~P85(f784(f784(f243(a1),x71961),x71963))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x71961),x71962)),f784(f784(f89(a1),x71963),x71962)))
% 11.41/11.18 [7199]~P85(f784(f784(f242(a859),x71992),x71993))+P85(f784(f784(f242(a859),f784(f784(f89(a859),x71991),x71992)),f784(f784(f89(a859),x71991),x71993)))
% 11.41/11.18 [7200]~P85(f784(f784(f242(a859),x72001),x72003))+P85(f784(f784(f242(a859),f784(f784(f89(a859),x72001),x72002)),f784(f784(f89(a859),x72003),x72002)))
% 11.41/11.18 [7201]~P85(f784(f784(f242(a859),x72012),x72013))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x72011),x72012)),f784(f784(f90(a859),x72011),x72013)))
% 11.41/11.18 [7202]~P85(f784(f784(f242(a859),x72022),x72023))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x72021),x72022)),f784(f784(f90(a859),x72021),x72023)))
% 11.41/11.18 [7203]~P85(f784(f784(f242(a859),x72031),x72033))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x72031),x72032)),f784(f784(f90(a859),x72033),x72032)))
% 11.41/11.18 [7204]~P85(f784(f784(f242(a859),x72041),x72043))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x72041),x72042)),f784(f784(f90(a859),x72043),x72042)))
% 11.41/11.18 [7205]~P85(f784(f784(f242(a859),x72051),x72053))+P85(f784(f784(f242(a859),f784(f784(f51(a859),x72051),x72052)),f784(f784(f51(a859),x72053),x72052)))
% 11.41/11.18 [7206]~P85(f784(f784(f242(a859),x72063),x72062))+P85(f784(f784(f242(a859),f784(f784(f3(a859),x72061),x72062)),f784(f784(f3(a859),x72061),x72063)))
% 11.41/11.18 [7207]~P85(f784(f784(f242(a859),x72071),x72073))+P85(f784(f784(f242(a859),f784(f784(f3(a859),x72071),x72072)),f784(f784(f3(a859),x72073),x72072)))
% 11.41/11.18 [7208]~P85(f784(f784(f242(a1),x72082),x72083))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x72081),x72082)),f784(f784(f89(a1),x72081),x72083)))
% 11.41/11.18 [7211]~P85(f784(f784(f289(a859),x72112),x72113))+P85(f784(f784(f289(a859),f784(f784(f90(a859),x72111),x72112)),f784(f784(f90(a859),x72111),x72113)))
% 11.41/11.18 [7298]E(x72981,x72982)+~P85(f784(f784(f347(x72983),x72981),f784(f784(f312(x72983),x72982),f187(f869(x72983,a852)))))
% 11.41/11.18 [7299]E(x72991,x72992)+~P85(f784(f784(f347(x72993),x72991),f784(f784(f312(x72993),x72992),f187(f869(x72993,a852)))))
% 11.41/11.18 [7301]~E(f784(f784(f111(f869(x73011,a852)),x73012),x73013),f187(f869(x73011,a852)))+P85(f784(f784(f242(f869(x73011,a852)),x73012),f784(f88(f869(x73011,a852)),x73013)))
% 11.41/11.18 [7307]P85(f784(f784(f347(f869(x73071,a852)),x73072),f784(f311(x73071),x73073)))+~P85(f784(f784(f242(f869(x73071,a852)),x73072),x73073))
% 11.41/11.18 [7308]P85(f784(f784(f347(f869(x73081,a852)),x73082),f784(f311(x73081),x73083)))+~P85(f784(f784(f242(f869(x73081,a852)),x73082),x73083))
% 11.41/11.18 [7365]E(f784(f784(f144(x73651),f784(f784(f155(x73651),x73652),x73653)),f784(f784(f133(x73651),f784(a160,x73653)),x73652)),f784(f784(f133(x73651),x73653),x73652))+~P85(f784(f784(f243(a859),x73653),f784(f188(f860(x73651)),x73652)))
% 11.41/11.18 [7395]P85(f784(f784(f347(f868(x73951,x73951)),x73952),f310(x73951,x73953)))+~P85(f784(f784(f347(f868(x73951,x73951)),x73952),x73953))
% 11.41/11.18 [7404]~P85(f784(f784(f347(f869(x74041,a852)),x74042),f784(f311(x74041),x74043)))+P85(f784(f784(f242(f869(x74041,a852)),x74042),x74043))
% 11.41/11.18 [7405]~P85(f784(f784(f347(f869(x74051,a852)),x74052),f784(f311(x74051),x74053)))+P85(f784(f784(f242(f869(x74051,a852)),x74052),x74053))
% 11.41/11.18 [7446]P85(f784(f784(f242(f869(x74461,a852)),x74462),f52(f869(x74461,a852),x74463)))+~P85(f784(f784(f347(f869(x74461,a852)),x74462),x74463))
% 11.41/11.18 [7474]~P136(x74741)+E(f784(f784(f90(x74741),f784(f784(f252(x74741),f784(f88(x74741),f87(x74741))),x74742)),f784(f784(f252(x74741),x74743),x74742)),f784(f784(f252(x74741),f784(f88(x74741),x74743)),x74742))
% 11.41/11.18 [7496]E(f784(f784(f155(x74961),x74962),f784(f784(f3(a859),f784(f188(f860(x74961)),x74962)),f784(a160,x74963))),f784(f784(f155(x74961),f784(f162(x74961),x74962)),x74963))+~P85(f784(f784(f243(a859),x74963),f784(f188(f860(x74961)),x74962)))
% 11.41/11.18 [7513]~E(f784(f784(f111(f869(x75131,a852)),f686(x75133,x75132,x75131)),x75133),f187(f869(x75131,a852)))+E(f784(f784(f111(f869(x75131,a852)),f52(f869(x75131,a852),x75132)),x75133),f187(f869(x75131,a852)))
% 11.41/11.18 [7577]~P85(f784(f784(f347(x75773),x75772),f784(f164(x75773),x75771)))+P85(f784(f784(f243(a859),f741(x75771,x75772,x75773)),f784(f188(f860(x75773)),x75771)))
% 11.41/11.18 [7585]P85(f784(f784(f347(x75851),f784(f784(f155(x75851),x75852),x75853)),f784(f164(x75851),x75852)))+~P85(f784(f784(f243(a859),x75853),f784(f188(f860(x75851)),x75852)))
% 11.41/11.18 [7693]P85(f784(f784(f242(f869(f860(x76931),a852)),f152(x76931,x76932)),f152(x76931,x76933)))+~P85(f784(f784(f242(f869(x76931,a852)),x76932),x76933))
% 11.41/11.18 [7722]E(f784(f784(f111(f869(x77221,a852)),f52(f869(x77221,a852),x77222)),x77223),f187(f869(x77221,a852)))+P85(f784(f784(f347(f869(x77221,a852)),f686(x77223,x77222,x77221)),x77222))
% 11.41/11.18 [7724]~P85(f784(f784(f347(f869(x77241,a852)),x77243),x77242))+P85(f784(f784(f242(f869(x77241,a852)),f53(f869(x77241,a852),x77242)),x77243))
% 11.41/11.18 [7726]E(f784(f784(f111(f869(x77261,a852)),x77262),x77263),f187(f869(x77261,a852)))+~P85(f784(f784(f242(f869(x77261,a852)),x77262),f784(f88(f869(x77261,a852)),x77263)))
% 11.41/11.18 [7779]E(f784(f784(f3(a859),f784(f784(f89(a859),f784(f157(a859),x77791)),x77792)),f784(f784(f155(a859),x77791),x77793)),f784(f157(a859),f784(f784(f151(a859,x77791),x77793),x77792)))+~P85(f784(f784(f243(a859),x77793),f784(f188(f860(a859)),x77791)))
% 11.41/11.18 [7829]P85(f784(f784(f243(a859),x78291),x78292))+~P85(f784(f784(f243(a859),f784(f784(f89(a859),x78293),x78291)),f784(f784(f89(a859),x78293),x78292)))
% 11.41/11.18 [7830]P85(f784(f784(f243(a859),x78301),x78302))+~P85(f784(f784(f243(a859),f784(f784(f90(a859),x78303),x78301)),f784(f784(f90(a859),x78303),x78302)))
% 11.41/11.18 [7831]P85(f784(f784(f243(a859),x78311),x78312))+~P85(f784(f784(f243(a859),f784(f784(f90(a859),x78311),x78313)),f784(f784(f90(a859),x78312),x78313)))
% 11.41/11.18 [7834]P85(f784(f784(f242(a859),x78341),x78342))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),x78343),x78341)),f784(f784(f89(a859),x78343),x78342)))
% 11.41/11.18 [7863]P85(f784(f784(f243(a859),f2(a859)),x78631))+~P85(f784(f784(f243(a859),f784(f784(f90(a859),x78632),x78631)),f784(f784(f90(a859),x78633),x78631)))
% 11.41/11.18 [7864]P85(f784(f784(f243(a859),f2(a859)),x78641))+~P85(f784(f784(f243(a859),f784(f784(f90(a859),x78641),x78642)),f784(f784(f90(a859),x78641),x78643)))
% 11.41/11.18 [7936]E(f254(x79361,x79362,x79363),x79362)+~P85(f784(f784(f242(f869(x79361,a852)),x79363),f784(f784(f312(x79361),x79362),f187(f869(x79361,a852)))))
% 11.41/11.18 [8015]E(f784(f784(f130(x80151),f784(f784(f165(x80151),x80152),x80153)),f784(f784(f144(x80151),f784(f784(f155(x80151),x80153),x80152)),f120(x80151))),f784(f784(f165(x80151),f784(a160,x80152)),x80153))+~P85(f784(f784(f243(a859),x80152),f784(f188(f860(x80151)),x80153)))
% 11.41/11.18 [8083]P85(f784(f784(f242(f869(f869(x80831,a852),a852)),f255(x80831,x80832)),f255(x80831,x80833)))+~P85(f784(f784(f242(f869(x80831,a852)),x80832),x80833))
% 11.41/11.18 [8122]~P85(f784(f132(x81221),x81223))+P85(f784(f132(x81221),f784(f784(f784(f180(f860(x81221),f860(x81221)),x81222),f161(x81221)),x81223)))
% 11.41/11.18 [8127]~P85(f784(f784(f243(a859),x81272),x81273))+P85(f784(f784(f243(a859),f784(f784(f90(a859),f784(a160,x81271)),x81272)),f784(f784(f90(a859),f784(a160,x81271)),x81273)))
% 11.41/11.18 [8128]~P85(f784(f784(f242(a859),x81282),x81283))+P85(f784(f784(f242(a859),f784(f784(f90(a859),f784(a160,x81281)),x81282)),f784(f784(f90(a859),f784(a160,x81281)),x81283)))
% 11.41/11.18 [8148]P85(f784(f784(f242(f869(f869(x81481,a852),a852)),f784(f311(x81481),x81482)),f784(f311(x81481),x81483)))+~P85(f784(f784(f242(f869(x81481,a852)),x81482),x81483))
% 11.41/11.18 [8305]~P85(f784(f784(f242(f869(x83051,a852)),x83053),x83052))+P85(f784(f784(f242(f869(x83051,a852)),f784(f88(f869(x83051,a852)),x83052)),f784(f88(f869(x83051,a852)),x83053)))
% 11.41/11.18 [8306]~P85(f784(f784(f242(f869(x83061,a852)),x83063),x83062))+P85(f784(f784(f242(f869(x83061,a852)),f784(f88(f869(x83061,a852)),x83062)),f784(f88(f869(x83061,a852)),x83063)))
% 11.41/11.18 [8345]E(f784(f313(a859,a859,f784(f784(f9(a859,a859,a859),f3(a859)),x83451)),f784(f304(a859,x83452),x83453)),f784(f304(a859,f784(f784(f3(a859),x83452),x83451)),f784(f784(f3(a859),x83453),x83451)))+~P85(f784(f784(f243(a859),x83451),x83453))
% 11.41/11.18 [8371]~P67(x83711)+E(f784(f784(f89(x83711),x83712),f784(f136(x83711,x83711,f89(x83711),f2(x83711)),x83713)),f784(f136(x83711,x83711,f89(x83711),x83712),x83713))
% 11.41/11.18 [8451]~P79(x84511)+P85(f784(f784(f242(x84511),f784(f84(x84511),f784(f784(f89(x84511),x84512),x84513))),f784(f784(f89(x84511),f784(f84(x84511),x84512)),f784(f84(x84511),x84513))))
% 11.41/11.18 [8452]~P79(x84521)+P85(f784(f784(f242(x84521),f784(f84(x84521),f784(f784(f3(x84521),x84522),x84523))),f784(f784(f89(x84521),f784(f84(x84521),x84522)),f784(f84(x84521),x84523))))
% 11.41/11.18 [8462]E(f784(f784(f89(a1),f784(f784(f90(a1),x84621),f60(a1,f784(f784(f51(a1),x84622),x84621),x84623))),f60(a1,x84622,x84621)),f60(a1,x84622,f784(f784(f90(a1),x84621),x84623)))+~P85(f784(f784(f243(a1),f2(a1)),x84623))
% 11.41/11.18 [8470]E(f784(f784(f130(x84701),f784(f784(f165(x84701),x84702),x84703)),f784(f784(f144(x84701),f784(f135(x84701),f784(f784(f133(x84701),x84702),x84703))),f120(x84701))),f784(f784(f165(x84701),f784(a160,x84702)),x84703))+~P85(f784(f784(f243(a859),x84702),f784(f188(f860(x84701)),x84703)))
% 11.41/11.18 [8489]E(f784(f275(x84891,f784(f784(f146(x84891,f868(a108,x84891)),f784(f251(a108,x84891),f87(a108))),x84892)),f784(a5,x84893)),f784(f784(f155(x84891),x84892),x84893))+~P85(f784(f784(f243(a859),x84893),f784(f188(f860(x84891)),x84892)))
% 11.41/11.18 [8546]P85(f784(f784(f347(f868(x85461,x85461)),x85462),f784(f784(f291(x85461,x85461,x85461),x85463),f310(x85461,x85463))))+~P85(f784(f784(f347(f868(x85461,x85461)),x85462),x85463))
% 11.41/11.18 [8562]P85(f784(f784(f243(a859),x85621),x85622))+~P85(f784(f784(f243(a859),f784(f784(f90(a859),f784(a160,x85623)),x85621)),f784(f784(f90(a859),f784(a160,x85623)),x85622)))
% 11.41/11.18 [8563]P85(f784(f784(f242(a859),x85631),x85632))+~P85(f784(f784(f242(a859),f784(f784(f90(a859),f784(a160,x85633)),x85631)),f784(f784(f90(a859),f784(a160,x85633)),x85632)))
% 11.41/11.18 [8574]P85(f784(f784(f242(f869(x85741,a852)),x85742),x85743))+~P85(f784(f784(f242(f869(x85741,a852)),f784(f88(f869(x85741,a852)),x85743)),f784(f88(f869(x85741,a852)),x85742)))
% 11.41/11.18 [8593]P85(f784(f132(x85931),x85932))+~P85(f784(f132(x85931),f784(f784(f784(f180(f860(x85931),f860(x85931)),x85933),f161(x85931)),x85932)))
% 11.41/11.18 [8659]E(f784(f287(x86591,x86591,f310(x86591,x86592)),x86593),x86593)+~P85(f784(f784(f242(f869(x86591,a852)),f784(f287(x86591,x86591,x86592),x86593)),x86593))
% 11.41/11.18 [8661]E(f784(f313(f868(x86611,x86612),x86612,f260(x86611,x86612)),f784(f164(f868(x86611,x86612)),x86613)),f177(x86611,x86612,f172(x86611,x86612,x86613)))+~P85(f784(f132(x86611),f784(f784(f146(f868(x86611,x86612),x86611),f250(x86611,x86612)),x86613)))
% 11.41/11.18 [8700]~P101(x87001)+P15(x87001,f784(f131(x87001,f784(f784(f9(x87001,x87001,a852),a343),f784(x87002,x87003))),x87003))
% 11.41/11.18 [8705]~P85(f784(f784(f242(a859),x87051),x87052))+P85(f784(f784(f242(a859),x87051),f784(f136(a859,a859,f89(a859),x87052),x87053)))
% 11.41/11.18 [8776]~P85(f784(f784(f347(f868(x87761,x87761)),x87762),f310(x87761,x87763)))+P85(f784(f784(f347(f868(x87761,x87761)),x87762),f784(f784(f180(f868(x87761,x87761),a852),f644(x87763,x87762,x87761)),x87763)))
% 11.41/11.18 [8847]~P67(x88471)+E(f784(f784(f89(x88471),x88472),f784(f136(x88471,x88471,f784(f9(x88471,x88471,x88471),f89(x88471)),f2(x88471)),f784(f162(x88471),x88473))),f784(f136(x88471,x88471,f89(x88471),x88472),x88473))
% 11.41/11.18 [9107]P52(x91071,x91072,x91073)+P85(f784(f784(f347(f868(x91071,x91072)),f784(f784(f251(x91071,x91072),f658(x91073,x91072,x91071)),f652(x91073,x91072,x91071))),x91073))
% 11.41/11.18 [9108]P52(x91081,x91082,x91083)+P85(f784(f784(f347(f868(x91081,x91082)),f784(f784(f251(x91081,x91082),f658(x91083,x91082,x91081)),f651(x91083,x91082,x91081))),x91083))
% 11.41/11.18 [9164]~P85(f784(f784(f347(f868(x91641,x91641)),x91642),f784(f784(f291(x91641,x91641,x91641),x91643),f310(x91641,x91643))))+P85(f784(f784(f347(f868(x91641,x91641)),x91642),f784(f784(f180(f868(x91641,x91641),a852),f649(x91643,x91642,x91641)),x91643)))
% 11.41/11.18 [9239]~P85(f784(f784(f242(f869(x92391,a852)),x92392),x92393))+P85(f784(f784(f242(f869(x92391,a852)),f784(f784(f9(x92391,f869(x92391,a852),a852),f347(x92391)),x92392)),f784(f784(f9(x92391,f869(x92391,a852),a852),f347(x92391)),x92393)))
% 11.41/11.18 [9295]~P85(f784(f784(f347(f868(f869(x92951,a852),f869(x92951,a852))),f784(f784(f251(f869(x92951,a852),f869(x92951,a852)),x92952),x92953)),f309(x92951)))+P85(f784(f784(f243(f869(x92951,a852)),x92952),x92953))
% 11.41/11.18 [9321]P53(x93211,x93212,x93213)+~P85(f784(f784(f347(f868(x93211,x93211)),f784(f784(f251(x93211,x93211),f640(x93213,x93212,x93211)),f639(x93213,x93212,x93211))),x93213))
% 11.41/11.18 [9322]P53(x93221,x93222,x93223)+~P85(f784(f784(f347(f868(x93221,x93221)),f784(f784(f251(x93221,x93221),f639(x93223,x93222,x93221)),f640(x93223,x93222,x93221))),x93223))
% 11.41/11.18 [9356]~P85(f784(f784(f347(f868(f860(x93561),f860(x93561))),f784(f784(f251(f860(x93561),f860(x93561)),x93562),x93562)),f141(x93561,x93563)))+P85(f784(f784(f347(f868(x93561,x93561)),f784(f784(f251(x93561,x93561),f767(x93562,x93563,x93561)),f767(x93562,x93563,x93561))),x93563))
% 11.41/11.18 [9400]P85(f784(f784(f242(f869(x94001,a852)),x94002),x94003))+~P85(f784(f784(f242(f869(x94001,a852)),f784(f784(f9(x94001,f869(x94001,a852),a852),f347(x94001)),x94002)),f784(f784(f9(x94001,f869(x94001,a852),a852),f347(x94001)),x94003)))
% 11.41/11.18 [9487]E(f784(f784(f3(a859),f784(f784(f8(a859,a859),x94871),f784(f267(a859),x94872))),f784(f784(f8(a859,a859),x94873),f784(f267(a859),x94872))),f784(f784(f8(a859,a859),f784(f784(f20(a859,a859,a859),f784(f784(f10(a859,f869(a859,a859),a859),f3(a859)),x94871)),x94873)),f784(f267(a859),x94872)))+~P85(f784(f784(f242(a859),f784(x94873,f353(x94872,x94871,x94873))),f784(x94871,f353(x94872,x94871,x94873))))
% 11.41/11.18 [9777]E(f784(f266(f868(x97771,x97772)),f784(f261(x97771,x97772,a852),f784(f784(f9(x97771,f869(x97772,f864(x97772)),f869(x97772,a852)),f784(f784(f10(f869(f864(x97772),a852),f869(f869(x97772,f864(x97772)),f869(x97772,a852)),x97771),f10(f864(x97772),a852,x97772)),f784(f784(f10(f864(x97772),f869(f864(x97772),a852),x97771),a343),f172(x97771,x97772,x97773)))),f237(x97772)))),f784(f164(f868(x97771,x97772)),x97773))+~P85(f784(f132(x97771),f784(f784(f146(f868(x97771,x97772),x97771),f250(x97771,x97772)),x97773)))
% 11.41/11.18 [5531]~P70(x55311)+E(f784(f784(f89(x55311),f784(f784(f3(x55311),x55312),x55313)),x55313),x55312)
% 11.41/11.18 [5532]~P70(x55321)+E(f784(f784(f3(x55321),f784(f784(f89(x55321),x55322),x55323)),x55323),x55322)
% 11.41/11.18 [5758]~P70(x57581)+E(f784(f784(f89(x57581),x57582),f784(f784(f89(x57581),f784(f88(x57581),x57582)),x57583)),x57583)
% 11.41/11.18 [5841]~P75(x58411)+E(f784(f784(f90(x58411),f784(f784(f252(x58411),x58412),x58413)),x58412),f784(f784(f252(x58411),x58412),f784(a160,x58413)))
% 11.41/11.18 [5842]~P86(x58421)+E(f784(f784(f90(x58421),f784(f784(f252(x58421),x58422),x58423)),x58422),f784(f784(f252(x58421),x58422),f784(a160,x58423)))
% 11.41/11.18 [6055]~P113(x60551)+E(f784(f84(x60551),f784(f784(f252(x60551),f784(f88(x60551),x60552)),x60553)),f784(f84(x60551),f784(f784(f252(x60551),x60552),x60553)))
% 11.41/11.18 [6106]~P75(x61061)+E(f784(f784(f90(x61061),f784(f784(f252(x61061),x61062),x61063)),x61062),f784(f784(f90(x61061),x61062),f784(f784(f252(x61061),x61062),x61063)))
% 11.41/11.18 [6166]E(f784(f784(f3(a108),f784(f784(f89(a108),x61661),x61662)),x61663),f279(x61661,x61662,x61663))+~P85(f784(f784(f243(a108),x61662),x61663))
% 11.41/11.18 [6188]~E(f784(f784(f133(x61881),x61883),x61882),f120(x61881))+P85(f784(f784(f242(a859),f784(f188(f860(x61881)),x61882)),x61883))
% 11.41/11.18 [6328]E(f784(f784(f90(a859),f784(f113(a859),x63281)),f784(f784(f90(a859),f784(f113(a859),x63282)),x63283)),f2(a859))+~P85(f784(f784(f243(a1),x63281),a92))
% 11.41/11.18 [6344]~P59(x63441)+E(f784(f784(f252(x63441),f784(f784(f293(x63441),f87(x63441)),x63442)),x63443),f784(f784(f293(x63441),f87(x63441)),f784(f784(f252(x63441),x63442),x63443)))
% 11.41/11.18 [6428]E(f784(f784(f3(a859),f784(f784(f89(a859),x64281),x64282)),x64283),f784(f784(f89(a859),x64281),f784(f784(f3(a859),x64282),x64283)))+~P85(f784(f784(f242(a859),x64283),x64282))
% 11.41/11.18 [6429]E(f784(f784(f3(a859),f784(f784(f89(a859),x64291),x64292)),x64293),f784(f784(f3(a859),x64291),f784(f784(f3(a859),x64293),x64292)))+~P85(f784(f784(f242(a859),x64292),x64293))
% 11.41/11.18 [6430]E(f784(f784(f3(a859),f784(f784(f89(a859),x64301),x64302)),x64303),f784(f784(f89(a859),x64301),f784(f784(f3(a859),x64302),x64303)))+~P85(f784(f784(f242(a859),x64303),x64302))
% 11.41/11.18 [6470]~P101(x64701)+P85(f784(f784(f242(x64701),f784(f784(f246(x64701),x64702),x64703)),x64703))
% 11.41/11.18 [6471]~P101(x64711)+P85(f784(f784(f242(x64711),f784(f784(f246(x64711),x64712),x64713)),x64712))
% 11.41/11.18 [6472]~P93(x64721)+P85(f784(f784(f242(x64721),f784(f784(f111(x64721),x64722),x64723)),x64723))
% 11.41/11.18 [6473]~P99(x64731)+P85(f784(f784(f242(x64731),f784(f784(f111(x64731),x64732),x64733)),x64733))
% 11.41/11.18 [6474]~P93(x64741)+P85(f784(f784(f242(x64741),f784(f784(f111(x64741),x64742),x64743)),x64742))
% 11.41/11.18 [6475]~P99(x64751)+P85(f784(f784(f242(x64751),f784(f784(f111(x64751),x64752),x64753)),x64752))
% 11.41/11.18 [6489]E(f784(f784(f51(a1),f784(f784(f51(a1),x64891),x64892)),x64893),f784(f784(f51(a1),x64891),f784(f784(f90(a1),x64892),x64893)))+~P85(f784(f784(f243(a1),f2(a1)),x64893))
% 11.41/11.18 [6542]~P86(x65421)+E(f784(f784(f89(x65421),f784(f784(f90(x65421),x65422),x65423)),x65423),f784(f784(f90(x65421),f784(f784(f89(x65421),x65422),f87(x65421))),x65423))
% 11.41/11.18 [6543]~P89(x65431)+E(f784(f784(f90(x65431),f784(f88(x65431),f784(f113(x65431),x65432))),x65433),f784(f784(f90(x65431),f784(f113(x65431),f784(f88(a1),x65432))),x65433))
% 11.41/11.18 [6615]~P67(x66151)+E(f784(f157(x66151),f784(f784(f146(x66152,x66151),f784(f18(x66151,x66152),f2(x66151))),x66153)),f2(x66151))
% 11.41/11.18 [6634]E(f784(f784(f89(a859),f784(f113(a859),x66341)),f784(f784(f89(a859),f784(f113(a859),x66342)),x66343)),f784(f784(f89(a859),f784(f113(a859),x66342)),x66343))+~P85(f784(a193,f784(f113(a1),x66341)))
% 11.41/11.18 [6649]~P6(x66491)+E(f53(x66491,f784(f784(f312(x66491),x66492),f784(f784(f312(x66491),x66493),f187(f869(x66491,a852))))),f784(f784(f111(x66491),x66492),x66493))
% 11.41/11.18 [6650]~P6(x66501)+E(f52(x66501,f784(f784(f312(x66501),x66502),f784(f784(f312(x66501),x66503),f187(f869(x66501,a852))))),f784(f784(f110(x66501),x66502),x66503))
% 11.41/11.18 [6674]E(f784(f784(f165(x66741),x66742),x66743),x66743)+~P85(f784(f784(f242(a859),f784(f188(f860(x66741)),x66743)),x66742))
% 11.41/11.18 [6685]E(f784(f784(f133(x66851),x66852),x66853),f120(x66851))+~P85(f784(f784(f242(a859),f784(f188(f860(x66851)),x66853)),x66852))
% 11.41/11.18 [6686]E(f784(f784(f133(x66861),x66862),x66863),f120(x66861))+~P85(f784(f784(f242(a859),f784(f188(f860(x66861)),x66863)),x66862))
% 11.41/11.18 [6697]E(f784(f784(f3(a859),f784(f784(f89(a859),x66971),x66972)),x66973),f784(f784(f89(a859),f784(f784(f3(a859),x66971),x66973)),x66972))+~P85(f784(f784(f242(a859),x66973),x66971))
% 11.41/11.18 [6698]E(f784(f784(f3(a859),f784(f784(f89(a859),x66981),x66982)),x66983),f784(f784(f89(a859),f784(f784(f3(a859),x66981),x66983)),x66982))+~P85(f784(f784(f242(a859),x66983),x66981))
% 11.41/11.18 [6712]~P85(f784(f784(f243(a859),x67121),x67123))+P85(f784(f784(f243(a859),f784(f784(f3(a859),x67121),x67122)),x67123))
% 11.41/11.18 [6740]~P101(x67401)+E(f154(x67401,x67402,f784(f784(f142(x67401,x67401,f7(x67401)),x67402),x67403)),x67403)
% 11.41/11.18 [6837]E(f784(f784(f3(a859),f784(f784(f89(a859),x68371),x68372)),f784(a160,x68373)),f784(f784(f3(a859),x68371),f784(a160,f784(f784(f3(a859),x68373),x68372))))+~P85(f784(f784(f242(a859),x68372),x68373))
% 11.41/11.18 [6838]~P113(x68381)+P85(f784(f784(f242(x68381),f2(x68381)),f784(f784(f252(x68381),f784(f84(x68381),x68382)),x68383)))
% 11.41/11.18 [6889]P25(x68891,x68892,x68893)+~P85(f784(f784(f242(f869(f858(x68891),a852)),x68893),x68892))
% 11.41/11.18 [6929]~P85(f784(f71(x69291),x69292))+P85(f784(f71(x69291),f784(f784(f3(f869(x69291,a852)),x69292),x69293)))
% 11.41/11.18 [6930]~P85(f784(f71(x69301),x69303))+P85(f784(f71(x69301),f784(f784(f111(f869(x69301,a852)),x69302),x69303)))
% 11.41/11.18 [6931]~P85(f784(f71(x69311),x69312))+P85(f784(f71(x69311),f784(f784(f111(f869(x69311,a852)),x69312),x69313)))
% 11.41/11.18 [7069]~P35(x70691,x70693)+P35(x70691,f784(f784(f111(f869(f868(x70691,x70691),a852)),x70692),x70693))
% 11.41/11.18 [7070]~P35(x70701,x70702)+P35(x70701,f784(f784(f111(f869(f868(x70701,x70701),a852)),x70702),x70703))
% 11.41/11.18 [7189]~P93(x71891)+E(f15(x71891,f784(f164(x71891),f784(f784(f144(x71891),x71892),x71893))),f784(f136(x71891,x71891,f110(x71891),x71892),x71893))
% 11.41/11.18 [7190]~P101(x71901)+E(f16(x71901,f784(f164(x71901),f784(f784(f144(x71901),x71902),x71903))),f784(f136(x71901,x71901,f186(x71901),x71902),x71903))
% 11.41/11.18 [7191]~P101(x71911)+E(f17(x71911,f784(f164(x71911),f784(f784(f144(x71911),x71912),x71913))),f784(f136(x71911,x71911,f246(x71911),x71912),x71913))
% 11.41/11.18 [7192]~P93(x71921)+E(f12(x71921,f784(f164(x71921),f784(f784(f144(x71921),x71922),x71923))),f784(f136(x71921,x71921,f111(x71921),x71922),x71923))
% 11.41/11.18 [7193]~P85(f784(f784(f289(a1),x71931),x71932))+P85(f784(f784(f289(a1),x71931),f784(f784(f89(a1),x71932),f784(f784(f90(a1),x71931),x71933))))
% 11.41/11.18 [7263]~P85(f784(f71(x72631),x72632))+P85(f784(f784(f242(a859),f784(f50(x72631),x72632)),f784(f50(x72631),f784(f784(f312(x72631),x72633),x72632))))
% 11.41/11.18 [7270]E(f784(f784(f110(f869(a859,a852)),f784(f304(a859,x72701),x72702)),f784(f304(a859,x72702),f784(f784(f89(a859),x72702),x72703))),f784(f304(a859,x72701),f784(f784(f89(a859),x72702),x72703)))+~P85(f784(f784(f242(a859),x72701),x72702))
% 11.41/11.18 [7280]P85(f784(f784(f243(a859),x72801),x72802))+~P85(f784(f784(f243(a859),f784(f784(f89(a859),x72801),x72803)),x72802))
% 11.41/11.18 [7281]P85(f784(f784(f242(a859),x72811),x72812))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),x72813),x72811)),x72812))
% 11.41/11.18 [7282]P85(f784(f784(f242(a859),x72821),x72822))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),x72821),x72823)),x72822))
% 11.41/11.18 [7283]P85(f784(f784(f242(a859),x72831),x72832))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),x72833),x72831)),x72832))
% 11.41/11.18 [7284]P85(f784(f784(f242(a859),x72841),x72842))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),x72841),x72843)),x72842))
% 11.41/11.18 [7326]~P101(x73261)+E(f13(x73261,f186(x73261),f784(f164(x73261),f784(f784(f144(x73261),x73262),x73263))),f784(f136(x73261,x73261,f186(x73261),x73262),x73263))
% 11.41/11.18 [7327]~P101(x73271)+E(f14(x73271,f246(x73271),f784(f164(x73271),f784(f784(f144(x73271),x73272),x73273))),f784(f136(x73271,x73271,f246(x73271),x73272),x73273))
% 11.41/11.18 [7331]~E(x73312,f187(f869(f868(x73311,x73311),a852)))+P85(f784(f784(f242(f869(f868(x73311,x73311),a852)),x73312),x73313))
% 11.41/11.18 [7439]E(f784(f784(f110(f869(x74391,a852)),x74392),f784(f784(f3(f869(x74391,a852)),x74393),x74392)),x74393)+~P85(f784(f784(f242(f869(x74391,a852)),x74392),x74393))
% 11.41/11.18 [7442]~P85(f784(f784(f243(a859),x74421),f784(f784(f3(a859),x74423),x74422)))+P85(f784(f784(f243(a859),f784(f784(f89(a859),x74421),x74422)),x74423))
% 11.41/11.18 [7443]~P85(f784(f784(f242(a859),x74431),f784(f784(f89(a859),x74433),x74432)))+P85(f784(f784(f242(a859),f784(f784(f3(a859),x74431),x74432)),x74433))
% 11.41/11.18 [7503]E(x75031,f120(x75032))+E(f784(f135(x75032),f784(f784(f784(f180(f860(x75032),f860(x75032)),x75033),f161(x75032)),x75031)),f784(f784(f155(x75032),x75031),f60(a859,x75033,f784(f188(f860(x75032)),x75031))))
% 11.41/11.18 [7512]E(f784(f784(f312(x75121),x75122),f784(f784(f3(f869(x75121,a852)),x75123),f784(f784(f312(x75121),x75122),f187(f869(x75121,a852))))),x75123)+~P85(f784(f784(f347(x75121),x75122),x75123))
% 11.41/11.18 [7676]P85(f784(f784(f243(a859),x76761),f784(f784(f3(a859),x76762),x76763)))+~P85(f784(f784(f243(a859),f784(f784(f89(a859),x76761),x76763)),x76762))
% 11.41/11.18 [7677]P85(f784(f784(f242(a859),x76771),f784(f784(f89(a859),x76772),x76773)))+~P85(f784(f784(f242(a859),f784(f784(f3(a859),x76771),x76773)),x76772))
% 11.41/11.18 [7696]P85(f784(f71(x76961),x76962))+~P85(f784(f71(x76961),f784(f784(f110(f869(x76961,a852)),x76963),x76962)))
% 11.41/11.18 [7697]P85(f784(f71(x76971),x76972))+~P85(f784(f71(x76971),f784(f784(f110(f869(x76971,a852)),x76972),x76973)))
% 11.41/11.18 [7778]~P43(x77781,x77783)+P85(f784(f784(f347(f868(x77781,x77781)),f784(f784(f251(x77781,x77781),x77782),x77782)),x77783))
% 11.41/11.18 [7828]P85(f784(f784(f289(a1),x78281),x78282))+~P85(f784(f784(f289(a1),x78281),f784(f784(f89(a1),x78282),f784(f784(f90(a1),x78281),x78283))))
% 11.41/11.18 [7908]E(f784(f784(f155(a859),f134(a859,f784(f304(a859,x79081),x79082))),x79083),f784(f784(f89(a859),x79081),x79083))+~P85(f784(f784(f243(a859),f784(f784(f89(a859),x79081),x79083)),x79082))
% 11.41/11.18 [7976]~P85(f784(f784(f194(f784(a29,x79761)),x79762),x79763))+P85(f784(f784(f194(f784(f241(a853),f784(a32,x79761))),x79762),x79763))
% 11.41/11.18 [7977]~P85(f784(f784(f194(f784(a29,x79771)),x79772),x79773))+P85(f784(f784(f194(f784(f241(a853),f784(a32,x79771))),x79772),x79773))
% 11.41/11.18 [7981]E(f784(f784(f165(a859),x79811),f134(a859,f784(f304(a859,x79812),x79813))),f134(a859,f784(f304(a859,x79812),f784(f784(f89(a859),x79812),x79811))))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),x79812),x79811)),x79813))
% 11.41/11.18 [8029]~P89(x80291)+E(f784(f784(f252(x80291),x80292),f784(f113(a859),f784(f784(f89(a1),x80293),x80293))),f784(f784(f95(x80291,x80291),f784(f784(f252(x80291),x80292),f784(f113(a859),x80293))),f784(f784(f20(x80291,x80291,x80291),f90(x80291)),f7(x80291))))
% 11.41/11.18 [8226]P85(f784(f784(f194(f784(a29,x82261)),x82262),x82263))+~P85(f784(f784(f194(f784(f241(a853),f784(a32,x82261))),x82262),x82263))
% 11.41/11.18 [8227]P85(f784(f784(f194(f784(a29,x82271)),x82272),x82273))+~P85(f784(f784(f194(f784(f241(a853),f784(a32,x82271))),x82272),x82273))
% 11.41/11.18 [8285]E(f784(f784(f130(x82851),f784(f784(f165(x82851),x82852),x82853)),f784(f784(f144(x82851),f784(f784(f155(x82851),x82853),x82852)),f784(f784(f133(x82851),f784(a160,x82852)),x82853))),x82853)+~P85(f784(f784(f243(a859),x82852),f784(f188(f860(x82851)),x82853)))
% 11.41/11.18 [8292]P85(f784(f784(f242(f869(x82921,a852)),f334(x82921,x82922)),f334(x82921,x82923)))+~P85(f784(f784(f242(f869(x82921,f869(x82921,a852))),x82923),x82922))
% 11.41/11.18 [8293]~P53(x82931,x82932,x82933)+P53(x82931,x82932,f784(f784(f3(f869(f868(x82931,x82931),a852)),x82933),f310(x82931,f187(f869(f868(x82931,x82931),a852)))))
% 11.41/11.18 [8315]P85(f784(f784(f242(f869(x83151,a852)),f335(x83151,x83152)),f335(x83151,x83153)))+~P85(f784(f784(f242(f869(f868(x83151,x83151),a852)),x83153),x83152))
% 11.41/11.18 [8322]~P121(x83221)+P85(f784(f784(f242(x83221),f2(x83221)),f784(f784(f89(x83221),f784(f784(f90(x83221),x83222),x83222)),f784(f784(f90(x83221),x83223),x83223))))
% 11.41/11.18 [8354]~P89(x83541)+E(f784(f784(f252(x83541),f784(f113(x83541),x83542)),f784(f113(a859),f784(f784(f89(a1),x83543),x83543))),f784(f784(f95(x83541,x83541),f784(f784(f252(x83541),f784(f113(x83541),x83542)),f784(f113(a859),x83543))),f784(f784(f20(x83541,x83541,x83541),f90(x83541)),f7(x83541))))
% 11.41/11.18 [8359]P85(f784(f784(f242(f869(x83591,a852)),f784(f286(x83591),x83592)),f784(f286(x83591),x83593)))+~P85(f784(f784(f242(f869(f868(x83591,x83591),a852)),x83592),x83593))
% 11.41/11.18 [8391]~P47(x83911,x83912)+~P85(f784(f784(f347(f868(x83911,x83911)),f784(f784(f251(x83911,x83911),x83913),x83913)),x83912))
% 11.41/11.18 [8392]~P35(x83921,x83922)+~P85(f784(f784(f347(f868(x83921,x83921)),f784(f784(f251(x83921,x83921),x83923),x83923)),x83922))
% 11.41/11.18 [8393]~P35(x83931,x83932)+~P85(f784(f784(f347(f868(x83931,x83931)),f784(f784(f251(x83931,x83931),x83933),x83933)),x83932))
% 11.41/11.18 [8432]~E(x84322,x84323)+P85(f784(f784(f347(f868(x84321,x84321)),f784(f784(f251(x84321,x84321),x84322),x84323)),f310(x84321,f187(f869(f868(x84321,x84321),a852)))))
% 11.41/11.18 [8453]P85(f784(f784(f242(f869(x84531,a852)),f53(f869(x84531,a852),x84532)),f53(f869(x84531,a852),x84533)))+~P85(f784(f784(f242(f869(f869(x84531,a852),a852)),x84533),x84532))
% 11.41/11.18 [8454]P85(f784(f784(f242(f869(x84541,a852)),f52(f869(x84541,a852),x84542)),f52(f869(x84541,a852),x84543)))+~P85(f784(f784(f242(f869(f869(x84541,a852),a852)),x84542),x84543))
% 11.41/11.18 [8508]~P9(x85081,x85083,x85082)+P85(f784(f784(f242(f869(f868(x85081,x85081),a852)),x85082),f784(f784(f258(x85081,x85081),x85083),f784(f18(f869(x85081,a852),x85081),x85083))))
% 11.41/11.18 [8509]~P46(x85091,x85093,x85092)+P85(f784(f784(f242(f869(f868(x85091,x85091),a852)),x85092),f784(f784(f258(x85091,x85091),x85093),f784(f18(f869(x85091,a852),x85091),x85093))))
% 11.41/11.18 [8547]~P79(x85471)+P85(f784(f784(f242(x85471),f784(f784(f3(x85471),f784(f84(x85471),x85472)),f784(f84(x85471),x85473))),f784(f84(x85471),f784(f784(f3(x85471),x85473),x85472))))
% 11.41/11.18 [8548]~P79(x85481)+P85(f784(f784(f242(x85481),f784(f784(f3(x85481),f784(f84(x85481),x85482)),f784(f84(x85481),x85483))),f784(f84(x85481),f784(f784(f3(x85481),x85482),x85483))))
% 11.41/11.18 [8572]P85(f784(f784(f242(f869(f868(x85721,x85721),a852)),f310(x85721,x85722)),f310(x85721,x85723)))+~P85(f784(f784(f242(f869(f868(x85721,x85721),a852)),x85722),x85723))
% 11.41/11.18 [8719]P53(x87191,x87192,x87193)+~P53(x87191,x87192,f784(f784(f3(f869(f868(x87191,x87191),a852)),x87193),f310(x87191,f187(f869(f868(x87191,x87191),a852)))))
% 11.41/11.18 [8738]P85(f784(f784(f242(f869(f868(f860(x87381),f860(x87381)),a852)),f150(x87381,x87382)),f150(x87381,x87383)))+~P85(f784(f784(f242(f869(f868(x87381,x87381),a852)),x87382),x87383))
% 11.41/11.18 [8739]P85(f784(f784(f242(f869(f868(f860(x87391),f860(x87391)),a852)),f149(x87391,x87392)),f149(x87391,x87393)))+~P85(f784(f784(f242(f869(f868(x87391,x87391),a852)),x87392),x87393))
% 11.41/11.18 [8756]~P46(x87561,x87563,x87562)+P85(f784(f784(f242(f869(f868(x87561,x87561),a852)),x87562),f784(f784(f291(x87561,x87561,x87561),f784(f288(x87561,x87561),x87562)),x87562)))
% 11.41/11.18 [8797]~P85(f784(f132(x87971),x87972))+E(f784(f131(x87971,f784(f784(f9(x87971,f869(x87971,a852),a852),f347(x87971)),f784(f164(x87971),f166(x87971,x87972,x87973)))),x87972),f166(x87971,x87972,x87973))
% 11.41/11.18 [8845]E(x88451,x88452)+~P85(f784(f784(f347(f868(x88453,x88453)),f784(f784(f251(x88453,x88453),x88451),x88452)),f310(x88453,f187(f869(f868(x88453,x88453),a852)))))
% 11.41/11.18 [8927]P85(f784(f784(f347(x89271),x89272),f335(x89271,x89273)))+P85(f784(f784(f347(f868(x89271,x89271)),f784(f784(f251(x89271,x89271),f537(x89273,x89272,x89271)),x89272)),x89273))
% 11.41/11.18 [8928]P85(f784(f784(f347(x89281),x89282),f335(x89281,x89283)))+P85(f784(f784(f347(f868(x89281,x89281)),f784(f784(f251(x89281,x89281),f631(x89283,x89282,x89281)),x89282)),x89283))
% 11.41/11.18 [8929]P85(f784(f784(f347(x89291),x89292),f335(x89291,x89293)))+P85(f784(f784(f347(f868(x89291,x89291)),f784(f784(f251(x89291,x89291),f633(x89293,x89292,x89291)),x89292)),x89293))
% 11.41/11.18 [9033]P85(f784(x90333,x90332))+E(f784(f266(x90331),f784(f784(f20(x90331,a852,a852),f784(f784(f10(a852,f869(a852,a852),x90331),a344),f784(a343,x90332))),x90333)),f187(f869(x90331,a852)))
% 11.41/11.18 [9053]~P79(x90531)+P85(f784(f784(f242(x90531),f784(f84(x90531),f784(f784(f3(x90531),f784(f84(x90531),x90532)),f784(f84(x90531),x90533)))),f784(f84(x90531),f784(f784(f3(x90531),x90532),x90533))))
% 11.41/11.18 [9066]~P85(f784(x90663,x90662))+E(f784(f266(x90661),f784(f784(f20(x90661,a852,a852),f784(f784(f10(a852,f869(a852,a852),x90661),a344),f784(a343,x90662))),x90663)),f784(f784(f312(x90661),x90662),f187(f869(x90661,a852))))
% 11.41/11.18 [9072]~P85(f784(f784(f347(f869(x90721,a852)),x90723),f784(f311(x90721),x90722)))+P85(f784(f255(x90721,f784(f784(f9(x90721,f869(x90721,a852),a852),f347(x90721)),x90722)),x90723))
% 11.41/11.18 [9106]P35(x91061,x91062)+P85(f784(f784(f347(f868(x91061,x91061)),f784(f784(f251(x91061,x91061),f784(f596(x91062,x91061),f784(a160,x91063))),f784(f596(x91062,x91061),x91063))),x91062))
% 11.41/11.18 [9231]P85(f784(f784(f347(f869(x92311,a852)),x92312),f784(f311(x92311),x92313)))+~P85(f784(f255(x92311,f784(f784(f9(x92311,f869(x92311,a852),a852),f347(x92311)),x92313)),x92312))
% 11.41/11.18 [9291]P85(f784(f784(f347(x92911),f784(f275(x92911,x92912),x92913)),f784(f164(x92911),f784(f784(f146(f868(a108,x92911),x92911),f260(a108,x92911)),x92912))))+~P85(f784(f784(f243(a108),x92913),f784(f157(a108),f784(f784(f146(f868(a108,x92911),a108),f250(a108,x92911)),x92912))))
% 11.41/11.18 [9339]P85(f784(f784(f242(f869(f868(f860(x93391),f860(x93391)),a852)),f150(x93391,x93392)),f784(f784(f258(f860(x93391),f860(x93391)),f152(x93391,x93393)),f784(f18(f869(f860(x93391),a852),f860(x93391)),f152(x93391,x93393)))))+~P85(f784(f784(f242(f869(f868(x93391,x93391),a852)),x93392),f784(f784(f258(x93391,x93391),x93393),f784(f18(f869(x93391,a852),x93391),x93393))))
% 11.41/11.18 [9359]P85(f784(f784(f347(x93591),f784(f250(x93591,f868(a108,a108)),f784(f273(x93591,x93592),x93593))),f784(f164(x93591),f784(f784(f146(f868(a108,x93591),x93591),f260(a108,x93591)),x93592))))+~P85(f784(f784(f243(a108),f2(a108)),f784(f157(a108),f784(f784(f146(f868(a108,x93591),a108),f250(a108,x93591)),x93592))))
% 11.41/11.18 [9373]~P85(f784(f784(f242(f869(f868(x93731,x93731),a852)),x93732),f784(f784(f258(x93731,x93731),x93733),f784(f18(f869(x93731,a852),x93731),x93733))))+P85(f784(f784(f242(f869(f868(x93731,x93731),a852)),f784(f784(f291(x93731,x93731,x93731),x93732),f310(x93731,x93732))),f784(f784(f258(x93731,x93731),x93733),f784(f18(f869(x93731,a852),x93731),x93733))))
% 11.41/11.18 [9664]~P35(x96641,x96642)+~P85(f784(f784(f347(f868(x96641,x96641)),f784(f784(f251(x96641,x96641),f784(x96643,f784(a160,f592(x96642,x96641,x96643)))),f784(x96643,f592(x96642,x96641,x96643)))),x96642))
% 11.41/11.18 [9665]~P35(x96651,x96652)+~P85(f784(f784(f347(f868(x96651,x96651)),f784(f784(f251(x96651,x96651),f784(x96653,f784(a160,f646(x96653,x96652,x96651)))),f784(x96653,f646(x96653,x96652,x96651)))),x96652))
% 11.41/11.18 [9919]P85(f784(f784(f242(f869(f868(f869(x99191,a852),f869(x99191,a852)),a852)),f784(f784(f291(f869(x99191,a852),f869(x99191,a852),f869(x99191,a852)),f337(x99191,x99192)),f784(f784(f110(f869(f868(f869(x99191,a852),f869(x99191,a852)),a852)),f337(x99191,x99193)),f784(f784(f312(f868(f869(x99191,a852),f869(x99191,a852))),f784(f784(f251(f869(x99191,a852),f869(x99191,a852)),f187(f869(x99191,a852))),f187(f869(x99191,a852)))),f187(f869(f868(f869(x99191,a852),f869(x99191,a852)),a852)))))),f337(x99191,x99192)))+~P85(f784(f784(f242(f869(f868(x99191,x99191),a852)),f784(f784(f291(x99191,x99191,x99191),x99192),x99193)),x99192))
% 11.41/11.18 [9920]P85(f784(f784(f242(f869(f868(f869(x99201,a852),f869(x99201,a852)),a852)),f784(f784(f291(f869(x99201,a852),f869(x99201,a852),f869(x99201,a852)),f338(x99201,x99202)),f784(f784(f110(f869(f868(f869(x99201,a852),f869(x99201,a852)),a852)),f338(x99201,x99203)),f784(f784(f312(f868(f869(x99201,a852),f869(x99201,a852))),f784(f784(f251(f869(x99201,a852),f869(x99201,a852)),f187(f869(x99201,a852))),f187(f869(x99201,a852)))),f187(f869(f868(f869(x99201,a852),f869(x99201,a852)),a852)))))),f338(x99201,x99202)))+~P85(f784(f784(f242(f869(f868(x99201,x99201),a852)),f784(f784(f291(x99201,x99201,x99201),x99202),x99203)),x99202))
% 11.41/11.18 [7188]~P85(f784(f784(f242(a859),x71882),x71881))+E(f784(f784(f3(a859),f784(a160,f784(f784(f3(a859),x71881),x71882))),x71883),f784(f784(f3(a859),f784(a160,x71881)),f784(f784(f89(a859),x71882),x71883)))
% 11.41/11.18 [7228]~P4(x72281)+E(f784(f784(f89(x72281),f60(x72281,x72282,x72283)),f784(f784(f90(x72281),f784(f784(f51(x72281),x72282),x72283)),x72283)),x72282)
% 11.41/11.18 [7447]E(f784(f784(f90(a859),f784(f113(a859),x74471)),f784(f784(f90(a859),f784(f113(a859),x74472)),x74473)),f784(f784(f90(a859),f784(f113(a859),f784(f784(f90(a1),x74471),x74472))),x74473))+P85(f784(f784(f243(a1),x74471),a92))
% 11.41/11.18 [7918]~P85(f784(f784(f242(a859),x79183),x79182))+P85(f784(f784(f242(a859),x79181),f784(f784(f3(a859),f784(f784(f89(a859),x79182),x79181)),x79183)))
% 11.41/11.18 [8112]~P85(f784(f784(f242(a859),x81121),x81122))+E(f784(f784(f130(a859),f134(a859,f784(f304(a859,x81121),x81122))),f134(a859,f784(f304(a859,x81122),f784(f784(f89(a859),x81122),x81123)))),f134(a859,f784(f304(a859,x81121),f784(f784(f89(a859),x81122),x81123))))
% 11.41/11.18 [8368]~P85(f784(f71(x83681),x83682))+E(f784(a160,f784(f50(x83681),f784(f784(f3(f869(x83681,a852)),x83682),f784(f784(f312(x83681),x83683),f187(f869(x83681,a852)))))),f784(f50(x83681),f784(f784(f312(x83681),x83683),x83682)))
% 11.41/11.18 [8412]~P85(f784(f71(x84121),x84122))+E(f784(f784(f89(a859),f87(a859)),f784(f50(x84121),f784(f784(f3(f869(x84121,a852)),x84122),f784(f784(f312(x84121),x84123),f187(f869(x84121,a852)))))),f784(f50(x84121),f784(f784(f312(x84121),x84123),x84122)))
% 11.41/11.18 [8581]E(f784(f784(f3(a859),f784(f50(x85811),x85812)),f784(f50(x85811),f784(f784(f111(f869(x85811,a852)),x85812),x85813))),f784(f50(x85811),f784(f784(f3(f869(x85811,a852)),x85812),x85813)))+~P85(f784(f71(x85811),f784(f784(f111(f869(x85811,a852)),x85812),x85813)))
% 11.41/11.18 [8794]~P7(f784(x87942,f428(x87942,x87943,x87941)))+E(f784(f109(a1),f784(f784(f8(x87941,a859),f784(f784(f10(a1,a859,x87941),a114),x87942)),x87943)),f784(f784(f8(x87941,a1),x87942),x87943))
% 11.41/11.18 [8795]~P7(f784(x87952,f478(x87952,x87953,x87951)))+E(f784(f109(a1),f784(f784(f11(x87951,a859),f784(f784(f10(a1,a859,x87951),a114),x87952)),x87953)),f784(f784(f11(x87951,a1),x87952),x87953))
% 11.41/11.18 [8830]~P85(f784(f71(x88301),x88303))+P85(f784(f784(f242(a859),f784(f784(f3(a859),f784(f50(x88301),x88302)),f784(f50(x88301),x88303))),f784(f50(x88301),f784(f784(f3(f869(x88301,a852)),x88302),x88303))))
% 11.41/11.18 [8853]P85(f784(f784(f347(x88531),f428(x88532,x88533,x88531)),x88533))+E(f784(f109(a1),f784(f784(f8(x88531,a859),f784(f784(f10(a1,a859,x88531),a114),x88532)),x88533)),f784(f784(f8(x88531,a1),x88532),x88533))
% 11.41/11.18 [8854]P85(f784(f784(f347(x88541),f478(x88542,x88543,x88541)),x88543))+E(f784(f109(a1),f784(f784(f11(x88541,a859),f784(f784(f10(a1,a859,x88541),a114),x88542)),x88543)),f784(f784(f11(x88541,a1),x88542),x88543))
% 11.41/11.18 [8921]E(f94(x89211,f784(f784(f9(x89211,f869(x89211,a852),a852),f347(x89211)),f784(f784(f3(f869(x89211,a852)),x89212),f784(f784(f312(x89211),x89213),f187(f869(x89211,a852)))))),f254(x89211,x89213,x89212))+P85(f784(f784(f242(f869(x89211,a852)),x89212),f784(f784(f312(x89211),x89213),f187(f869(x89211,a852)))))
% 11.41/11.18 [9232]E(f784(f784(f146(f860(x92321),x92321),f784(f784(f9(f860(x92321),a859,x92321),f155(x92321)),x92322)),f784(f131(f860(x92321),f784(f784(f10(a859,a852,f860(x92321)),f784(f243(a859),x92322)),f188(f860(x92321)))),x92323)),f784(f784(f155(f860(x92321)),f170(x92321,x92323)),x92322))+~P85(f784(f784(f243(a859),x92322),f784(f188(f860(f860(x92321))),f170(x92321,x92323))))
% 11.41/11.18 [9532]~P85(f784(f784(f347(f868(x95321,x95321)),x95322),f310(x95321,x95323)))+P85(f784(f784(f347(f868(x95321,x95321)),x95322),f784(f784(f54(a859,f869(f868(x95321,x95321),a852)),f249(f869(a859,a852))),f784(f784(f9(a859,f869(f868(x95321,x95321),a852),f869(f868(x95321,x95321),a852)),f180(f868(x95321,x95321),a852)),x95323))))
% 11.41/11.18 [9589]~P85(f784(f784(f242(f869(x95891,a852)),f784(f784(f54(a859,f869(x95891,a852)),f784(f304(a859,f2(a859)),f411(x95893,x95892,x95891))),x95892)),x95893))+P85(f784(f784(f242(f869(x95891,a852)),f784(f784(f54(a859,f869(x95891,a852)),f249(f869(a859,a852))),x95892)),x95893))
% 11.41/11.18 [9641]~P85(f784(f784(f243(a1),f2(a1)),x96413))+P85(f784(f784(f243(a1),x96411),f784(f784(f89(a1),x96412),f784(f784(f90(a1),f784(f784(f89(a1),f784(f84(a1),f784(f784(f3(a1),x96412),x96411))),f87(a1))),x96413))))
% 11.41/11.18 [9651]~P35(x96511,f784(f784(f110(f869(f868(x96511,x96511),a852)),x96512),x96513))+P35(x96511,f784(f784(f110(f869(f868(x96511,x96511),a852)),f784(f784(f110(f869(f868(x96511,x96511),a852)),f784(f784(f291(x96511,x96511,x96511),x96512),x96512)),f784(f784(f291(x96511,x96511,x96511),x96513),x96512))),x96513))
% 11.41/11.18 [9716]P35(x97161,f784(f784(f110(f869(f868(x97161,x97161),a852)),x97162),x97163))+~P35(x97161,f784(f784(f110(f869(f868(x97161,x97161),a852)),f784(f784(f110(f869(f868(x97161,x97161),a852)),f784(f784(f291(x97161,x97161,x97161),x97162),x97162)),f784(f784(f291(x97161,x97161,x97161),x97163),x97162))),x97163))
% 11.41/11.18 [9314]~P136(x93141)+E(f784(f112(x93141),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x93142),x93143)),f187(f869(f868(a859,a859),a852)))))),f784(f784(f3(x93141),f784(f109(x93141),x93142)),f784(f109(x93141),x93143)))
% 11.41/11.18 [9391]P85(f784(x93913,x93912))+E(f784(f266(x93911),f784(f784(f20(x93911,a852,a852),f784(f784(f10(a852,f869(a852,a852),x93911),a344),f784(f784(f9(x93911,x93911,a852),a343),x93912))),x93913)),f187(f869(x93911,a852)))
% 11.41/11.18 [9393]~P85(f784(x93933,x93932))+E(f784(f266(x93931),f784(f784(f20(x93931,a852,a852),f784(f784(f10(a852,f869(a852,a852),x93931),a344),f784(f784(f9(x93931,x93931,a852),a343),x93932))),x93933)),f784(f784(f312(x93931),x93932),f187(f869(x93931,a852))))
% 11.41/11.18 [9708]~P85(f784(f71(x97081),x97083))+E(f784(f784(f74(x97081,f869(x97081,a852),f784(f784(f10(f869(x97081,a852),f869(f869(x97081,a852),f869(x97081,a852)),x97081),f784(f9(f869(x97081,a852),f869(x97081,a852),f869(x97081,a852)),f3(f869(x97081,a852)))),f784(f784(f9(x97081,f869(x97081,a852),f869(x97081,a852)),f312(x97081)),f187(f869(x97081,a852))))),x97082),x97083),f784(f784(f3(f869(x97081,a852)),x97082),x97083))
% 11.41/11.18 [9741]~P85(f784(f784(f243(a1),f2(a1)),x97413))+P85(f784(f784(f243(a1),f784(f784(f3(a1),x97411),f784(f784(f90(a1),f784(f784(f89(a1),f784(f84(a1),f784(f784(f3(a1),x97411),x97412))),f87(a1))),x97413))),x97412))
% 11.41/11.18 [9989]~P85(f784(f784(f347(x99891),x99893),f335(x99891,x99892)))+P85(f784(f334(x99891,f784(f784(f9(x99891,f869(f868(x99891,x99891),a852),f869(x99891,a852)),f784(f784(f10(f869(x99891,f869(f869(f868(x99891,x99891),a852),a852)),f869(f869(f868(x99891,x99891),a852),f869(x99891,a852)),x99891),f9(x99891,f869(f868(x99891,x99891),a852),a852)),f784(f784(f10(f869(x99891,f868(x99891,x99891)),f869(x99891,f869(f869(f868(x99891,x99891),a852),a852)),x99891),f784(f10(f868(x99891,x99891),f869(f869(f868(x99891,x99891),a852),a852),x99891),f347(f868(x99891,x99891)))),f251(x99891,x99891)))),x99892)),x99893))
% 11.41/11.18 [10001]P85(f784(f784(f347(x100011),x100012),f335(x100011,x100013)))+~P85(f784(f334(x100011,f784(f784(f9(x100011,f869(f868(x100011,x100011),a852),f869(x100011,a852)),f784(f784(f10(f869(x100011,f869(f869(f868(x100011,x100011),a852),a852)),f869(f869(f868(x100011,x100011),a852),f869(x100011,a852)),x100011),f9(x100011,f869(f868(x100011,x100011),a852),a852)),f784(f784(f10(f869(x100011,f868(x100011,x100011)),f869(x100011,f869(f869(f868(x100011,x100011),a852),a852)),x100011),f784(f10(f868(x100011,x100011),f869(f869(f868(x100011,x100011),a852),a852),x100011),f347(f868(x100011,x100011)))),f251(x100011,x100011)))),x100013)),x100012))
% 11.41/11.18 [9587]~P85(f784(f71(x95871),f784(f266(x95871),x95873)))+P85(f784(f71(x95871),f784(f266(x95871),f784(f784(f20(x95871,a852,a852),f784(f784(f10(a852,f869(a852,a852),x95871),a344),x95872)),x95873))))
% 11.41/11.18 [9588]~P85(f784(f71(x95881),f784(f266(x95881),x95882)))+P85(f784(f71(x95881),f784(f266(x95881),f784(f784(f20(x95881,a852,a852),f784(f784(f10(a852,f869(a852,a852),x95881),a344),x95882)),x95883))))
% 11.41/11.18 [9675]P85(f784(f71(x96751),f784(f266(x96751),x96752)))+~P85(f784(f71(x96751),f784(f266(x96751),f784(f784(f20(x96751,a852,a852),f784(f784(f10(a852,f869(a852,a852),x96751),a345),x96753)),x96752))))
% 11.41/11.18 [9676]P85(f784(f71(x96761),f784(f266(x96761),x96762)))+~P85(f784(f71(x96761),f784(f266(x96761),f784(f784(f20(x96761,a852,a852),f784(f784(f10(a852,f869(a852,a852),x96761),a345),x96762)),x96763))))
% 11.41/11.18 [9974]~P85(f784(f71(x99741),x99742))+P85(f784(f71(f860(x99741)),f784(f266(f860(x99741)),f784(f784(f20(f860(x99741),a852,a852),f784(f784(f10(a852,f869(a852,a852),f860(x99741)),a344),f784(f784(f9(f860(x99741),f869(x99741,a852),a852),f784(f784(f10(f869(x99741,a852),f869(f869(x99741,a852),a852),f860(x99741)),f242(f869(x99741,a852))),f164(x99741))),x99742))),f784(f784(f9(f860(x99741),a859,a852),f784(f784(f10(a859,f869(a859,a852),f860(x99741)),a343),f188(f860(x99741)))),x99743)))))
% 11.41/11.18 [9975]~P85(f784(f71(x99751),x99752))+P85(f784(f71(f860(x99751)),f784(f266(f860(x99751)),f784(f784(f20(f860(x99751),a852,a852),f784(f784(f10(a852,f869(a852,a852),f860(x99751)),a344),f784(f784(f9(f860(x99751),f869(x99751,a852),a852),f784(f784(f10(f869(x99751,a852),f869(f869(x99751,a852),a852),f860(x99751)),f242(f869(x99751,a852))),f164(x99751))),x99752))),f784(f784(f9(f860(x99751),a859,a852),f784(f784(f10(a859,f869(a859,a852),f860(x99751)),f242(a859)),f188(f860(x99751)))),x99753)))))
% 11.41/11.18 [9689]~P86(x96891)+E(f784(f784(f252(x96891),x96892),f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x96893)),f784(f784(f90(x96891),f784(f784(f252(x96891),x96892),x96893)),f784(f784(f252(x96891),x96892),x96893)))
% 11.41/11.18 [9720]~P75(x97201)+E(f784(f784(f252(x97201),f784(f784(f252(x97201),x97202),x97203)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f784(f252(x97201),x97202),f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97203)))
% 11.41/11.18 [9781]~P136(x97811)+E(f784(f784(f252(x97811),f784(f88(x97811),x97812)),f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97813)),f784(f784(f252(x97811),x97812),f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97813)))
% 11.41/11.18 [9924]~P113(x99241)+P85(f784(f784(f242(x99241),f2(x99241)),f784(f784(f89(x99241),f784(f784(f252(x99241),x99242),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99241),x99243),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))))
% 11.41/11.18 [9791]~P86(x97911)+E(f784(f784(f252(x97911),x97912),f784(a160,f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97913))),f784(f784(f90(x97911),x97912),f784(f784(f90(x97911),f784(f784(f252(x97911),x97912),x97913)),f784(f784(f252(x97911),x97912),x97913))))
% 11.41/11.18 [9843]~P75(x98431)+E(f784(f784(f90(x98431),x98432),f784(f784(f252(x98431),f784(f784(f252(x98431),x98432),x98433)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x98431),x98432),f784(a160,f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x98433))))
% 11.41/11.18 [9886]~P113(x98861)+P85(f784(f784(f242(x98861),f2(x98861)),f784(f784(f252(x98861),x98862),f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x98863))))
% 11.41/11.18 [9953]~P89(x99531)+E(f784(f784(f89(x99531),f784(f784(f89(x99531),f784(f784(f252(x99531),x99532),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99531),x99533),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))),f784(f784(f90(x99531),f784(f784(f90(x99531),f784(f113(x99531),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x99532)),x99533)),f784(f784(f252(x99531),f784(f784(f89(x99531),x99532),x99533)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.18 [9954]~P89(x99541)+E(f784(f784(f3(x99541),f784(f784(f89(x99541),f784(f784(f252(x99541),x99542),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99541),x99543),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))),f784(f784(f90(x99541),f784(f784(f90(x99541),f784(f113(x99541),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x99542)),x99543)),f784(f784(f252(x99541),f784(f784(f3(x99541),x99542),x99543)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.18 [4601]E(x46011,x46012)+~E(f30(x46013,x46011),f30(x46014,x46012))
% 11.41/11.18 [4602]E(x46021,x46022)+~E(f30(x46021,x46023),f30(x46022,x46024))
% 11.41/11.18 [4603]E(x46031,x46032)+~E(f38(x46033,x46031),f38(x46034,x46032))
% 11.41/11.18 [4604]E(x46041,x46042)+~E(f38(x46041,x46043),f38(x46042,x46044))
% 11.41/11.18 [4605]E(x46051,x46052)+~E(f37(x46053,x46051),f37(x46054,x46052))
% 11.41/11.18 [4606]E(x46061,x46062)+~E(f37(x46061,x46063),f37(x46062,x46064))
% 11.41/11.18 [5722]P38(f37(x57221,x57223),x57222,x57224,x57222)+P85(f784(x57221,x57222))
% 11.41/11.18 [5723]P38(f37(x57231,x57233),x57232,x57234,x57232)+P85(f784(x57231,x57232))
% 11.41/11.18 [6876]~P38(x68761,x68762,x68763,x68764)+P38(x68761,x68762,f784(a160,x68763),x68764)
% 11.41/11.18 [7716]P26(x77161,x77162,x77163,x77164)+~E(f530(x77164,x77163,x77162,x77161),f533(x77164,x77163,x77162,x77161))
% 11.41/11.18 [8212]~P26(x82121,f864(x82122),x82124,f175(x82121,x82122,x82124))+P26(x82121,f864(x82122),f176(x82121,x82122,x82123,x82124),f175(x82121,x82122,x82124))
% 11.41/11.18 [8426]~P26(x84261,f864(x84262),f176(x84261,x84262,x84264,x84263),f175(x84261,x84262,x84263))+P26(x84261,f864(x84262),x84263,f175(x84261,x84262,x84263))
% 11.41/11.18 [4941]E(x49411,x49412)+~E(f784(f784(a314,x49413),x49411),f784(f784(a314,x49414),x49412))
% 11.41/11.18 [4942]E(x49421,x49422)+~E(f784(f784(a314,x49421),x49423),f784(f784(a314,x49422),x49424))
% 11.41/11.18 [4970]~P18(x49703,x49701,x49704)+E(f784(f784(x49701,x49702),x49702),x49702)
% 11.41/11.18 [4971]~P28(x49714,x49711,x49713)+E(f784(f784(x49711,x49712),x49713),x49712)
% 11.41/11.18 [4973]E(x49731,x49732)+~E(f784(f326(x49733,x49734),x49731),f784(f326(x49733,x49734),x49732))
% 11.41/11.18 [4974]E(x49741,x49742)+~E(f784(f326(x49743,x49744),x49741),f784(f326(x49743,x49744),x49742))
% 11.41/11.18 [4975]E(x49751,x49752)+~E(f784(f322(x49753,x49754),x49751),f784(f322(x49753,x49754),x49752))
% 11.41/11.18 [4976]E(x49761,x49762)+~E(f784(f322(x49763,x49764),x49761),f784(f322(x49763,x49764),x49762))
% 11.41/11.18 [5248]~E(x52484,f187(f869(x52481,a852)))+E(f784(f313(x52481,x52482,x52483),x52484),f187(f869(x52482,a852)))
% 11.41/11.18 [5249]~E(x52494,f187(f869(x52491,a852)))+E(f784(f313(x52491,x52492,x52493),x52494),f187(f869(x52492,a852)))
% 11.41/11.18 [5511]~E(f784(f313(x55112,x55113,x55114),x55111),f187(f869(x55113,a852)))+E(x55111,f187(f869(x55112,a852)))
% 11.41/11.18 [5512]~E(f784(f313(x55122,x55123,x55124),x55121),f187(f869(x55123,a852)))+E(x55121,f187(f869(x55122,a852)))
% 11.41/11.18 [5803]~P101(x58032)+E(f784(f784(f142(x58031,x58032,x58033),x58034),f120(x58031)),f784(f784(f144(x58031),x58034),f120(x58031)))
% 11.41/11.18 [5839]E(f784(x58391,x58392),f190(x58393))+P85(f784(f784(f347(x58394),x58392),f175(x58394,x58393,x58391)))
% 11.41/11.18 [6160]~E(x61601,f187(f869(x61602,a852)))+~P85(f784(f72(x61602,x61603,x61601),x61604))
% 11.41/11.18 [6181]~P56(x61811,x61813,x61814,x61812)+P85(f784(f71(x61811),x61812))
% 11.41/11.18 [6182]~P56(x61821,x61823,x61822,x61824)+P85(f784(f71(x61821),x61822))
% 11.41/11.18 [6189]~P56(x61892,x61893,x61894,x61891)+~E(x61891,f187(f869(x61892,a852)))
% 11.41/11.18 [6220]~P100(x62201)+E(f784(f784(f111(f869(x62201,a852)),f784(f304(x62201,x62202),x62203)),f305(x62201,x62203,x62204)),f187(f869(x62201,a852)))
% 11.41/11.18 [6248]~P85(f784(f784(x62483,x62484),x62482))+P85(f784(f784(f347(x62481),x62482),f297(x62481,x62483,x62484)))
% 11.41/11.18 [6249]~P85(f784(f784(x62493,x62494),x62492))+P85(f784(f784(f347(x62491),x62492),f296(x62491,x62493,x62494)))
% 11.41/11.18 [6250]~P85(f784(f784(x62503,x62502),x62504))+P85(f784(f784(f347(x62501),x62502),f300(x62501,x62503,x62504)))
% 11.41/11.18 [6251]~P85(f784(f784(x62513,x62512),x62514))+P85(f784(f784(f347(x62511),x62512),f298(x62511,x62513,x62514)))
% 11.41/11.18 [6403]~P100(x64031)+E(f784(f784(f111(f869(x64031,a852)),f305(x64031,x64032,x64033)),f307(x64031,x64033,x64034)),f187(f869(x64031,a852)))
% 11.41/11.18 [6404]~P100(x64041)+E(f784(f784(f111(f869(x64041,a852)),f305(x64041,x64042,x64043)),f308(x64041,x64043,x64044)),f187(f869(x64041,a852)))
% 11.41/11.18 [6405]~P100(x64051)+E(f784(f784(f111(f869(x64051,a852)),f307(x64051,x64052,x64053)),f307(x64051,x64053,x64054)),f187(f869(x64051,a852)))
% 11.41/11.18 [6406]~P100(x64061)+E(f784(f784(f111(f869(x64061,a852)),f307(x64061,x64062,x64063)),f308(x64061,x64063,x64064)),f187(f869(x64061,a852)))
% 11.41/11.18 [6407]~P100(x64071)+E(f784(f784(f111(f869(x64071,a852)),f308(x64071,x64072,x64073)),f305(x64071,x64073,x64074)),f187(f869(x64071,a852)))
% 11.41/11.18 [6445]P85(f784(f784(x64451,x64452),f601(x64452,x64451)))+~P85(f784(f256(x64453,x64454,x64451),x64452))
% 11.41/11.18 [6498]~E(f784(x64981,x64982),f190(x64983))+~P85(f784(f784(f347(x64984),x64982),f175(x64984,x64983,x64981)))
% 11.41/11.18 [6580]~P112(x65801)+E(f189(x65801,x65802,f784(a160,x65803),x65804),f189(x65801,x65802,x65803,f784(x65802,x65804)))
% 11.41/11.18 [6643]~P85(f784(f784(f347(x66434),x66433),f297(x66434,x66431,x66432)))+P85(f784(f784(x66431,x66432),x66433))
% 11.41/11.18 [6644]~P85(f784(f784(f347(x66444),x66443),f296(x66444,x66441,x66442)))+P85(f784(f784(x66441,x66442),x66443))
% 11.41/11.18 [6645]~P85(f784(f784(f347(x66454),x66452),f300(x66454,x66451,x66453)))+P85(f784(f784(x66451,x66452),x66453))
% 11.41/11.18 [6646]~P85(f784(f784(f347(x66464),x66462),f298(x66464,x66461,x66463)))+P85(f784(f784(x66461,x66462),x66463))
% 11.41/11.18 [6727]E(f784(f50(f870(x67271,x67272)),f327(x67271,x67272,x67273,x67274)),f2(a859))+P85(f784(f71(x67272),x67274))
% 11.41/11.18 [6728]E(f784(f50(f870(x67281,x67282)),f327(x67281,x67282,x67283,x67284)),f2(a859))+P85(f784(f71(x67281),x67283))
% 11.41/11.18 [6936]~P16(x69364,x69361,x69362)+E(f784(f82(x69361,x69361,x69361,f784(x69362,x69363)),f784(x69362,x69363)),f784(x69362,x69363))
% 11.41/11.18 [7173]E(f282(x71731,x71732,x71733,x71734),f784(f251(f869(a108,f869(a852,f864(f861(x71731)))),f868(a108,a108)),f56(x71731)))+~P85(f784(f784(f242(a108),x71733),f2(a108)))
% 11.41/11.18 [7239]~P38(f784(a29,x72391),x72392,f784(a160,x72393),x72394)+P38(f784(f241(a853),f784(a32,x72391)),x72392,x72393,x72394)
% 11.41/11.18 [7275]P38(f784(a29,x72751),x72752,f784(a160,x72753),x72754)+~P38(f784(f241(a853),f784(a32,x72751)),x72752,x72753,x72754)
% 11.41/11.18 [7276]P38(f784(a29,x72761),x72762,f784(a160,x72763),x72764)+~P38(f784(f241(a853),f784(a32,x72761)),x72762,x72763,x72764)
% 11.41/11.18 [7575]~P38(f784(a29,x75754),x75753,x75752,x75751)+E(f784(a160,f476(x75751,x75752,x75753,x75754)),x75752)
% 11.41/11.18 [7844]~E(x78442,x78443)+P85(f784(f784(f347(f868(x78441,x78441)),f784(f784(f251(x78441,x78441),x78442),x78443)),f310(x78441,x78444)))
% 11.41/11.18 [7870]~P26(x78701,x78702,x78703,f249(f869(x78701,a852)))+E(f784(f86(x78701,x78702,f249(f869(x78701,a852)),x78703),f784(x78703,x78704)),x78704)
% 11.41/11.18 [7961]~P85(f784(f784(f347(f860(x79611)),f784(f784(f144(x79611),x79614),x79612)),f152(x79611,x79613)))+P85(f784(f784(f347(f860(x79611)),x79612),f152(x79611,x79613)))
% 11.41/11.18 [7962]~P85(f784(f784(f347(f860(x79621)),f784(f784(f130(x79621),x79624),x79622)),f152(x79621,x79623)))+P85(f784(f784(f347(f860(x79621)),x79622),f152(x79621,x79623)))
% 11.41/11.18 [7963]~P85(f784(f784(f347(f860(x79631)),f784(f784(f130(x79631),x79632),x79634)),f152(x79631,x79633)))+P85(f784(f784(f347(f860(x79631)),x79632),f152(x79631,x79633)))
% 11.41/11.18 [8036]~P38(f784(a29,x80361),x80362,x80364,x80363)+P38(f784(f241(a853),f784(a32,x80361)),x80362,f476(x80363,x80364,x80362,x80361),x80363)
% 11.41/11.18 [8073]P26(x80734,x80733,x80731,x80732)+E(f784(x80731,f530(x80732,x80731,x80733,x80734)),f784(x80731,f533(x80732,x80731,x80733,x80734)))
% 11.41/11.18 [8082]E(f176(x80821,x80822,x80823,x80824),f176(x80821,x80822,x80824,x80823))+~E(f784(f784(f111(f869(x80821,a852)),f175(x80821,x80822,x80823)),f175(x80821,x80822,x80824)),f187(f869(x80821,a852)))
% 11.41/11.18 [8177]~P26(x81772,x81771,x81774,x81773)+P26(x81771,x81772,f86(x81772,x81771,x81773,x81774),f784(f313(x81772,x81771,x81774),x81773))
% 11.41/11.18 [8313]P35(f868(x83132,x83134),f285(x83132,x83134,x83131,x83133))+P85(f784(x83131,f595(x83132,x83133,x83134,x83131)))
% 11.41/11.18 [8433]E(x84331,x84332)+~P85(f784(f784(f347(f868(x84333,x84333)),f784(f784(f251(x84333,x84333),x84331),x84332)),f270(x84333,x84334)))
% 11.41/11.18 [8498]~P85(f784(f71(f870(x84983,x84981)),f327(x84983,x84981,x84984,x84982)))+P85(f784(f71(x84981),x84982))
% 11.41/11.18 [8499]~P85(f784(f71(f870(x84991,x84993)),f327(x84991,x84993,x84992,x84994)))+P85(f784(f71(x84991),x84992))
% 11.41/11.18 [8500]~P85(f784(f71(f870(x85003,x85001)),f327(x85003,x85001,x85004,x85002)))+P85(f784(f71(x85001),x85002))
% 11.41/11.18 [8501]~P85(f784(f71(f870(x85011,x85013)),f327(x85011,x85013,x85012,x85014)))+P85(f784(f71(x85011),x85012))
% 11.41/11.18 [8663]P35(f868(x86631,x86632),f285(x86631,x86632,x86633,x86634))+~P35(x86632,f784(x86634,f595(x86631,x86634,x86632,x86633)))
% 11.41/11.18 [9167]E(f784(f784(f151(x91671,x91672),f750(x91673,x91674,x91672,x91671)),f751(x91673,x91674,x91672,x91671)),x91674)+~P85(f784(f784(f347(f868(f860(x91671),f860(x91671))),f784(f784(f251(f860(x91671),f860(x91671)),x91672),x91674)),f149(x91671,x91673)))
% 11.41/11.18 [9171]~P85(f784(f784(f347(f868(f860(x91711),f860(x91711))),f784(f784(f251(f860(x91711),f860(x91711)),x91712),x91713)),f139(x91711,x91714)))+P85(f784(f784(f347(f868(f860(x91711),f860(x91711))),f784(f784(f251(f860(x91711),f860(x91711)),x91712),x91713)),f141(x91711,x91714)))
% 11.41/11.18 [9266]P85(f784(f71(x92661),x92662))+~P85(f784(f784(f347(f868(f869(x92661,a852),f869(x92661,a852))),f784(f784(f251(f869(x92661,a852),f869(x92661,a852)),x92663),x92662)),f338(x92661,x92664)))
% 11.41/11.18 [9267]P85(f784(f71(x92671),x92672))+~P85(f784(f784(f347(f868(f869(x92671,a852),f869(x92671,a852))),f784(f784(f251(f869(x92671,a852),f869(x92671,a852)),x92672),x92673)),f338(x92671,x92674)))
% 11.41/11.18 [9270]~E(x92701,f187(f869(x92702,a852)))+~P85(f784(f784(f347(f868(f869(x92702,a852),f869(x92702,a852))),f784(f784(f251(f869(x92702,a852),f869(x92702,a852)),x92703),x92701)),f338(x92702,x92704)))
% 11.41/11.18 [9897]P13(x98971,x98972,x98973,x98974)+~P85(f784(f784(f261(x98971,x98971,a852),f784(f784(f9(x98971,f869(x98971,x98972),f869(x98971,a852)),f784(f784(f10(f869(x98972,a852),f869(f869(x98971,x98972),f869(x98971,a852)),x98971),f10(x98972,a852,x98971)),f784(f784(f10(x98972,f869(x98972,a852),x98971),a343),x98974))),x98974)),f608(x98974,x98973,x98972,x98971)))
% 11.41/11.18 [4870]~E(x48704,f120(x48701))+E(f784(f784(f146(x48701,x48702),x48703),x48704),f120(x48702))
% 11.41/11.18 [4871]~E(x48714,f120(x48711))+E(f784(f784(f146(x48711,x48712),x48713),x48714),f120(x48712))
% 11.41/11.18 [4872]~E(x48724,f190(x48721))+E(f784(f784(f206(x48721,x48722),x48723),x48724),f190(x48722))
% 11.41/11.18 [4873]~E(x48732,f120(x48731))+E(f784(f784(f151(x48731,x48732),x48733),x48734),f120(x48731))
% 11.41/11.18 [5111]E(x51111,f120(x51112))+~E(f784(f784(f146(x51112,x51113),x51114),x51111),f120(x51113))
% 11.41/11.18 [5112]E(x51121,f190(x51122))+~E(f784(f784(f206(x51122,x51123),x51124),x51121),f190(x51123))
% 11.41/11.18 [5113]E(x51131,f120(x51132))+~E(f784(f784(f146(x51132,x51133),x51134),x51131),f120(x51133))
% 11.41/11.18 [5114]E(x51141,f120(x51142))+~E(f784(f784(f151(x51142,x51141),x51143),x51144),f120(x51142))
% 11.41/11.18 [5143]E(x51431,x51432)+~E(f784(f784(f130(x51433),x51434),x51431),f784(f784(f130(x51433),x51434),x51432))
% 11.41/11.18 [5144]E(x51441,x51442)+~E(f784(f784(f130(x51443),x51441),x51444),f784(f784(f130(x51443),x51442),x51444))
% 11.41/11.18 [5284]P85(f784(x52843,x52842))+E(f154(x52841,x52842,f784(f131(x52841,x52843),x52844)),f784(f131(x52841,x52843),x52844))
% 11.41/11.18 [5295]E(x52951,x52952)+~E(f134(a859,f784(f304(a859,x52951),x52953)),f784(f784(f144(a859),x52952),x52954))
% 11.41/11.18 [5343]~P27(x53432,x53433)+P27(x53431,f784(f784(f83(x53432,x53431),x53433),x53434))
% 11.41/11.18 [5344]~P35(x53442,x53443)+P35(x53441,f784(f784(f290(x53442,x53441),x53443),x53444))
% 11.41/11.18 [5553]~E(x55531,f120(x55532))+~E(f784(f784(f130(x55532),x55533),f784(f784(f144(x55532),x55534),f120(x55532))),x55531)
% 11.41/11.18 [5586]E(f138(x55861,x55862),x55863)+~E(f784(f784(f130(x55861),x55864),f784(f784(f144(x55861),x55863),f120(x55861))),x55862)
% 11.41/11.18 [5587]E(f121(x55871,x55872),x55873)+~E(f784(f784(f130(x55871),x55873),f784(f784(f144(x55871),x55874),f120(x55871))),x55872)
% 11.41/11.18 [5695]~E(f134(a859,f784(f304(a859,x56951),x56952)),f784(f784(f144(a859),x56953),x56954))+P85(f784(f784(f243(a859),x56951),x56952))
% 11.41/11.18 [5794]~E(f784(f113(a859),x57944),f2(a859))+E(f784(f784(f155(x57941),f784(f784(f144(x57941),x57942),x57943)),f784(f113(a859),x57944)),x57942)
% 11.41/11.18 [5902]E(x59021,f784(f784(f130(x59022),f784(f162(x59022),x59023)),f784(f784(f144(x59022),x59024),f120(x59022))))+~E(f784(f162(x59022),x59021),f784(f784(f144(x59022),x59024),x59023))
% 11.41/11.18 [6082]~P100(x60821)+E(f784(f784(f111(f869(x60821,a852)),f784(f304(x60821,x60822),x60823)),f784(f304(x60821,x60823),x60824)),f187(f869(x60821,a852)))
% 11.41/11.18 [6117]~P68(x61171)+E(f784(f157(x61171),f784(f784(f146(a1,x61171),x61172),f169(x61173,x61174))),f784(f784(f8(a1,x61171),x61172),f784(f164(a1),f169(x61173,x61174))))
% 11.41/11.18 [6118]~P68(x61181)+E(f784(f784(f8(a1,x61181),x61182),f784(f164(a1),f169(x61183,x61184))),f784(f157(x61181),f784(f784(f146(a1,x61181),x61182),f169(x61183,x61184))))
% 11.41/11.18 [6263]~E(x62632,f784(f784(f130(x62631),f784(f162(x62631),x62634)),f784(f784(f144(x62631),x62633),f120(x62631))))+E(f784(f162(x62631),x62632),f784(f784(f144(x62631),x62633),x62634))
% 11.41/11.18 [6279]~P20(x62792,x62793,x62794,x62791)+E(f784(x62791,f187(f869(x62792,a852))),f41(x62793))
% 11.41/11.18 [6309]~P100(x63091)+E(f784(f784(f111(f869(x63091,a852)),f308(x63091,x63092,x63093)),f784(f304(x63091,x63093),x63094)),f187(f869(x63091,a852)))
% 11.41/11.18 [6395]~P38(x63951,x63952,x63954,x63953)+P85(f784(f784(f194(x63951),x63952),x63953))
% 11.41/11.18 [6396]~P38(x63961,x63962,x63964,x63963)+P85(f784(f784(f194(x63961),x63962),x63963))
% 11.41/11.18 [6529]E(x65291,f187(f869(x65292,a852)))+~E(f327(x65293,x65292,x65294,x65291),f187(f869(f870(x65293,x65292),a852)))
% 11.41/11.18 [6530]E(x65301,f187(f869(x65302,a852)))+~E(f327(x65302,x65303,x65301,x65304),f187(f869(f870(x65302,x65303),a852)))
% 11.41/11.18 [6609]~P85(f784(f257(x66093,x66094,x66091),x66092))+P85(f784(f784(x66091,f594(x66092,x66091)),x66092))
% 11.41/11.18 [6639]E(f784(f113(a859),x66391),f2(a859))+E(f784(f784(f155(x66392),f784(f784(f144(x66392),x66393),x66394)),f784(f113(a859),x66391)),f784(f784(f155(x66392),x66394),f784(f784(f3(a859),f784(f113(a859),x66391)),f87(a859))))
% 11.41/11.18 [6657]~P85(f784(f71(x66572),x66574))+P85(f784(f71(x66571),f784(f313(x66572,x66571,x66573),x66574)))
% 11.41/11.18 [6896]~P26(x68962,x68961,x68963,x68964)+E(f784(f50(x68961),f784(f313(x68962,x68961,x68963),x68964)),f784(f50(x68962),x68964))
% 11.41/11.18 [6916]E(f784(f313(x69161,x69162,x69163),f784(f315(x69161,x69162,x69163),x69164)),x69164)+~E(f784(f313(x69161,x69162,x69163),f249(f869(x69161,a852))),f249(f869(x69162,a852)))
% 11.41/11.18 [7340]~P26(x73401,x73402,x73403,f249(f869(x73401,a852)))+E(f784(f315(x73401,x73402,x73403),f784(f313(x73401,x73402,x73403),x73404)),x73404)
% 11.41/11.18 [7788]~P85(f784(f784(f347(f860(x77881)),f784(f784(f144(x77881),x77882),x77884)),f152(x77881,x77883)))+P85(f784(f784(f347(x77881),x77882),x77883))
% 11.41/11.18 [7915]~P85(f784(f784(f347(x79151),x79152),f784(f164(x79151),f154(x79151,x79154,x79153))))+P85(f784(f784(f347(x79151),x79152),f784(f164(x79151),x79153)))
% 11.41/11.18 [7916]~P85(f784(f784(f347(x79161),x79162),f784(f164(x79161),f166(x79161,x79163,x79164))))+P85(f784(f784(f347(x79161),x79162),f784(f164(x79161),x79163)))
% 11.41/11.18 [7917]~P85(f784(f784(f347(x79171),x79172),f784(f164(x79171),f166(x79171,x79173,x79174))))+P85(f784(f784(f347(x79171),x79172),f784(f164(x79171),x79173)))
% 11.41/11.18 [8210]~P68(x82101)+E(f784(f784(f8(a859,x82101),f784(f784(f10(a859,x82101,a859),x82102),a160)),f784(f304(a859,x82103),x82104)),f784(f784(f8(a859,x82101),x82102),f784(f304(a859,f784(a160,x82103)),f784(a160,x82104))))
% 11.41/11.18 [8219]~P68(x82191)+E(f784(f784(f8(a859,x82191),f784(f784(f10(a859,x82191,a859),x82192),a160)),f305(a859,x82193,x82194)),f784(f784(f8(a859,x82191),x82192),f305(a859,f784(a160,x82193),f784(a160,x82194))))
% 11.41/11.18 [8352]~P26(x83521,x83523,x83524,f249(f869(x83521,a852)))+P26(x83521,f869(x83522,x83523),f784(f784(f10(x83523,f869(x83522,x83523),x83521),f18(x83523,x83522)),x83524),f249(f869(x83521,a852)))
% 11.41/11.18 [8442]~P26(x84422,x84421,x84424,x84423)+E(f784(f313(x84421,x84422,f86(x84422,x84421,x84423,x84424)),f784(f313(x84422,x84421,x84424),x84423)),x84423)
% 11.41/11.18 [8502]~P85(f784(f784(f347(f868(x85021,x85021)),f784(f784(f251(x85021,x85021),x85022),x85024)),f270(x85021,x85023)))+P85(f784(f784(f347(x85021),x85022),x85023))
% 11.41/11.18 [8577]E(f784(f784(f784(f81(x85771,f864(x85772)),f784(f18(f864(x85772),x85771),f190(x85772))),x85773),f784(f237(x85772),f539(x85773,x85774,x85772,x85771))),x85774)+~E(f175(x85771,x85772,x85774),f784(f784(f312(x85771),x85773),f187(f869(x85771,a852))))
% 11.41/11.18 [8696]~E(f784(f784(f8(x86961,a859),x86964),x86963),f784(a160,x86962))+P85(f784(f784(f347(x86961),f375(x86962,x86963,x86964,x86961)),x86963))
% 11.41/11.18 [8712]~E(f784(f784(f8(x87124,a859),x87121),x87123),f784(a160,x87122))+P85(f784(f784(f243(a859),f2(a859)),f784(x87121,f375(x87122,x87123,x87121,x87124))))
% 11.41/11.18 [8722]~P85(f784(f71(x87222),x87224))+P85(f784(f784(f242(a859),f784(f50(x87221),f784(f313(x87222,x87221,x87223),x87224))),f784(f50(x87222),x87224)))
% 11.41/11.18 [8723]E(f784(f784(f251(x87231,x87232),f712(x87233,x87234,x87232,x87231)),f713(x87233,x87234,x87232,x87231)),x87234)+~P85(f784(f784(f347(f868(x87231,x87232)),x87234),f784(f288(x87232,x87231),x87233)))
% 11.41/11.18 [8732]P26(x87321,x87322,x87323,x87324)+P85(f784(f784(f347(x87321),f530(x87324,x87323,x87322,x87321)),x87324))
% 11.41/11.18 [8733]P26(x87331,x87332,x87333,x87334)+P85(f784(f784(f347(x87331),f533(x87334,x87333,x87332,x87331)),x87334))
% 11.41/11.18 [8786]P13(x87861,x87862,x87863,x87864)+P85(f784(f784(f347(f868(x87861,x87861)),f608(x87864,x87863,x87862,x87861)),x87863))
% 11.41/11.18 [8836]P85(f784(x88361,x88362))+~P85(f784(x88361,f784(f784(f251(x88363,x88364),f838(x88364,x88363,x88361)),f839(x88364,x88363,x88361))))
% 11.41/11.18 [8848]E(f784(f188(f860(x88481)),x88482),f784(f188(f860(x88481)),x88483))+~P85(f784(f784(f347(f868(f860(x88481),f860(x88481))),f784(f784(f251(f860(x88481),f860(x88481)),x88482),x88483)),f139(x88481,x88484)))
% 11.41/11.18 [8849]E(f784(f188(f860(x88491)),x88492),f784(f188(f860(x88491)),x88493))+~P85(f784(f784(f347(f868(f860(x88491),f860(x88491))),f784(f784(f251(f860(x88491),f860(x88491)),x88492),x88493)),f150(x88491,x88494)))
% 11.41/11.18 [8850]E(f784(f188(f860(x88501)),x88502),f784(f188(f860(x88501)),x88503))+~P85(f784(f784(f347(f868(f860(x88501),f860(x88501))),f784(f784(f251(f860(x88501),f860(x88501)),x88502),x88503)),f150(x88501,x88504)))
% 11.41/11.18 [8851]E(f784(f188(f860(x88511)),x88512),f784(f188(f860(x88511)),x88513))+~P85(f784(f784(f347(f868(f860(x88511),f860(x88511))),f784(f784(f251(f860(x88511),f860(x88511)),x88512),x88513)),f150(x88511,x88514)))
% 11.41/11.18 [8852]E(f784(f188(f860(x88521)),x88522),f784(f188(f860(x88521)),x88523))+~P85(f784(f784(f347(f868(f860(x88521),f860(x88521))),f784(f784(f251(f860(x88521),f860(x88521)),x88522),x88523)),f149(x88521,x88524)))
% 11.41/11.18 [8925]P85(f784(f784(f242(a859),f147(x89251,x89252,x89253)),f147(x89251,x89254,x89253)))+P85(f784(f784(f347(x89251),f770(x89254,x89252,x89253,x89251)),f784(f164(x89251),x89253)))
% 11.41/11.18 [8926]E(f784(f188(f860(x89261)),x89262),f784(f188(f860(x89261)),x89263))+~P85(f784(f784(f347(f868(f860(x89261),f860(x89261))),f784(f784(f251(f860(x89261),f860(x89261)),x89262),x89263)),f310(f860(x89261),f149(x89261,x89264))))
% 11.41/11.18 [9038]P85(f784(f784(f289(a859),x90381),x90382))+P85(f784(f784(f242(f869(a859,a852)),f292(a859,f289(a859),x90381,x90382)),f292(a859,f289(a859),x90383,x90384)))
% 11.41/11.18 [9148]~P26(x91481,x91482,x91483,x91484)+~P85(f784(f784(f243(a859),f784(f50(x91482),f784(f313(x91481,x91482,x91483),x91484))),f784(f50(x91481),x91484)))
% 11.41/11.18 [9177]~P85(f784(f784(f347(f868(f860(x91771),f860(x91771))),f784(f784(f251(f860(x91771),f860(x91771)),x91772),x91773)),f149(x91771,x91774)))+P85(f784(f784(f347(f868(f860(x91771),f860(x91771))),f784(f784(f251(f860(x91771),f860(x91771)),x91772),x91773)),f150(x91771,f310(x91771,x91774))))
% 11.41/11.18 [9180]~P85(f784(f784(f347(f868(f860(x91801),f860(x91801))),f784(f784(f251(f860(x91801),f860(x91801)),x91802),x91803)),f150(x91801,x91804)))+P85(f784(f784(f347(f868(f860(x91801),f860(x91801))),f784(f784(f251(f860(x91801),f860(x91801)),x91802),x91803)),f310(f860(x91801),f149(x91801,x91804))))
% 11.41/11.18 [9194]P85(f784(f784(f347(f868(x91941,x91941)),f784(f784(f251(x91941,x91941),x91942),x91943)),f310(x91941,x91944)))+~P85(f784(f784(f347(f868(x91941,x91941)),f784(f784(f251(x91941,x91941),x91942),x91943)),f784(f784(f291(x91941,x91941,x91941),x91944),f310(x91941,x91944))))
% 11.41/11.18 [9262]P85(f784(f784(f289(a859),x92621),x92622))+~P85(f784(f784(f243(f869(a859,a852)),f292(a859,f289(a859),x92623,x92624)),f292(a859,f289(a859),x92621,x92622)))
% 11.41/11.18 [9374]E(f784(f784(f130(x93741),f753(x93742,x93743,x93744,x93741)),f784(f784(f144(x93741),f754(x93742,x93743,x93744,x93741)),f756(x93742,x93743,x93744,x93741))),x93744)+~P85(f784(f784(f347(f868(f860(x93741),f860(x93741))),f784(f784(f251(f860(x93741),f860(x93741)),x93744),x93743)),f149(x93741,x93742)))
% 11.41/11.18 [9375]E(f784(f784(f130(x93751),f753(x93752,x93753,x93754,x93751)),f784(f784(f144(x93751),f755(x93752,x93753,x93754,x93751)),f756(x93752,x93753,x93754,x93751))),x93753)+~P85(f784(f784(f347(f868(f860(x93751),f860(x93751))),f784(f784(f251(f860(x93751),f860(x93751)),x93754),x93753)),f149(x93751,x93752)))
% 11.41/11.18 [9447]P85(f784(f784(f347(f868(x94471,x94471)),f784(f784(f251(x94471,x94471),x94472),f668(x94473,x94474,x94472,x94471))),f310(x94471,x94473)))+~P85(f784(f784(f347(f868(x94471,x94471)),f784(f784(f251(x94471,x94471),x94472),x94474)),f784(f784(f291(x94471,x94471,x94471),x94473),f310(x94471,x94473))))
% 11.41/11.18 [9515]P85(f784(f784(f242(a859),f147(x95151,x95152,x95153)),f147(x95151,x95154,x95153)))+~P85(f784(f784(f243(a859),f784(x95152,f770(x95154,x95152,x95153,x95151))),f784(x95154,f770(x95154,x95152,x95153,x95151))))
% 11.41/11.18 [9584]P85(f784(f784(f347(f868(x95841,x95841)),f784(f784(f251(x95841,x95841),f667(x95842,x95843,x95844,x95841)),x95843)),f310(x95841,x95842)))+~P85(f784(f784(f347(f868(x95841,x95841)),f784(f784(f251(x95841,x95841),x95844),x95843)),f784(f784(f291(x95841,x95841,x95841),x95842),f310(x95841,x95842))))
% 11.41/11.18 [5124]~E(x51242,x51243)+E(f154(x51241,x51242,f784(f784(f144(x51241),x51243),x51244)),x51244)
% 11.41/11.18 [5137]~E(x51372,f2(a859))+E(f784(f784(f165(x51371),x51372),f784(f784(f144(x51371),x51373),x51374)),f120(x51371))
% 11.41/11.18 [5306]~P84(x53062)+E(f784(f784(f88(f869(x53061,x53062)),x53063),x53064),f784(f88(x53062),f784(x53063,x53064)))
% 11.41/11.18 [5307]~P84(x53072)+E(f784(f784(f88(f869(x53071,x53072)),x53073),x53074),f784(f88(x53072),f784(x53073,x53074)))
% 11.41/11.18 [5319]~E(x53192,f2(a859))+E(f784(f784(f133(x53191),x53192),f784(f784(f144(x53191),x53193),x53194)),f784(f784(f144(x53191),x53193),x53194))
% 11.41/11.18 [5320]P85(f784(x53202,x53203))+E(f784(f131(x53201,x53202),f784(f784(f144(x53201),x53203),x53204)),f784(f131(x53201,x53202),x53204))
% 11.41/11.18 [5454]~E(x54542,x54544)+P85(f784(f784(f784(f312(x54541),x54542),x54543),x54544))
% 11.41/11.18 [5462]E(x54621,f120(x54622))+E(f138(x54623,f784(f784(f146(x54622,x54623),x54624),x54621)),f784(x54624,f138(x54622,x54621)))
% 11.41/11.18 [5473]~E(x54731,f73(x54732,x54734))+E(f784(x54731,f784(f784(f312(x54732),x54733),f187(f869(x54732,a852)))),x54733)
% 11.41/11.18 [5487]~E(f784(f113(a859),x54872),f2(a859))+E(f784(f784(f165(x54871),f784(f113(a859),x54872)),f784(f784(f144(x54871),x54873),x54874)),f120(x54871))
% 11.41/11.18 [5507]E(x55071,f120(x55072))+E(f784(f135(x55073),f784(f784(f146(x55072,x55073),x55074),x55071)),f784(x55074,f784(f135(x55072),x55071)))
% 11.41/11.18 [5605]~P85(f784(x56053,x56054))+P85(f784(f784(f784(f312(x56051),x56052),x56053),x56054))
% 11.41/11.18 [5712]~E(f784(f113(a859),x57122),f2(a859))+E(f784(f784(f133(x57121),f784(f113(a859),x57122)),f784(f784(f144(x57121),x57123),x57124)),f784(f784(f144(x57121),x57123),x57124))
% 11.41/11.18 [5730]~P19(x57302,x57304,x57301)+E(f784(x57301,f784(f784(f312(x57302),x57303),f187(f869(x57302,a852)))),x57303)
% 11.41/11.18 [5754]~E(x57542,x57543)+P85(f784(f784(f347(x57541),x57542),f784(f784(f312(x57541),x57543),x57544)))
% 11.41/11.18 [5755]~E(x57552,x57553)+P85(f784(f784(f347(x57551),x57552),f784(f784(f312(x57551),x57553),x57554)))
% 11.41/11.18 [5759]~P86(x57591)+E(f784(f784(f89(x57591),x57592),f784(f784(f89(x57591),x57593),x57594)),f784(f784(f89(x57591),x57593),f784(f784(f89(x57591),x57592),x57594)))
% 11.41/11.18 [5760]~P86(x57601)+E(f784(f784(f90(x57601),x57602),f784(f784(f90(x57601),x57603),x57604)),f784(f784(f90(x57601),x57603),f784(f784(f90(x57601),x57602),x57604)))
% 11.41/11.18 [5761]~P101(x57611)+E(f784(f784(f246(x57611),x57612),f784(f784(f246(x57611),x57613),x57614)),f784(f784(f246(x57611),x57613),f784(f784(f246(x57611),x57612),x57614)))
% 11.41/11.18 [5762]~P101(x57621)+E(f784(f784(f246(x57621),x57622),f784(f784(f246(x57621),x57623),x57624)),f784(f784(f246(x57621),x57623),f784(f784(f246(x57621),x57622),x57624)))
% 11.41/11.18 [5763]~P101(x57631)+E(f784(f784(f186(x57631),x57632),f784(f784(f186(x57631),x57633),x57634)),f784(f784(f186(x57631),x57633),f784(f784(f186(x57631),x57632),x57634)))
% 11.41/11.18 [5764]~P101(x57641)+E(f784(f784(f186(x57641),x57642),f784(f784(f186(x57641),x57643),x57644)),f784(f784(f186(x57641),x57643),f784(f784(f186(x57641),x57642),x57644)))
% 11.41/11.18 [5765]~P93(x57651)+E(f784(f784(f110(x57651),x57652),f784(f784(f110(x57651),x57653),x57654)),f784(f784(f110(x57651),x57653),f784(f784(f110(x57651),x57652),x57654)))
% 11.41/11.18 [5766]~P98(x57661)+E(f784(f784(f110(x57661),x57662),f784(f784(f110(x57661),x57663),x57664)),f784(f784(f110(x57661),x57663),f784(f784(f110(x57661),x57662),x57664)))
% 11.41/11.18 [5767]~P98(x57671)+E(f784(f784(f110(x57671),x57672),f784(f784(f110(x57671),x57673),x57674)),f784(f784(f110(x57671),x57673),f784(f784(f110(x57671),x57672),x57674)))
% 11.41/11.18 [5768]~P93(x57681)+E(f784(f784(f111(x57681),x57682),f784(f784(f111(x57681),x57683),x57684)),f784(f784(f111(x57681),x57683),f784(f784(f111(x57681),x57682),x57684)))
% 11.41/11.18 [5769]~P99(x57691)+E(f784(f784(f111(x57691),x57692),f784(f784(f111(x57691),x57693),x57694)),f784(f784(f111(x57691),x57693),f784(f784(f111(x57691),x57692),x57694)))
% 11.41/11.18 [5770]~P99(x57701)+E(f784(f784(f111(x57701),x57702),f784(f784(f111(x57701),x57703),x57704)),f784(f784(f111(x57701),x57703),f784(f784(f111(x57701),x57702),x57704)))
% 11.41/11.18 [5777]E(x57771,x57772)+E(f154(x57773,x57771,f784(f784(f144(x57773),x57772),x57774)),f784(f784(f144(x57773),x57772),f154(x57773,x57771,x57774)))
% 11.41/11.18 [5792]~P85(f784(x57922,x57923))+E(f784(f131(x57921,x57922),f784(f784(f144(x57921),x57923),x57924)),f784(f784(f144(x57921),x57923),f784(f131(x57921,x57922),x57924)))
% 11.41/11.18 [5878]~E(x58784,f187(f869(x58781,a852)))+E(f784(f313(x58781,x58782,f784(f18(x58782,x58781),x58783)),x58784),f187(f869(x58782,a852)))
% 11.41/11.18 [5986]E(x59861,f187(f869(x59862,a852)))+E(f784(f784(f54(x59862,f869(x59863,a852)),x59861),f784(f18(f869(x59863,a852),x59862),x59864)),x59864)
% 11.41/11.18 [5987]E(x59871,f187(f869(x59872,a852)))+E(f784(f784(f55(x59872,f869(x59873,a852)),x59871),f784(f18(f869(x59873,a852),x59872),x59874)),x59874)
% 11.41/11.18 [5996]~E(x59964,f187(f869(x59962,a852)))+E(f784(f784(f258(x59961,x59962),x59963),f784(f18(f869(x59962,a852),x59961),x59964)),f187(f869(f868(x59961,x59962),a852)))
% 11.41/11.18 [5997]~E(x59973,f187(f869(x59971,a852)))+E(f784(f784(f258(x59971,x59972),x59973),f784(f18(f869(x59972,a852),x59971),x59974)),f187(f869(f868(x59971,x59972),a852)))
% 11.41/11.18 [6048]E(x60481,f2(a859))+E(f784(f784(f133(x60482),x60481),f784(f784(f144(x60482),x60483),x60484)),f784(f784(f133(x60482),f784(f784(f3(a859),x60481),f87(a859))),x60484))
% 11.41/11.18 [6074]E(x60741,f187(f869(x60742,a852)))+E(f784(f313(x60742,x60743,f784(f18(x60743,x60742),x60744)),x60741),f784(f784(f312(x60743),x60744),f187(f869(x60743,a852))))
% 11.41/11.18 [6077]E(f784(f315(x60771,x60772,f784(f18(x60772,x60771),x60773)),x60774),f187(f869(x60771,a852)))+P85(f784(f784(f347(x60772),x60773),x60774))
% 11.41/11.18 [6144]~E(x61443,f187(f869(x61441,a852)))+E(f784(f784(f54(x61441,f869(x61442,a852)),x61443),f784(f18(f869(x61442,a852),x61441),x61444)),f187(f869(x61442,a852)))
% 11.41/11.18 [6145]~E(x61453,f187(f869(x61451,a852)))+E(f784(f784(f55(x61451,f869(x61452,a852)),x61453),f784(f18(f869(x61452,a852),x61451),x61454)),f249(f869(x61452,a852)))
% 11.41/11.18 [6147]~P4(x61471)+E(f60(x61471,f784(f784(f90(x61471),x61472),x61473),f784(f784(f90(x61471),x61472),x61474)),f784(f784(f90(x61471),x61472),f60(x61471,x61473,x61474)))
% 11.41/11.18 [6319]E(f784(f315(x63191,x63192,f784(f18(x63192,x63191),x63193)),x63194),f249(f869(x63191,a852)))+~P85(f784(f784(f347(x63192),x63193),x63194))
% 11.41/11.18 [6340]~P85(f784(f784(f347(x63401),x63402),x63404))+P85(f784(f784(f347(x63401),x63402),f784(f784(f312(x63401),x63403),x63404)))
% 11.41/11.18 [6341]~P85(f784(f784(f347(x63411),x63412),x63414))+P85(f784(f784(f347(x63411),x63412),f784(f784(f312(x63411),x63413),x63414)))
% 11.41/11.18 [6342]~P85(f784(f784(f347(x63421),x63422),x63424))+P85(f784(f784(f347(x63421),x63422),f784(f784(f312(x63421),x63423),x63424)))
% 11.41/11.18 [6355]~E(x63553,f784(f784(f3(a859),f784(f188(f860(x63551)),x63552)),f87(a859)))+E(f121(x63551,f784(f784(f151(x63551,x63552),x63553),x63554)),f121(x63551,x63552))
% 11.41/11.18 [6380]~P101(x63801)+E(f784(f784(f111(f869(x63801,a852)),f784(f303(x63801),x63802)),f305(x63801,x63803,x63804)),f305(x63801,x63803,f784(f784(f246(x63801),x63802),x63804)))
% 11.41/11.18 [6381]~P101(x63811)+E(f784(f784(f111(f869(x63811,a852)),f784(f268(x63811),x63812)),f305(x63811,x63813,x63814)),f305(x63811,f784(f784(f186(x63811),x63812),x63813),x63814))
% 11.41/11.18 [6397]E(f784(f784(f111(f869(x63971,a852)),x63972),f784(f784(f312(x63971),x63973),x63974)),f784(f784(f111(f869(x63971,a852)),x63972),x63974))+P85(f784(f784(f347(x63971),x63973),x63972))
% 11.41/11.18 [6398]E(f784(f784(f111(f869(x63981,a852)),x63982),f784(f784(f312(x63981),x63983),x63984)),f784(f784(f111(f869(x63981,a852)),x63982),x63984))+P85(f784(f784(f347(x63981),x63983),x63982))
% 11.41/11.18 [6410]E(f154(x64101,x64102,f784(f784(f130(x64101),x64103),x64104)),f784(f784(f130(x64101),x64103),f154(x64101,x64102,x64104)))+P85(f784(f784(f347(x64101),x64102),f784(f164(x64101),x64103)))
% 11.41/11.18 [6415]~P75(x64151)+E(f784(f784(f90(x64151),f784(f784(f252(x64151),x64152),x64153)),f784(f784(f252(x64151),x64152),x64154)),f784(f784(f252(x64151),x64152),f784(f784(f89(a859),x64153),x64154)))
% 11.41/11.18 [6416]~P86(x64161)+E(f784(f784(f90(x64161),f784(f784(f252(x64161),x64162),x64163)),f784(f784(f252(x64161),x64162),x64164)),f784(f784(f252(x64161),x64162),f784(f784(f89(a859),x64163),x64164)))
% 11.41/11.18 [6452]~P86(x64521)+E(f784(f784(f89(x64521),f784(f784(f90(x64521),x64522),x64523)),f784(f784(f90(x64521),x64522),x64524)),f784(f784(f90(x64521),x64522),f784(f784(f89(x64521),x64523),x64524)))
% 11.41/11.18 [6453]~P101(x64531)+E(f784(f784(f186(x64531),f784(f784(f246(x64531),x64532),x64533)),f784(f784(f246(x64531),x64532),x64534)),f784(f784(f246(x64531),x64532),f784(f784(f186(x64531),x64533),x64534)))
% 11.41/11.18 [6454]~P101(x64541)+E(f784(f784(f246(x64541),f784(f784(f186(x64541),x64542),x64543)),f784(f784(f186(x64541),x64542),x64544)),f784(f784(f186(x64541),x64542),f784(f784(f246(x64541),x64543),x64544)))
% 11.41/11.18 [6455]~P97(x64551)+E(f784(f784(f111(x64551),f784(f784(f110(x64551),x64552),x64553)),f784(f784(f110(x64551),x64552),x64554)),f784(f784(f110(x64551),x64552),f784(f784(f111(x64551),x64553),x64554)))
% 11.41/11.18 [6456]~P97(x64561)+E(f784(f784(f110(x64561),f784(f784(f111(x64561),x64562),x64563)),f784(f784(f111(x64561),x64562),x64564)),f784(f784(f111(x64561),x64562),f784(f784(f110(x64561),x64563),x64564)))
% 11.41/11.18 [6492]~P4(x64921)+E(f60(x64921,f784(f784(f90(x64921),x64922),x64923),f784(f784(f90(x64921),x64924),x64923)),f784(f784(f90(x64921),f60(x64921,x64922,x64924)),x64923))
% 11.41/11.18 [6495]~E(f784(f188(f860(x64951)),x64953),f784(f188(f860(x64952)),x64954))+E(f784(f784(f146(f868(x64951,x64952),x64952),f260(x64951,x64952)),f784(f784(f173(x64951,x64952),x64953),x64954)),x64954)
% 11.41/11.18 [6496]~E(f784(f188(f860(x64961)),x64963),f784(f188(f860(x64962)),x64964))+E(f784(f784(f146(f868(x64961,x64962),x64961),f250(x64961,x64962)),f784(f784(f173(x64961,x64962),x64963),x64964)),x64963)
% 11.41/11.18 [6506]~P4(x65061)+E(f60(x65061,f784(f784(f89(x65061),x65062),f60(x65061,x65063,x65064)),x65064),f60(x65061,f784(f784(f89(x65061),x65062),x65063),x65064))
% 11.41/11.18 [6507]~P4(x65071)+E(f60(x65071,f784(f784(f90(x65071),x65072),f60(x65071,x65073,x65074)),x65074),f60(x65071,f784(f784(f90(x65071),x65072),x65073),x65074))
% 11.41/11.18 [6508]~P5(x65081)+E(f60(x65081,f784(f784(f3(x65081),x65082),f60(x65081,x65083,x65084)),x65084),f60(x65081,f784(f784(f3(x65081),x65082),x65083),x65084))
% 11.41/11.18 [6509]~P4(x65091)+E(f60(x65091,f784(f784(f89(x65091),x65092),f60(x65091,x65093,x65094)),x65094),f60(x65091,f784(f784(f89(x65091),x65092),x65093),x65094))
% 11.41/11.18 [6592]~P101(x65921)+E(f784(f784(f111(f869(x65921,a852)),f305(x65921,x65922,x65923)),f784(f303(x65921),x65924)),f305(x65921,x65922,f784(f784(f246(x65921),x65923),x65924)))
% 11.41/11.18 [6593]~P101(x65931)+E(f784(f784(f111(f869(x65931,a852)),f305(x65931,x65932,x65933)),f784(f268(x65931),x65934)),f305(x65931,f784(f784(f186(x65931),x65932),x65934),x65933))
% 11.41/11.18 [6596]~E(f784(f188(f860(x65961)),x65963),f784(f188(f860(x65962)),x65964))+E(f784(f784(f173(x65961,x65962),f784(f162(x65961),x65963)),f784(f162(x65962),x65964)),f784(f162(f868(x65961,x65962)),f784(f784(f173(x65961,x65962),x65963),x65964)))
% 11.41/11.18 [6605]E(x66051,f784(f784(f3(a859),f784(f188(f860(x66052)),x66053)),f87(a859)))+E(f121(x66052,f784(f784(f151(x66052,x66053),x66051),x66054)),f784(f784(f151(x66052,f121(x66052,x66053)),x66051),x66054))
% 11.41/11.18 [6622]~P85(f784(f132(x66222),x66224))+P85(f784(f132(f868(x66221,x66222)),f784(f784(f173(x66221,x66222),x66223),x66224)))
% 11.41/11.18 [6623]~P85(f784(f132(x66231),x66233))+P85(f784(f132(f868(x66231,x66232)),f784(f784(f173(x66231,x66232),x66233),x66234)))
% 11.41/11.18 [6720]E(x67201,f784(f784(f784(a196,x67202),x67203),f784(x67204,x67202)))+~P85(f784(f784(f194(f30(x67203,x67204)),x67202),x67201))
% 11.41/11.18 [6899]E(f784(f784(f51(a859),x68991),x68992),x68993)+~P85(f784(f63(x68991,x68992),f784(f784(f251(a859,a859),x68993),x68994)))
% 11.41/11.18 [6925]E(f60(a859,x69251,x69252),x69253)+~P85(f784(f63(x69251,x69252),f784(f784(f251(a859,a859),x69254),x69253)))
% 11.41/11.18 [6928]P85(f784(f132(x69281),x69282))+~P85(f784(f132(x69283),f784(f784(f146(x69281,x69283),x69284),x69282)))
% 11.41/11.18 [7007]E(f154(x70071,x70072,f784(f784(f130(x70071),x70073),x70074)),f784(f784(f130(x70071),f154(x70071,x70072,x70073)),x70074))+~P85(f784(f784(f347(x70071),x70072),f784(f164(x70071),x70073)))
% 11.41/11.18 [7075]E(f784(f113(a859),x70751),f2(a859))+E(f784(f784(f133(x70752),f784(f113(a859),x70751)),f784(f784(f144(x70752),x70753),x70754)),f784(f784(f133(x70752),f784(f784(f3(a859),f784(f113(a859),x70751)),f87(a859))),x70754))
% 11.41/11.18 [7101]~P4(x71011)+E(f60(x71011,f784(f784(f89(x71011),f60(x71011,x71012,x71013)),x71014),x71013),f60(x71011,f784(f784(f89(x71011),x71012),x71014),x71013))
% 11.41/11.18 [7102]~P4(x71021)+E(f60(x71021,f784(f784(f90(x71021),f60(x71021,x71022,x71023)),x71024),x71023),f60(x71021,f784(f784(f90(x71021),x71022),x71024),x71023))
% 11.41/11.18 [7103]~P5(x71031)+E(f60(x71031,f784(f784(f3(x71031),f60(x71031,x71032,x71033)),x71034),x71033),f60(x71031,f784(f784(f3(x71031),x71032),x71034),x71033))
% 11.41/11.18 [7104]~P4(x71041)+E(f60(x71041,f784(f784(f89(x71041),f60(x71041,x71042,x71043)),x71044),x71043),f60(x71041,f784(f784(f89(x71041),x71042),x71044),x71043))
% 11.41/11.18 [7105]~P4(x71051)+E(f60(x71051,f784(f784(f90(x71051),f60(x71051,x71052,x71053)),x71054),x71053),f60(x71051,f784(f784(f90(x71051),x71052),x71054),x71053))
% 11.41/11.18 [7310]~E(x73101,f784(f784(f144(x73102),x73103),x73104))+~P85(f784(f784(f242(a859),f784(f188(f860(x73102)),x73101)),f784(f188(f860(x73102)),x73104)))
% 11.41/11.18 [7481]~E(f172(x74811,x74812,x74813),f172(x74811,x74812,x74814))+E(f784(f313(f868(x74811,x74812),x74811,f250(x74811,x74812)),f784(f164(f868(x74811,x74812)),x74813)),f784(f313(f868(x74811,x74812),x74811,f250(x74811,x74812)),f784(f164(f868(x74811,x74812)),x74814)))
% 11.41/11.18 [7524]P26(x75241,x75242,x75243,f784(f164(x75241),x75244))+~P85(f784(f132(x75242),f784(f784(f146(x75241,x75242),x75243),x75244)))
% 11.41/11.18 [7601]~P85(f784(f784(f242(f869(x76011,a852)),x76012),x76014))+P85(f784(f784(f242(f869(x76011,a852)),x76012),f784(f784(f312(x76011),x76013),x76014)))
% 11.41/11.18 [7636]~P4(x76361)+E(f60(x76361,f784(f784(f89(x76361),f60(x76361,x76362,x76363)),f60(x76361,x76364,x76363)),x76363),f60(x76361,f784(f784(f89(x76361),x76362),x76364),x76363))
% 11.41/11.18 [7637]~P4(x76371)+E(f60(x76371,f784(f784(f90(x76371),f60(x76371,x76372,x76373)),f60(x76371,x76374,x76373)),x76373),f60(x76371,f784(f784(f90(x76371),x76372),x76374),x76373))
% 11.41/11.18 [7638]~P5(x76381)+E(f60(x76381,f784(f784(f3(x76381),f60(x76381,x76382,x76383)),f60(x76381,x76384,x76383)),x76383),f60(x76381,f784(f784(f3(x76381),x76382),x76384),x76383))
% 11.41/11.18 [7738]~E(f784(x77384,f664(x77384,x77383,x77381,x77382)),f249(f869(x77382,a852)))+E(f784(f784(f55(x77381,f869(x77382,a852)),x77383),x77384),f249(f869(x77382,a852)))
% 11.41/11.18 [7739]~E(f784(x77394,f422(x77394,x77393,x77391,x77392)),f187(f869(x77392,a852)))+E(f784(f784(f54(x77391,f869(x77392,a852)),x77393),x77394),f187(f869(x77392,a852)))
% 11.41/11.18 [7740]~E(f784(x77404,f425(x77404,x77403,x77402,x77401)),f187(f869(x77402,a852)))+E(f784(f784(f54(x77401,f869(x77402,a852)),x77403),x77404),f187(f869(x77402,a852)))
% 11.41/11.18 [7741]~E(f784(x77414,f665(x77414,x77413,x77412,x77411)),f249(f869(x77412,a852)))+E(f784(f784(f55(x77411,f869(x77412,a852)),x77413),x77414),f249(f869(x77412,a852)))
% 11.41/11.18 [8129]P85(f784(x81291,x81292))+~P85(f784(f784(f347(x81293),x81292),f784(f784(f111(f869(x81293,a852)),x81294),f784(f266(x81293),x81291))))
% 11.41/11.18 [8167]~P85(f784(f784(f242(f869(x81671,a852)),x81673),x81674))+P85(f784(f784(f242(f869(x81671,a852)),f784(f784(f312(x81671),x81672),x81673)),f784(f784(f312(x81671),x81672),x81674)))
% 11.41/11.18 [8208]P85(f784(f784(f347(x82081),x82082),x82083))+~P85(f784(f784(f347(x82081),x82082),f784(f784(f111(f869(x82081,a852)),x82083),f784(f266(x82081),x82084))))
% 11.41/11.18 [8335]P85(f784(f784(f194(x83351),x83352),f575(x83353,x83352,x83354,x83351)))+~P85(f784(f784(f194(f38(x83351,x83354)),x83352),x83353))
% 11.41/11.18 [8336]P85(f784(f784(f194(x83361),x83362),f807(x83363,x83362,x83364,x83361)))+~P85(f784(f784(f194(f38(x83361,x83364)),x83362),x83363))
% 11.41/11.18 [8456]~P85(f784(f784(f243(a859),f784(x84564,x84562)),f784(x84564,x84563)))+P85(f784(f784(f347(f868(x84561,x84561)),f784(f784(f251(x84561,x84561),x84562),x84563)),f784(f784(f290(a859,x84561),a247),x84564)))
% 11.41/11.18 [8603]P26(f860(x86031),f860(x86032),f784(f146(x86031,x86032),x86033),x86034)+~P26(x86031,x86032,x86033,f52(f869(x86031,a852),f784(f313(f860(x86031),f869(x86031,a852),f164(x86031)),x86034)))
% 11.41/11.18 [8713]E(f784(f784(f55(x87131,f869(x87132,a852)),x87133),x87134),f249(f869(x87132,a852)))+P85(f784(f784(f347(x87131),f664(x87134,x87133,x87131,x87132)),x87133))
% 11.41/11.18 [8714]E(f784(f784(f54(x87141,f869(x87142,a852)),x87143),x87144),f187(f869(x87142,a852)))+P85(f784(f784(f347(x87141),f422(x87144,x87143,x87141,x87142)),x87143))
% 11.41/11.18 [8715]E(f784(f784(f54(x87151,f869(x87152,a852)),x87153),x87154),f187(f869(x87152,a852)))+P85(f784(f784(f347(x87151),f425(x87154,x87153,x87152,x87151)),x87153))
% 11.41/11.18 [8716]E(f784(f784(f55(x87161,f869(x87162,a852)),x87163),x87164),f249(f869(x87162,a852)))+P85(f784(f784(f347(x87161),f665(x87164,x87163,x87162,x87161)),x87163))
% 11.41/11.18 [8751]P85(f784(f784(f243(a859),f784(x87511,x87512)),f784(x87511,x87513)))+~P85(f784(f784(f347(f868(x87514,x87514)),f784(f784(f251(x87514,x87514),x87512),x87513)),f784(f784(f290(a859,x87514),a247),x87511)))
% 11.41/11.18 [8800]P85(f784(f784(f194(x88001),f575(x88002,x88003,x88001,x88004)),x88002))+~P85(f784(f784(f194(f38(x88004,x88001)),x88003),x88002))
% 11.41/11.18 [8801]P85(f784(f784(f194(x88011),f807(x88012,x88013,x88011,x88014)),x88012))+~P85(f784(f784(f194(f38(x88014,x88011)),x88013),x88012))
% 11.41/11.18 [8914]P85(f784(f784(f347(x89141),f507(x89142,x89143,x89144,x89141)),x89143))+~P85(f784(f784(f347(f869(x89141,a852)),x89144),f784(f784(f69(x89141),x89143),x89142)))
% 11.41/11.18 [8917]E(x89171,x89172)+~P85(f784(f784(f347(f868(x89173,x89173)),f784(f784(f251(x89173,x89173),x89171),x89172)),f784(f784(f180(f868(x89173,x89173),a852),f2(a859)),x89174)))
% 11.41/11.18 [8988]E(f784(f287(x89881,x89881,x89882),f784(f784(f312(x89881),f507(x89882,x89883,x89884,x89881)),f187(f869(x89881,a852)))),x89884)+~P85(f784(f784(f347(f869(x89881,a852)),x89884),f784(f784(f69(x89881),x89883),x89882)))
% 11.41/11.18 [8999]~P85(f784(f784(f347(f868(x89991,x89991)),f784(f784(f251(x89991,x89991),x89993),x89992)),f310(x89991,x89994)))+P85(f784(f784(f347(f868(x89991,x89991)),f784(f784(f251(x89991,x89991),x89992),x89993)),f310(x89991,f784(f288(x89991,x89991),x89994))))
% 11.41/11.18 [9012]~P4(x90121)+E(f784(f784(f89(x90121),f784(f784(f89(x90121),f784(f784(f90(x90121),x90122),f784(f784(f51(x90121),x90123),x90122))),f60(x90121,x90123,x90122))),x90124),f784(f784(f89(x90121),x90123),x90124))
% 11.41/11.18 [9020]~P85(f784(f784(f347(x90201),x90203),x90204))+P85(f784(f784(f347(f869(x90201,a852)),f784(f287(x90201,x90201,x90202),f784(f784(f312(x90201),x90203),f187(f869(x90201,a852))))),f784(f784(f69(x90201),x90204),x90202)))
% 11.41/11.18 [9030]P85(f784(f784(f347(f868(x90301,x90301)),f784(f784(f251(x90301,x90301),x90302),x90303)),f310(x90301,x90304)))+~P85(f784(f784(f347(f868(x90301,x90301)),f784(f784(f251(x90301,x90301),x90303),x90302)),f310(x90301,f784(f288(x90301,x90301),x90304))))
% 11.41/11.18 [9114]E(f784(f784(f151(x91141,f784(f162(x91141),x91142)),f784(f784(f3(a859),f784(f784(f3(a859),f784(f188(f860(x91141)),x91142)),x91143)),f87(a859))),x91144),f784(f162(x91141),f784(f784(f151(x91141,x91142),x91143),x91144)))+~P85(f784(f784(f243(a859),x91143),f784(f188(f860(x91141)),x91142)))
% 11.41/11.18 [9152]~P26(x91522,x91521,x91523,f249(f869(x91522,a852)))+P85(f784(f784(f242(f869(x91521,a852)),f784(f313(x91522,x91521,x91523),f784(f88(f869(x91522,a852)),x91524))),f784(f88(f869(x91521,a852)),f784(f313(x91522,x91521,x91523),x91524))))
% 11.41/11.18 [9160]~P6(x91601)+E(f784(f136(x91601,x91602,f784(f9(x91602,x91601,x91601),f784(f784(f10(x91601,f869(x91601,x91601),x91602),f110(x91601)),x91603)),f187(x91601)),x91604),f784(f784(f54(x91602,x91601),f784(f164(x91602),x91604)),x91603))
% 11.41/11.18 [9161]~P6(x91611)+E(f784(f136(x91611,x91612,f784(f9(x91612,x91611,x91611),f784(f784(f10(x91611,f869(x91611,x91611),x91612),f111(x91611)),x91613)),f249(x91611)),x91614),f784(f784(f55(x91612,x91611),f784(f164(x91612),x91614)),x91613))
% 11.41/11.18 [9225]~P85(f784(f784(f347(f868(f860(x92254),f860(x92254))),f784(f784(f251(f860(x92254),f860(x92254)),x92253),x92252)),f149(x92254,x92251)))+P85(f784(f784(f243(a859),f750(x92251,x92252,x92253,x92254)),f784(f188(f860(x92254)),x92253)))
% 11.41/11.18 [9226]~P4(x92261)+E(f784(f784(f89(x92261),f784(f784(f89(x92261),f784(f784(f90(x92261),f784(f784(f51(x92261),x92262),x92263)),x92263)),f60(x92261,x92262,x92263))),x92264),f784(f784(f89(x92261),x92262),x92264))
% 11.41/11.18 [9254]~P85(f784(f784(f347(f868(f860(x92541),f860(x92541))),f784(f784(f251(f860(x92541),f860(x92541)),x92542),x92543)),f784(f288(f860(x92541),f860(x92541)),f149(x92541,x92544))))+P85(f784(f784(f347(f868(f860(x92541),f860(x92541))),f784(f784(f251(f860(x92541),f860(x92541)),x92542),x92543)),f149(x92541,f784(f288(x92541,x92541),x92544))))
% 11.41/11.18 [9255]P85(f784(f784(f347(f868(f860(x92551),f860(x92551))),f784(f784(f251(f860(x92551),f860(x92551)),x92552),x92553)),f784(f288(f860(x92551),f860(x92551)),f149(x92551,x92554))))+~P85(f784(f784(f347(f868(f860(x92551),f860(x92551))),f784(f784(f251(f860(x92551),f860(x92551)),x92552),x92553)),f149(x92551,f784(f288(x92551,x92551),x92554))))
% 11.41/11.18 [9293]~P85(f784(f784(f347(x92931),x92933),f784(f271(x92931,x92932),x92934)))+P85(f784(f784(f347(f868(x92931,x92932)),f784(f784(f251(x92931,x92932),x92933),f602(x92934,x92932,x92933,x92931))),x92934))
% 11.41/11.18 [9294]~P85(f784(f784(f347(x92941),x92943),f784(f271(x92941,x92942),x92944)))+P85(f784(f784(f347(f868(x92941,x92942)),f784(f784(f251(x92941,x92942),x92943),f603(x92944,x92942,x92943,x92941))),x92944))
% 11.41/11.18 [9420]~P85(f784(f71(f864(x94201)),f784(f313(x94202,f864(x94201),x94203),f249(f869(x94202,a852)))))+P85(f784(f71(f864(x94201)),f784(f313(x94202,f864(x94201),f176(x94202,x94201,x94203,f172(x94202,x94201,x94204))),f249(f869(x94202,a852)))))
% 11.41/11.18 [9442]~P85(f784(f784(f347(f868(x94421,x94421)),f784(f784(f251(x94421,x94421),x94422),x94424)),f784(f784(f291(x94421,x94421,x94421),x94423),f310(x94421,x94423))))+P85(f784(f784(f347(f868(x94421,x94421)),f784(f784(f251(x94421,x94421),x94422),f667(x94423,x94424,x94422,x94421))),x94423))
% 11.41/11.18 [9611]~P85(f784(f784(f347(f868(x96112,x96111)),x96114),f784(f288(x96111,x96112),x96113)))+P85(f784(f784(f347(f868(x96111,x96112)),f784(f784(f251(x96111,x96112),f713(x96113,x96114,x96111,x96112)),f712(x96113,x96114,x96111,x96112))),x96113))
% 11.41/11.18 [9635]~P85(f784(f784(f347(f868(f860(x96351),f860(x96351))),f784(f784(f251(f860(x96351),f860(x96351)),x96354),x96353)),f149(x96351,x96352)))+P85(f784(f784(f347(f868(x96351,x96351)),f784(f784(f251(x96351,x96351),f754(x96352,x96353,x96354,x96351)),f755(x96352,x96353,x96354,x96351))),x96352))
% 11.41/11.18 [9710]~P85(f784(f784(f347(f868(f860(x97101),f860(x97101))),f784(f784(f251(f860(x97101),f860(x97101)),x97102),x97104)),f149(x97101,x97103)))+P85(f784(f784(f347(f868(x97101,x97101)),f784(f784(f251(x97101,x97101),f784(f784(f155(x97101),x97102),f750(x97103,x97104,x97102,x97101))),f751(x97103,x97104,x97102,x97101))),x97103))
% 11.41/11.18 [9731]~P85(f784(f71(x97312),x97314))+E(f784(f784(f784(f75(f869(x97311,a852),x97312,f110(f869(x97311,a852))),f784(f784(f9(x97312,f869(x97311,a852),f869(x97311,a852)),f784(f784(f10(x97311,f869(f869(x97311,a852),f869(x97311,a852)),x97312),f312(x97311)),x97313)),f187(f869(x97311,a852)))),f187(f869(x97311,a852))),x97314),f784(f313(x97312,x97311,x97313),x97314))
% 11.41/11.18 [9851]~P26(x98511,x98512,x98513,f249(f869(x98511,a852)))+P85(f784(f784(f242(f869(x98511,a852)),f784(f315(x98511,x98512,x98513),f784(f784(f312(x98512),x98514),f187(f869(x98512,a852))))),f784(f784(f312(x98511),f94(x98511,f784(f784(f9(x98511,x98512,a852),f784(f784(f10(x98512,f869(x98512,a852),x98511),a343),x98513)),x98514))),f187(f869(x98511,a852)))))
% 11.41/11.18 [5516]~E(f784(f784(f130(x55161),x55162),x55164),x55163)+E(f784(f784(f165(x55161),f784(f188(f860(x55161)),x55162)),x55163),x55162)
% 11.41/11.18 [5517]~E(f784(f784(f130(x55172),x55173),x55171),x55174)+E(x55171,f784(f784(f133(x55172),f784(f188(f860(x55172)),x55173)),x55174))
% 11.41/11.18 [5528]~E(x55284,f2(a859))+E(f784(f784(f155(x55281),f784(f784(f144(x55281),x55282),x55283)),x55284),x55282)
% 11.41/11.18 [6058]~P86(x60581)+E(f784(f784(f252(x60581),f784(f784(f252(x60581),x60582),x60583)),x60584),f784(f784(f252(x60581),x60582),f784(f784(f90(a859),x60583),x60584)))
% 11.41/11.18 [6059]~P75(x60591)+E(f784(f784(f252(x60591),f784(f784(f252(x60591),x60592),x60593)),x60594),f784(f784(f252(x60591),x60592),f784(f784(f90(a859),x60593),x60594)))
% 11.41/11.18 [6075]E(x60751,f2(a859))+E(f784(f784(f155(x60752),f784(f784(f144(x60752),x60753),x60754)),x60751),f784(f784(f155(x60752),x60754),f784(f784(f3(a859),x60751),f87(a859))))
% 11.41/11.18 [6099]~P86(x60991)+E(f784(f784(f89(x60991),f784(f784(f89(x60991),x60992),x60993)),x60994),f784(f784(f89(x60991),x60992),f784(f784(f89(x60991),x60993),x60994)))
% 11.41/11.18 [6100]~P86(x61001)+E(f784(f784(f90(x61001),f784(f784(f90(x61001),x61002),x61003)),x61004),f784(f784(f90(x61001),x61002),f784(f784(f90(x61001),x61003),x61004)))
% 11.41/11.18 [6101]~P116(x61011)+E(f784(f784(f293(x61011),f784(f784(f90(x61011),x61012),x61013)),x61014),f784(f784(f90(x61011),x61012),f784(f784(f293(x61011),x61013),x61014)))
% 11.41/11.18 [6102]~P2(x61021)+E(f784(f784(f89(x61021),f784(f784(f89(x61021),x61022),x61023)),x61024),f784(f784(f89(x61021),x61022),f784(f784(f89(x61021),x61023),x61024)))
% 11.41/11.18 [6103]~P86(x61031)+E(f784(f784(f89(x61031),f784(f784(f89(x61031),x61032),x61033)),x61034),f784(f784(f89(x61031),x61032),f784(f784(f89(x61031),x61033),x61034)))
% 11.41/11.18 [6104]~P86(x61041)+E(f784(f784(f90(x61041),f784(f784(f90(x61041),x61042),x61043)),x61044),f784(f784(f90(x61041),x61042),f784(f784(f90(x61041),x61043),x61044)))
% 11.41/11.18 [6105]~P65(x61051)+E(f784(f784(f90(x61051),f784(f784(f90(x61051),x61052),x61053)),x61054),f784(f784(f90(x61051),x61052),f784(f784(f90(x61051),x61053),x61054)))
% 11.41/11.18 [6107]~P101(x61071)+E(f784(f784(f246(x61071),f784(f784(f246(x61071),x61072),x61073)),x61074),f784(f784(f246(x61071),x61072),f784(f784(f246(x61071),x61073),x61074)))
% 11.41/11.18 [6108]~P101(x61081)+E(f784(f784(f246(x61081),f784(f784(f246(x61081),x61082),x61083)),x61084),f784(f784(f246(x61081),x61082),f784(f784(f246(x61081),x61083),x61084)))
% 11.41/11.18 [6109]~P101(x61091)+E(f784(f784(f186(x61091),f784(f784(f186(x61091),x61092),x61093)),x61094),f784(f784(f186(x61091),x61092),f784(f784(f186(x61091),x61093),x61094)))
% 11.41/11.18 [6110]~P101(x61101)+E(f784(f784(f186(x61101),f784(f784(f186(x61101),x61102),x61103)),x61104),f784(f784(f186(x61101),x61102),f784(f784(f186(x61101),x61103),x61104)))
% 11.41/11.18 [6111]~P93(x61111)+E(f784(f784(f110(x61111),f784(f784(f110(x61111),x61112),x61113)),x61114),f784(f784(f110(x61111),x61112),f784(f784(f110(x61111),x61113),x61114)))
% 11.41/11.18 [6112]~P98(x61121)+E(f784(f784(f110(x61121),f784(f784(f110(x61121),x61122),x61123)),x61124),f784(f784(f110(x61121),x61122),f784(f784(f110(x61121),x61123),x61124)))
% 11.41/11.18 [6113]~P98(x61131)+E(f784(f784(f110(x61131),f784(f784(f110(x61131),x61132),x61133)),x61134),f784(f784(f110(x61131),x61132),f784(f784(f110(x61131),x61133),x61134)))
% 11.41/11.18 [6114]~P93(x61141)+E(f784(f784(f111(x61141),f784(f784(f111(x61141),x61142),x61143)),x61144),f784(f784(f111(x61141),x61142),f784(f784(f111(x61141),x61143),x61144)))
% 11.41/11.18 [6115]~P99(x61151)+E(f784(f784(f111(x61151),f784(f784(f111(x61151),x61152),x61153)),x61154),f784(f784(f111(x61151),x61152),f784(f784(f111(x61151),x61153),x61154)))
% 11.41/11.18 [6116]~P99(x61161)+E(f784(f784(f111(x61161),f784(f784(f111(x61161),x61162),x61163)),x61164),f784(f784(f111(x61161),x61162),f784(f784(f111(x61161),x61163),x61164)))
% 11.41/11.18 [6127]~P4(x61271)+E(f60(x61271,f784(f784(f89(x61271),x61272),f784(f784(f90(x61271),x61273),x61274)),x61274),f60(x61271,x61272,x61274))
% 11.41/11.18 [6128]~P4(x61281)+E(f60(x61281,f784(f784(f89(x61281),x61282),f784(f784(f90(x61281),x61283),x61284)),x61283),f60(x61281,x61282,x61283))
% 11.41/11.18 [6264]E(f784(f784(f155(x62641),f784(f784(f165(x62641),x62642),x62643)),x62644),f784(f784(f155(x62641),x62643),x62644))+~P85(f784(f784(f243(a859),x62644),x62642))
% 11.41/11.18 [6450]~P86(x64501)+E(f784(f784(f89(x64501),f784(f784(f89(x64501),x64502),x64503)),x64504),f784(f784(f89(x64501),f784(f784(f89(x64501),x64502),x64504)),x64503))
% 11.41/11.18 [6451]~P86(x64511)+E(f784(f784(f90(x64511),f784(f784(f90(x64511),x64512),x64513)),x64514),f784(f784(f90(x64511),f784(f784(f90(x64511),x64512),x64514)),x64513))
% 11.41/11.18 [6512]~P112(x65122)+E(f784(f784(f8(x65121,x65122),f784(f18(x65122,x65121),x65123)),x65124),f784(f784(f90(x65122),f784(f109(x65122),f784(f50(x65121),x65124))),x65123))
% 11.41/11.18 [6688]E(f784(f784(f111(f869(x66881,a852)),f784(f784(f312(x66881),x66882),x66883)),x66884),f784(f784(f111(f869(x66881,a852)),x66883),x66884))+P85(f784(f784(f347(x66881),x66882),x66884))
% 11.41/11.18 [6689]E(f784(f784(f111(f869(x66891,a852)),f784(f784(f312(x66891),x66892),x66893)),x66894),f784(f784(f111(f869(x66891,a852)),x66893),x66894))+P85(f784(f784(f347(x66891),x66892),x66894))
% 11.41/11.18 [6763]~P74(x67631)+E(f784(f784(f246(x67631),f784(f784(f89(x67631),x67632),x67633)),f784(f784(f89(x67631),x67634),x67633)),f784(f784(f89(x67631),f784(f784(f246(x67631),x67632),x67634)),x67633))
% 11.41/11.18 [6764]~P74(x67641)+E(f784(f784(f186(x67641),f784(f784(f89(x67641),x67642),x67643)),f784(f784(f89(x67641),x67644),x67643)),f784(f784(f89(x67641),f784(f784(f186(x67641),x67642),x67644)),x67643))
% 11.41/11.18 [6765]~P86(x67651)+E(f784(f784(f89(x67651),f784(f784(f90(x67651),x67652),x67653)),f784(f784(f90(x67651),x67654),x67653)),f784(f784(f90(x67651),f784(f784(f89(x67651),x67652),x67654)),x67653))
% 11.41/11.18 [6766]~P110(x67661)+E(f784(f784(f89(x67661),f784(f784(f90(x67661),x67662),x67663)),f784(f784(f90(x67661),x67664),x67663)),f784(f784(f90(x67661),f784(f784(f89(x67661),x67662),x67664)),x67663))
% 11.41/11.18 [6767]~P77(x67671)+E(f784(f784(f246(x67671),f784(f784(f3(x67671),x67672),x67673)),f784(f784(f3(x67671),x67674),x67673)),f784(f784(f3(x67671),f784(f784(f246(x67671),x67672),x67674)),x67673))
% 11.41/11.18 [6768]~P77(x67681)+E(f784(f784(f186(x67681),f784(f784(f3(x67681),x67682),x67683)),f784(f784(f3(x67681),x67684),x67683)),f784(f784(f3(x67681),f784(f784(f186(x67681),x67682),x67684)),x67683))
% 11.41/11.18 [6769]~P86(x67691)+E(f784(f784(f90(x67691),f784(f784(f252(x67691),x67692),x67693)),f784(f784(f252(x67691),x67694),x67693)),f784(f784(f252(x67691),f784(f784(f90(x67691),x67692),x67694)),x67693))
% 11.41/11.18 [6770]~P71(x67701)+E(f784(f784(f90(x67701),f784(f784(f252(x67701),x67702),x67703)),f784(f784(f252(x67701),x67704),x67703)),f784(f784(f252(x67701),f784(f784(f90(x67701),x67702),x67704)),x67703))
% 11.41/11.18 [6771]~P59(x67711)+E(f784(f784(f293(x67711),f784(f784(f252(x67711),x67712),x67713)),f784(f784(f252(x67711),x67714),x67713)),f784(f784(f252(x67711),f784(f784(f293(x67711),x67712),x67714)),x67713))
% 11.41/11.18 [6772]~P116(x67721)+E(f784(f784(f89(x67721),f784(f784(f293(x67721),x67722),x67723)),f784(f784(f293(x67721),x67724),x67723)),f784(f784(f293(x67721),f784(f784(f89(x67721),x67722),x67724)),x67723))
% 11.41/11.18 [6773]~P116(x67731)+E(f784(f784(f3(x67731),f784(f784(f293(x67731),x67732),x67733)),f784(f784(f293(x67731),x67734),x67733)),f784(f784(f293(x67731),f784(f784(f3(x67731),x67732),x67734)),x67733))
% 11.41/11.18 [6774]~P101(x67741)+E(f784(f784(f186(x67741),f784(f784(f246(x67741),x67742),x67743)),f784(f784(f246(x67741),x67744),x67743)),f784(f784(f246(x67741),f784(f784(f186(x67741),x67742),x67744)),x67743))
% 11.41/11.18 [6775]~P101(x67751)+E(f784(f784(f246(x67751),f784(f784(f186(x67751),x67752),x67753)),f784(f784(f186(x67751),x67754),x67753)),f784(f784(f186(x67751),f784(f784(f246(x67751),x67752),x67754)),x67753))
% 11.41/11.18 [6776]~P97(x67761)+E(f784(f784(f111(x67761),f784(f784(f110(x67761),x67762),x67763)),f784(f784(f110(x67761),x67764),x67763)),f784(f784(f110(x67761),f784(f784(f111(x67761),x67762),x67764)),x67763))
% 11.41/11.18 [6777]~P97(x67771)+E(f784(f784(f110(x67771),f784(f784(f111(x67771),x67772),x67773)),f784(f784(f111(x67771),x67774),x67773)),f784(f784(f111(x67771),f784(f784(f110(x67771),x67772),x67774)),x67773))
% 11.41/11.18 [6778]~P86(x67781)+E(f784(f784(f89(x67781),f784(f784(f90(x67781),x67782),x67783)),f784(f784(f90(x67781),x67784),x67783)),f784(f784(f90(x67781),f784(f784(f89(x67781),x67782),x67784)),x67783))
% 11.41/11.18 [6813]E(f784(f784(f151(x68131,x68132),x68133),x68134),x68132)+~P85(f784(f784(f242(a859),f784(f188(f860(x68131)),x68132)),x68133))
% 11.41/11.18 [6839]~P85(f784(x68393,x68394))+P85(f784(f784(f784(f110(f869(x68391,a852)),x68392),x68393),x68394))
% 11.41/11.18 [6840]~P85(f784(x68403,x68404))+P85(f784(f784(f784(f110(f869(x68401,a852)),x68402),x68403),x68404))
% 11.41/11.18 [6841]~P85(f784(x68412,x68414))+P85(f784(f784(f784(f110(f869(x68411,a852)),x68412),x68413),x68414))
% 11.41/11.18 [6842]~P85(f784(x68422,x68424))+P85(f784(f784(f784(f110(f869(x68421,a852)),x68422),x68423),x68424))
% 11.41/11.18 [6864]E(f784(f784(f155(x68641),f784(f784(f130(x68641),x68642),x68643)),x68644),f784(f784(f155(x68641),x68642),x68644))+~P85(f784(f784(f243(a859),x68644),f784(f188(f860(x68641)),x68642)))
% 11.41/11.18 [6873]E(f784(f784(f3(f869(x68731,a852)),f784(f784(f312(x68731),x68732),x68733)),x68734),f784(f784(f3(f869(x68731,a852)),x68733),x68734))+~P85(f784(f784(f347(x68731),x68732),x68734))
% 11.41/11.18 [6874]E(f784(f784(f3(f869(x68741,a852)),f784(f784(f312(x68741),x68742),x68743)),x68744),f784(f784(f3(f869(x68741,a852)),x68743),x68744))+~P85(f784(f784(f347(x68741),x68742),x68744))
% 11.41/11.18 [6914]~E(f134(a859,f784(f304(a859,x69141),x69142)),f784(f784(f144(a859),x69144),x69143))+E(f134(a859,f784(f304(a859,f784(f784(f89(a859),x69141),f87(a859))),x69142)),x69143)
% 11.41/11.18 [6982]E(x69821,f2(a859))+E(f784(f784(f144(x69822),x69823),f784(f784(f165(x69822),f784(f784(f3(a859),x69821),f87(a859))),x69824)),f784(f784(f165(x69822),x69821),f784(f784(f144(x69822),x69823),x69824)))
% 11.41/11.18 [7086]E(f784(f784(f155(x70861),x70862),f784(f784(f3(a859),x70863),f784(f188(f860(x70861)),x70864))),f784(f784(f155(x70861),f784(f784(f130(x70861),x70864),x70862)),x70863))+P85(f784(f784(f243(a859),x70863),f784(f188(f860(x70861)),x70864)))
% 11.41/11.18 [7112]E(f784(f784(f111(f869(x71121,a852)),x71122),f784(f784(f312(x71121),x71123),x71124)),f784(f784(f312(x71121),x71123),f784(f784(f111(f869(x71121,a852)),x71122),x71124)))+~P85(f784(f784(f347(x71121),x71123),x71122))
% 11.41/11.18 [7113]E(f784(f784(f111(f869(x71131,a852)),x71132),f784(f784(f312(x71131),x71133),x71134)),f784(f784(f312(x71131),x71133),f784(f784(f111(f869(x71131,a852)),x71132),x71134)))+~P85(f784(f784(f347(x71131),x71133),x71132))
% 11.41/11.18 [7147]E(f784(f784(f155(x71471),f784(f784(f151(x71471,x71472),x71473),x71474)),x71473),x71474)+~P85(f784(f784(f243(a859),x71473),f784(f188(f860(x71471)),x71472)))
% 11.41/11.18 [7168]E(x71681,f187(f869(x71682,a852)))+E(f784(f313(f868(x71683,x71682),x71683,f250(x71683,x71682)),f784(f784(f258(x71683,x71682),x71684),f784(f18(f869(x71682,a852),x71683),x71681))),x71684)
% 11.41/11.18 [7169]E(x71691,f187(f869(x71692,a852)))+E(f784(f313(f868(x71692,x71693),x71693,f260(x71692,x71693)),f784(f784(f258(x71692,x71693),x71691),f784(f18(f869(x71693,a852),x71692),x71694))),x71694)
% 11.41/11.18 [7253]E(f784(f784(f3(f869(x72531,a852)),f784(f784(f312(x72531),x72532),x72533)),x72534),f784(f784(f312(x72531),x72532),f784(f784(f3(f869(x72531,a852)),x72533),x72534)))+P85(f784(f784(f347(x72531),x72532),x72534))
% 11.41/11.18 [7294]~E(x72944,f187(f869(x72942,a852)))+E(f784(f313(f868(x72941,x72942),x72941,f250(x72941,x72942)),f784(f784(f258(x72941,x72942),x72943),f784(f18(f869(x72942,a852),x72941),x72944))),f187(f869(x72941,a852)))
% 11.41/11.18 [7295]~E(x72953,f187(f869(x72951,a852)))+E(f784(f313(f868(x72951,x72952),x72952,f260(x72951,x72952)),f784(f784(f258(x72951,x72952),x72953),f784(f18(f869(x72952,a852),x72951),x72954))),f187(f869(x72952,a852)))
% 11.41/11.18 [7352]~P85(f784(f784(f347(x73521),x73522),x73524))+P85(f784(f784(f347(x73521),x73522),f784(f784(f110(f869(x73521,a852)),x73523),x73524)))
% 11.41/11.18 [7353]~P85(f784(f784(f347(x73531),x73532),x73534))+P85(f784(f784(f347(x73531),x73532),f784(f784(f110(f869(x73531,a852)),x73533),x73534)))
% 11.41/11.18 [7354]~P85(f784(f784(f347(x73541),x73542),x73544))+P85(f784(f784(f347(x73541),x73542),f784(f784(f110(f869(x73541,a852)),x73543),x73544)))
% 11.41/11.18 [7355]~P85(f784(f784(f347(x73551),x73552),x73553))+P85(f784(f784(f347(x73551),x73552),f784(f784(f110(f869(x73551,a852)),x73553),x73554)))
% 11.41/11.18 [7356]~P85(f784(f784(f347(x73561),x73562),x73563))+P85(f784(f784(f347(x73561),x73562),f784(f784(f110(f869(x73561,a852)),x73563),x73564)))
% 11.41/11.18 [7357]~P85(f784(f784(f347(x73571),x73572),x73573))+P85(f784(f784(f347(x73571),x73572),f784(f784(f110(f869(x73571,a852)),x73573),x73574)))
% 11.41/11.18 [7378]E(f784(f784(f111(f869(x73781,a852)),f784(f784(f312(x73781),x73782),x73783)),x73784),f784(f784(f312(x73781),x73782),f784(f784(f111(f869(x73781,a852)),x73783),x73784)))+~P85(f784(f784(f347(x73781),x73782),x73784))
% 11.41/11.18 [7379]E(f784(f784(f111(f869(x73791,a852)),f784(f784(f312(x73791),x73792),x73793)),x73794),f784(f784(f312(x73791),x73792),f784(f784(f111(f869(x73791,a852)),x73793),x73794)))+~P85(f784(f784(f347(x73791),x73792),x73794))
% 11.41/11.18 [7655]P85(f784(x76551,x76552))+~P85(f784(f784(f784(f111(f869(x76553,a852)),x76554),x76551),x76552))
% 11.41/11.18 [7656]P85(f784(x76561,x76562))+~P85(f784(f784(f784(f111(f869(x76563,a852)),x76561),x76564),x76562))
% 11.41/11.18 [7657]P85(f784(x76571,x76572))+~P85(f784(f784(f784(f111(f869(x76573,a852)),x76574),x76571),x76572))
% 11.41/11.18 [7658]P85(f784(x76581,x76582))+~P85(f784(f784(f784(f111(f869(x76583,a852)),x76581),x76584),x76582))
% 11.41/11.18 [7661]E(f784(f784(f8(x76611,a859),x76612),f784(f784(f3(f869(x76611,a852)),x76613),f784(f784(f312(x76611),x76614),f187(f869(x76611,a852))))),f784(f784(f8(x76611,a859),x76612),x76613))+P85(f784(f784(f347(x76611),x76614),x76613))
% 11.41/11.18 [7667]~P68(x76671)+E(f784(f157(x76671),f784(f784(f146(a859,x76671),x76672),f134(a859,f784(f304(a859,x76673),x76674)))),f784(f784(f8(a859,x76671),x76672),f784(f164(a859),f134(a859,f784(f304(a859,x76673),x76674)))))
% 11.41/11.18 [7668]~P68(x76681)+E(f784(f784(f8(a859,x76681),x76682),f784(f164(a859),f134(a859,f784(f304(a859,x76683),x76684)))),f784(f157(x76681),f784(f784(f146(a859,x76681),x76682),f134(a859,f784(f304(a859,x76683),x76684)))))
% 11.41/11.18 [7781]~E(x77813,x77814)+P85(f784(f72(x77811,x77812,f784(f784(f312(x77811),x77813),f187(f869(x77811,a852)))),x77814))
% 11.41/11.18 [7877]P85(f784(f784(f347(x78771),x78772),f784(f164(x78771),x78773)))+~P85(f784(f784(f347(x78771),x78772),f784(f164(x78771),f784(f784(f165(x78771),x78774),x78773))))
% 11.41/11.18 [7878]P85(f784(f784(f347(x78781),x78782),f784(f164(x78781),x78783)))+~P85(f784(f784(f347(x78781),x78782),f784(f164(x78781),f784(f784(f133(x78781),x78784),x78783))))
% 11.41/11.18 [7948]P85(f784(f784(f347(x79481),x79482),x79483))+~P85(f784(f784(f347(x79481),x79482),f784(f784(f111(f869(x79481,a852)),x79484),x79483)))
% 11.41/11.18 [7949]P85(f784(f784(f347(x79491),x79492),x79493))+~P85(f784(f784(f347(x79491),x79492),f784(f784(f3(f869(x79491,a852)),x79493),x79494)))
% 11.41/11.18 [7950]P85(f784(f784(f347(x79501),x79502),x79503))+~P85(f784(f784(f347(x79501),x79502),f784(f784(f3(f869(x79501,a852)),x79503),x79504)))
% 11.41/11.18 [7951]P85(f784(f784(f347(x79511),x79512),x79513))+~P85(f784(f784(f347(x79511),x79512),f784(f784(f3(f869(x79511,a852)),x79513),x79514)))
% 11.41/11.18 [7952]P85(f784(f784(f347(x79521),x79522),x79523))+~P85(f784(f784(f347(x79521),x79522),f784(f784(f111(f869(x79521,a852)),x79524),x79523)))
% 11.41/11.18 [7953]P85(f784(f784(f347(x79531),x79532),x79533))+~P85(f784(f784(f347(x79531),x79532),f784(f784(f111(f869(x79531,a852)),x79534),x79533)))
% 11.41/11.18 [7954]P85(f784(f784(f347(x79541),x79542),x79543))+~P85(f784(f784(f347(x79541),x79542),f784(f784(f111(f869(x79541,a852)),x79543),x79544)))
% 11.41/11.18 [7955]P85(f784(f784(f347(x79551),x79552),x79553))+~P85(f784(f784(f347(x79551),x79552),f784(f784(f111(f869(x79551,a852)),x79553),x79554)))
% 11.41/11.18 [7956]P85(f784(f784(f347(x79561),x79562),x79563))+~P85(f784(f784(f347(x79561),x79562),f784(f784(f111(f869(x79561,a852)),x79563),x79564)))
% 11.41/11.18 [7973]E(f784(f784(f130(x79731),f784(f784(f165(x79731),x79732),x79733)),f784(f784(f144(x79731),x79734),f784(f784(f133(x79731),f784(a160,x79732)),x79733))),f784(f784(f151(x79731,x79733),x79732),x79734))+~P85(f784(f784(f243(a859),x79732),f784(f188(f860(x79731)),x79733)))
% 11.41/11.18 [7996]P85(f784(f784(f347(x79961),x79962),x79963))+~P85(f784(f784(f242(f869(x79961,a852)),f784(f784(f312(x79961),x79962),x79964)),x79963))
% 11.41/11.18 [8023]~P85(f784(f784(f347(x80231),x80232),x80233))+~P85(f784(f784(f347(x80231),x80232),f784(f784(f3(f869(x80231,a852)),x80234),x80233)))
% 11.41/11.18 [8024]~P85(f784(f784(f347(x80241),x80242),x80243))+~P85(f784(f784(f347(x80241),x80242),f784(f784(f3(f869(x80241,a852)),x80244),x80243)))
% 11.41/11.18 [8025]~P85(f784(f784(f347(x80251),x80252),x80253))+~P85(f784(f784(f347(x80251),x80252),f784(f784(f3(f869(x80251,a852)),x80254),x80253)))
% 11.41/11.18 [8058]~P85(f784(f784(f243(a859),x80584),f784(f188(f860(x80581)),x80583)))+P85(f784(f784(f347(x80581),x80582),f784(f164(x80581),f784(f784(f151(x80581,x80583),x80584),x80582))))
% 11.41/11.18 [8099]E(f784(f113(a859),x80991),f2(a859))+E(f784(f784(f144(x80992),x80993),f784(f784(f165(x80992),f784(f784(f3(a859),f784(f113(a859),x80991)),f87(a859))),x80994)),f784(f784(f165(x80992),f784(f113(a859),x80991)),f784(f784(f144(x80992),x80993),x80994)))
% 11.41/11.18 [8108]E(f784(f784(f155(x81081),f784(f784(f133(x81081),x81082),x81083)),x81084),f784(f784(f155(x81081),x81083),f784(f784(f89(a859),x81082),x81084)))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),x81082),x81084)),f784(f188(f860(x81081)),x81083)))
% 11.41/11.18 [8117]~P112(x81172)+E(f784(f784(f8(x81171,x81172),f784(f784(f10(a859,x81172,x81171),f109(x81172)),x81173)),x81174),f784(f109(x81172),f784(f784(f8(x81171,a859),x81173),x81174)))
% 11.41/11.18 [8118]~P136(x81182)+E(f784(f784(f8(x81181,x81182),f784(f784(f10(a1,x81182,x81181),f112(x81182)),x81183)),x81184),f784(f112(x81182),f784(f784(f8(x81181,a1),x81183),x81184)))
% 11.41/11.18 [8169]~P62(x81692)+E(f784(f784(f11(x81691,x81692),f784(f784(f10(x81692,x81692,x81691),f84(x81692)),x81693)),x81694),f784(f84(x81692),f784(f784(f11(x81691,x81692),x81693),x81694)))
% 11.41/11.18 [8170]~P3(x81702)+E(f784(f784(f8(x81701,x81702),f784(f784(f10(x81702,x81702,x81701),f88(x81702)),x81703)),x81704),f784(f88(x81702),f784(f784(f8(x81701,x81702),x81703),x81704)))
% 11.41/11.18 [8172]E(f784(f784(f8(x81721,a859),x81722),f784(f784(f3(f869(x81721,a852)),x81723),f784(f784(f312(x81721),x81724),f187(f869(x81721,a852))))),f784(f784(f3(a859),f784(f784(f8(x81721,a859),x81722),x81723)),f784(x81722,x81724)))+~P85(f784(f784(f347(x81721),x81724),x81723))
% 11.41/11.18 [8191]P85(f784(f784(f242(f869(x81911,a852)),x81912),x81913))+~P85(f784(f784(f242(f869(x81911,a852)),f784(f784(f312(x81911),x81914),x81912)),x81913))
% 11.41/11.18 [8400]P35(x84001,x84002)+~P35(x84001,f784(f784(f312(f868(x84001,x84001)),f784(f784(f251(x84001,x84001),x84003),x84004)),x84002))
% 11.41/11.18 [8401]P55(x84011,x84012)+~P55(x84011,f784(f784(f312(f868(x84011,x84011)),f784(f784(f251(x84011,x84011),x84013),x84014)),x84012))
% 11.41/11.18 [8409]~P101(x84091)+E(f784(f784(f142(x84091,x84091,f7(x84091)),x84092),f784(f784(f142(x84091,x84091,f7(x84091)),x84093),x84094)),f784(f784(f142(x84091,x84091,f7(x84091)),x84093),f784(f784(f142(x84091,x84091,f7(x84091)),x84092),x84094)))
% 11.41/11.18 [8419]E(x84191,x84192)+~P85(f784(f72(x84193,x84194,f784(f784(f312(x84193),x84191),f187(f869(x84193,a852)))),x84192))
% 11.41/11.18 [8423]E(f784(f172(x84231,x84232,x84233),x84234),f190(x84232))+P85(f784(f784(f347(x84231),x84234),f784(f313(f868(x84231,x84232),x84231,f250(x84231,x84232)),f784(f164(f868(x84231,x84232)),x84233))))
% 11.41/11.18 [8429]E(f784(f784(f130(x84291),f784(f784(f165(x84291),x84292),x84293)),f784(f784(f165(x84291),x84294),f784(f784(f133(x84291),x84292),x84293))),f784(f784(f165(x84291),f784(f784(f89(a859),x84292),x84294)),x84293))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),x84292),x84294)),f784(f188(f860(x84291)),x84293)))
% 11.41/11.18 [8471]P85(f784(f71(x84711),x84712))+~E(x84712,f784(f313(a859,x84711,x84713),f784(f266(a859),f784(f784(f9(a859,a859,a852),f243(a859)),x84714))))
% 11.41/11.18 [8472]P85(f784(f71(x84721),x84722))+~E(x84722,f784(f313(a859,x84721,x84723),f784(f266(a859),f784(f784(f9(a859,a859,a852),f243(a859)),x84724))))
% 11.41/11.18 [8492]~P83(x84921)+E(f784(f136(x84921,x84921,f89(x84921),f784(f784(f89(x84921),x84922),x84923)),x84924),f784(f784(f89(x84921),x84922),f784(f136(x84921,x84921,f89(x84921),x84923),x84924)))
% 11.41/11.18 [8524]P85(f784(f784(f242(f869(x85241,a852)),f784(f271(x85241,x85242),x85243)),f784(f271(x85241,x85242),x85244)))+~P85(f784(f784(f242(f869(f868(x85241,x85242),a852)),x85243),x85244))
% 11.41/11.18 [8535]~P85(f784(f784(f242(a859),x85352),x85354))+P85(f784(f784(f242(f869(x85351,a852)),f784(f164(x85351),f784(f784(f165(x85351),x85352),x85353))),f784(f164(x85351),f784(f784(f165(x85351),x85354),x85353))))
% 11.41/11.18 [8536]~P85(f784(f784(f242(a859),x85364),x85362))+P85(f784(f784(f242(f869(x85361,a852)),f784(f164(x85361),f784(f784(f133(x85361),x85362),x85363))),f784(f164(x85361),f784(f784(f133(x85361),x85364),x85363))))
% 11.41/11.18 [8579]~P85(f784(f71(x85791),f784(f784(f3(f869(x85791,a852)),x85792),x85794)))+P85(f784(f71(x85791),f784(f784(f3(f869(x85791,a852)),x85792),f784(f784(f312(x85791),x85793),x85794))))
% 11.41/11.18 [8613]P85(f784(f784(f347(f868(x86131,x86131)),x86132),f310(x86131,x86133)))+~P85(f784(f784(f347(f868(x86131,x86131)),x86132),f784(f784(f180(f868(x86131,x86131),a852),x86134),x86133)))
% 11.41/11.18 [8614]P85(f784(f784(f347(f868(x86141,x86141)),x86142),f310(x86141,x86143)))+~P85(f784(f784(f347(f868(x86141,x86141)),x86142),f784(f784(f180(f868(x86141,x86141),a852),x86144),x86143)))
% 11.41/11.18 [8689]~P85(f784(f71(x86891),f784(f784(f3(f869(x86891,a852)),x86892),f784(f784(f312(x86891),x86894),x86893))))+P85(f784(f71(x86891),f784(f784(f3(f869(x86891,a852)),x86892),x86893)))
% 11.41/11.18 [8755]P85(f784(f784(f347(f868(x87551,x87552)),f784(f784(f251(x87551,x87552),x87553),x87554)),f187(f869(f868(x87551,x87552),a852))))+~P85(f784(f784(f187(f869(x87551,f869(x87552,a852))),x87553),x87554))
% 11.41/11.18 [8835]~E(f784(f172(x88351,x88352,x88353),x88354),f190(x88352))+~P85(f784(f784(f347(x88351),x88354),f784(f313(f868(x88351,x88352),x88351,f250(x88351,x88352)),f784(f164(f868(x88351,x88352)),x88353))))
% 11.41/11.18 [8871]~P101(x88711)+P85(f784(f784(f242(x88711),f784(f784(f186(x88711),x88712),f784(f784(f246(x88711),x88713),x88714))),f784(f784(f246(x88711),f784(f784(f186(x88711),x88712),x88713)),f784(f784(f186(x88711),x88712),x88714))))
% 11.41/11.18 [8872]~P93(x88721)+P85(f784(f784(f242(x88721),f784(f784(f110(x88721),x88722),f784(f784(f111(x88721),x88723),x88724))),f784(f784(f111(x88721),f784(f784(f110(x88721),x88722),x88723)),f784(f784(f110(x88721),x88722),x88724))))
% 11.41/11.18 [8891]~P85(f784(f784(f347(f868(x88911,x88912)),f784(f784(f251(x88911,x88912),x88913),x88914)),f187(f869(f868(x88911,x88912),a852))))+P85(f784(f784(f187(f869(x88911,f869(x88912,a852))),x88913),x88914))
% 11.41/11.18 [9015]E(x90151,x90152)+~P85(f784(f784(f347(f868(x90153,x90153)),f784(f784(f251(x90153,x90153),x90151),x90152)),f784(f164(f868(x90153,x90153)),f784(f784(f173(x90153,x90153),x90154),x90154))))
% 11.41/11.18 [9047]~P85(f784(f784(f347(f868(x90471,x90471)),f784(f784(f251(x90471,x90471),x90473),x90472)),f310(x90471,x90474)))+~P35(x90471,f784(f784(f312(f868(x90471,x90471)),f784(f784(f251(x90471,x90471),x90472),x90473)),x90474))
% 11.41/11.18 [9048]~P85(f784(f784(f347(f868(x90481,x90481)),f784(f784(f251(x90481,x90481),x90483),x90482)),f310(x90481,x90484)))+~P55(x90481,f784(f784(f312(f868(x90481,x90481)),f784(f784(f251(x90481,x90481),x90482),x90483)),x90484))
% 11.41/11.18 [9061]P85(f784(f784(f347(x90611),x90612),f784(f164(x90611),x90613)))+~P85(f784(f784(f347(f868(x90611,x90611)),f784(f784(f251(x90611,x90611),x90612),x90614)),f784(f164(f868(x90611,x90611)),f784(f784(f173(x90611,x90611),x90613),x90613))))
% 11.41/11.18 [9093]~P101(x90931)+P85(f784(f784(f242(x90931),f784(f784(f186(x90931),f784(f784(f246(x90931),x90932),x90933)),f784(f784(f246(x90931),x90932),x90934))),f784(f784(f246(x90931),x90932),f784(f784(f186(x90931),x90933),x90934))))
% 11.41/11.18 [9094]~P93(x90941)+P85(f784(f784(f242(x90941),f784(f784(f110(x90941),f784(f784(f111(x90941),x90942),x90943)),f784(f784(f111(x90941),x90942),x90944))),f784(f784(f111(x90941),x90942),f784(f784(f110(x90941),x90943),x90944))))
% 11.41/11.18 [9129]P85(f784(f784(f347(f868(x91291,x91291)),f784(f784(f251(x91291,x91291),x91292),x91293)),f784(f784(f291(x91291,x91291,x91291),x91294),f310(x91291,x91294))))+~P85(f784(f784(f347(f868(x91291,x91291)),f784(f784(f251(x91291,x91291),x91292),x91293)),x91294))
% 11.41/11.18 [9157]~E(f784(f313(x91572,x91571,x91573),f249(f869(x91572,a852))),f249(f869(x91571,a852)))+P85(f784(f784(f242(f869(x91571,a852)),f784(f88(f869(x91571,a852)),f784(f313(x91572,x91571,x91573),x91574))),f784(f313(x91572,x91571,x91573),f784(f88(f869(x91572,a852)),x91574))))
% 11.41/11.18 [9457]P85(f784(f784(f347(f868(x94571,x94571)),f784(f784(f251(x94571,x94571),x94572),x94573)),f784(f288(x94571,x94571),f784(f784(f291(x94571,x94571,x94571),x94574),f310(x94571,x94574)))))+~P85(f784(f784(f347(f868(x94571,x94571)),f784(f784(f251(x94571,x94571),x94572),x94573)),f784(f784(f291(x94571,x94571,x94571),f784(f288(x94571,x94571),x94574)),f310(x94571,f784(f288(x94571,x94571),x94574)))))
% 11.41/11.18 [9458]~P85(f784(f784(f347(f868(x94581,x94581)),f784(f784(f251(x94581,x94581),x94582),x94583)),f784(f288(x94581,x94581),f784(f784(f291(x94581,x94581,x94581),x94584),f310(x94581,x94584)))))+P85(f784(f784(f347(f868(x94581,x94581)),f784(f784(f251(x94581,x94581),x94582),x94583)),f784(f784(f291(x94581,x94581,x94581),f784(f288(x94581,x94581),x94584)),f310(x94581,f784(f288(x94581,x94581),x94584)))))
% 11.41/11.18 [9484]~P85(f784(f784(f347(x94842),x94844),f784(f269(x94841,x94842),x94843)))+P85(f784(f784(f347(f868(x94841,x94842)),f784(f784(f251(x94841,x94842),f598(x94843,x94841,x94844,x94842)),x94844)),x94843))
% 11.41/11.18 [9485]~P85(f784(f784(f347(x94852),x94854),f784(f269(x94851,x94852),x94853)))+P85(f784(f784(f347(f868(x94851,x94852)),f784(f784(f251(x94851,x94852),f599(x94853,x94851,x94854,x94852)),x94854)),x94853))
% 11.41/11.18 [9505]~P85(f784(f784(f347(x95051),x95054),f784(f784(f110(f869(x95051,a852)),x95052),x95053)))+P85(f784(f784(f784(f110(f869(x95051,a852)),f784(f784(f9(x95051,f869(x95051,a852),a852),f347(x95051)),x95052)),f784(f784(f9(x95051,f869(x95051,a852),a852),f347(x95051)),x95053)),x95054))
% 11.41/11.18 [9506]~P85(f784(f784(f347(x95061),x95064),f784(f784(f111(f869(x95061,a852)),x95062),x95063)))+P85(f784(f784(f784(f111(f869(x95061,a852)),f784(f784(f9(x95061,f869(x95061,a852),a852),f347(x95061)),x95062)),f784(f784(f9(x95061,f869(x95061,a852),a852),f347(x95061)),x95063)),x95064))
% 11.41/11.18 [9582]~P85(f784(f784(f347(f868(x95821,x95821)),f784(f784(f251(x95821,x95821),x95824),x95823)),f784(f784(f291(x95821,x95821,x95821),x95822),f310(x95821,x95822))))+P85(f784(f784(f347(f868(x95821,x95821)),f784(f784(f251(x95821,x95821),f668(x95822,x95823,x95824,x95821)),x95823)),x95822))
% 11.41/11.18 [9622]P85(f784(f784(f347(x96221),x96222),f784(f784(f110(f869(x96221,a852)),x96223),x96224)))+~P85(f784(f784(f784(f110(f869(x96221,a852)),f784(f784(f9(x96221,f869(x96221,a852),a852),f347(x96221)),x96223)),f784(f784(f9(x96221,f869(x96221,a852),a852),f347(x96221)),x96224)),x96222))
% 11.41/11.18 [9623]P85(f784(f784(f347(x96231),x96232),f784(f784(f111(f869(x96231,a852)),x96233),x96234)))+~P85(f784(f784(f784(f111(f869(x96231,a852)),f784(f784(f9(x96231,f869(x96231,a852),a852),f347(x96231)),x96233)),f784(f784(f9(x96231,f869(x96231,a852),a852),f347(x96231)),x96234)),x96232))
% 11.41/11.18 [9902]P33(x99021,f784(f784(f9(x99021,f869(f868(x99021,x99021),a852),f869(x99021,a852)),f784(f784(f10(f869(x99021,f869(f869(f868(x99021,x99021),a852),a852)),f869(f869(f868(x99021,x99021),a852),f869(x99021,a852)),x99021),f9(x99021,f869(f868(x99021,x99021),a852),a852)),f784(f784(f10(f869(x99021,f868(x99021,x99021)),f869(x99021,f869(f869(f868(x99021,x99021),a852),a852)),x99021),f784(f10(f868(x99021,x99021),f869(f869(f868(x99021,x99021),a852),a852),x99021),f347(f868(x99021,x99021)))),f251(x99021,x99021)))),x99022),x99023,x99024)+~P85(f784(f784(f347(f868(f860(x99021),f860(x99021))),f784(f784(f251(f860(x99021),f860(x99021)),x99023),x99024)),f150(x99021,x99022)))
% 11.41/11.18 [9906]P56(x99061,f784(f784(f9(x99061,f869(f868(x99061,x99061),a852),f869(x99061,a852)),f784(f784(f10(f869(x99061,f869(f869(f868(x99061,x99061),a852),a852)),f869(f869(f868(x99061,x99061),a852),f869(x99061,a852)),x99061),f9(x99061,f869(f868(x99061,x99061),a852),a852)),f784(f784(f10(f869(x99061,f868(x99061,x99061)),f869(x99061,f869(f869(f868(x99061,x99061),a852),a852)),x99061),f784(f10(f868(x99061,x99061),f869(f869(f868(x99061,x99061),a852),a852),x99061),f347(f868(x99061,x99061)))),f251(x99061,x99061)))),x99062),x99063,x99064)+~P85(f784(f784(f347(f868(f869(x99061,a852),f869(x99061,a852))),f784(f784(f251(f869(x99061,a852),f869(x99061,a852)),x99063),x99064)),f338(x99061,x99062)))
% 11.41/11.18 [9933]E(x99331,x99332)+~E(f784(f784(f9(x99333,f869(f868(x99333,x99334),a852),f869(x99334,a852)),f784(f784(f10(f869(x99334,f869(f869(f868(x99333,x99334),a852),a852)),f869(f869(f868(x99333,x99334),a852),f869(x99334,a852)),x99333),f9(x99334,f869(f868(x99333,x99334),a852),a852)),f784(f784(f10(f869(x99334,f868(x99333,x99334)),f869(x99334,f869(f869(f868(x99333,x99334),a852),a852)),x99333),f784(f10(f868(x99333,x99334),f869(f869(f868(x99333,x99334),a852),a852),x99334),f347(f868(x99333,x99334)))),f251(x99333,x99334)))),x99331),f784(f784(f9(x99333,f869(f868(x99333,x99334),a852),f869(x99334,a852)),f784(f784(f10(f869(x99334,f869(f869(f868(x99333,x99334),a852),a852)),f869(f869(f868(x99333,x99334),a852),f869(x99334,a852)),x99333),f9(x99334,f869(f868(x99333,x99334),a852),a852)),f784(f784(f10(f869(x99334,f868(x99333,x99334)),f869(x99334,f869(f869(f868(x99333,x99334),a852),a852)),x99333),f784(f10(f868(x99333,x99334),f869(f869(f868(x99333,x99334),a852),a852),x99334),f347(f868(x99333,x99334)))),f251(x99333,x99334)))),x99332))
% 11.41/11.18 [9936]~P33(x99361,f784(f784(f9(x99361,f869(f868(x99361,x99361),a852),f869(x99361,a852)),f784(f784(f10(f869(x99361,f869(f869(f868(x99361,x99361),a852),a852)),f869(f869(f868(x99361,x99361),a852),f869(x99361,a852)),x99361),f9(x99361,f869(f868(x99361,x99361),a852),a852)),f784(f784(f10(f869(x99361,f868(x99361,x99361)),f869(x99361,f869(f869(f868(x99361,x99361),a852),a852)),x99361),f784(f10(f868(x99361,x99361),f869(f869(f868(x99361,x99361),a852),a852),x99361),f347(f868(x99361,x99361)))),f251(x99361,x99361)))),x99364),x99362,x99363)+P85(f784(f784(f347(f868(f860(x99361),f860(x99361))),f784(f784(f251(f860(x99361),f860(x99361)),x99362),x99363)),f150(x99361,x99364)))
% 11.41/11.18 [9937]~P56(x99371,f784(f784(f9(x99371,f869(f868(x99371,x99371),a852),f869(x99371,a852)),f784(f784(f10(f869(x99371,f869(f869(f868(x99371,x99371),a852),a852)),f869(f869(f868(x99371,x99371),a852),f869(x99371,a852)),x99371),f9(x99371,f869(f868(x99371,x99371),a852),a852)),f784(f784(f10(f869(x99371,f868(x99371,x99371)),f869(x99371,f869(f869(f868(x99371,x99371),a852),a852)),x99371),f784(f10(f868(x99371,x99371),f869(f869(f868(x99371,x99371),a852),a852),x99371),f347(f868(x99371,x99371)))),f251(x99371,x99371)))),x99374),x99372,x99373)+P85(f784(f784(f347(f868(f869(x99371,a852),f869(x99371,a852))),f784(f784(f251(f869(x99371,a852),f869(x99371,a852)),x99372),x99373)),f338(x99371,x99374)))
% 11.41/11.18 [7427]~P89(x74271)+E(f784(f784(f89(x74271),f784(f113(x74271),x74272)),f784(f784(f89(x74271),f784(f113(x74271),x74273)),x74274)),f784(f784(f89(x74271),f784(f113(x74271),f784(f784(f89(a1),x74272),x74273))),x74274))
% 11.41/11.18 [7428]~P89(x74281)+E(f784(f784(f89(x74281),f784(f113(x74281),x74282)),f784(f784(f3(x74281),f784(f113(x74281),x74283)),x74284)),f784(f784(f3(x74281),f784(f113(x74281),f784(f784(f89(a1),x74282),x74283))),x74284))
% 11.41/11.18 [7429]~P89(x74291)+E(f784(f784(f90(x74291),f784(f113(x74291),x74292)),f784(f784(f90(x74291),f784(f113(x74291),x74293)),x74294)),f784(f784(f90(x74291),f784(f113(x74291),f784(f784(f90(a1),x74292),x74293))),x74294))
% 11.41/11.18 [7475]~P112(x74751)+E(f784(f157(x74751),f784(f784(f146(x74752,x74751),f784(f18(x74751,x74752),x74753)),x74754)),f784(f784(f90(x74751),f784(f109(x74751),f784(f188(f860(x74752)),x74754))),x74753))
% 11.41/11.18 [7710]E(f784(f275(x77101,f784(f784(f144(f868(a108,x77101)),x77102),x77103)),x77104),f784(f260(a108,x77101),x77102))+~P85(f784(f784(f243(a108),x77104),f784(f250(a108,x77101),x77102)))
% 11.41/11.18 [7758]~P89(x77581)+E(f784(f784(f89(x77581),f784(f113(x77581),x77582)),f784(f784(f3(x77581),x77583),f784(f113(x77581),x77584))),f784(f784(f89(x77581),f784(f113(x77581),f784(f784(f89(a1),x77582),f784(f88(a1),x77584)))),x77583))
% 11.41/11.18 [7889]E(f784(f275(x78891,x78892),f784(f784(f3(a108),x78893),f784(f250(a108,x78891),x78894))),f784(f275(x78891,f784(f784(f144(f868(a108,x78891)),x78894),x78892)),x78893))+P85(f784(f784(f243(a108),x78893),f784(f250(a108,x78891),x78894)))
% 11.41/11.18 [8317]~P85(f784(f784(f347(x83171),x83172),f784(f164(x83171),f121(x83171,x83174))))+P85(f784(f784(f347(x83171),x83172),f784(f164(x83171),f121(x83171,f784(f784(f130(x83171),x83173),x83174)))))
% 11.41/11.18 [8318]~P85(f784(f784(f347(x83181),x83182),f784(f164(x83181),f121(x83181,x83183))))+P85(f784(f784(f347(x83181),x83182),f784(f164(x83181),f121(x83181,f784(f784(f130(x83181),x83183),x83184)))))
% 11.41/11.18 [8341]E(f784(f784(f110(f869(x83411,a852)),f784(f784(f111(f869(x83411,a852)),x83412),x83413)),x83414),f784(f784(f111(f869(x83411,a852)),x83412),f784(f784(f110(f869(x83411,a852)),x83413),x83414)))+~P85(f784(f784(f242(f869(x83411,a852)),x83414),x83412))
% 11.41/11.18 [8627]~E(f784(f784(f110(f869(x86271,a852)),f784(f784(f111(f869(x86271,a852)),x86273),x86274)),x86272),f784(f784(f111(f869(x86271,a852)),x86273),f784(f784(f110(f869(x86271,a852)),x86274),x86272)))+P85(f784(f784(f242(f869(x86271,a852)),x86272),x86273))
% 11.41/11.18 [8878]~P85(f784(f784(f242(f869(x88781,a852)),x88782),f784(f784(f110(f869(x88781,a852)),x88783),x88784)))+P85(f784(f784(f242(f869(x88781,a852)),f784(f784(f3(f869(x88781,a852)),x88782),x88783)),x88784))
% 11.41/11.18 [8996]P85(f784(f784(f242(f869(x89961,a852)),x89962),f784(f784(f110(f869(x89961,a852)),x89963),x89964)))+~P85(f784(f784(f242(f869(x89961,a852)),f784(f784(f3(f869(x89961,a852)),x89962),x89963)),x89964))
% 11.41/11.18 [9075]~P79(x90751)+E(f784(f84(x90751),f784(f784(f8(x90752,x90751),f784(f784(f10(x90751,x90751,x90752),f84(x90751)),x90753)),x90754)),f784(f784(f8(x90752,x90751),f784(f784(f10(x90751,x90751,x90752),f84(x90751)),x90753)),x90754))
% 11.41/11.18 [9218]~P79(x92181)+P85(f784(f784(f242(x92181),f2(x92181)),f784(f784(f8(x92182,x92181),f784(f784(f10(x92181,x92181,x92182),f84(x92181)),x92183)),x92184)))
% 11.41/11.18 [9221]~P3(x92211)+E(f784(f157(x92211),f784(f784(f146(x92212,x92211),f784(f82(x92211,x92211,x92212,f88(x92211)),x92213)),x92214)),f784(f88(x92211),f784(f157(x92211),f784(f784(f146(x92212,x92211),x92213),x92214))))
% 11.41/11.18 [9358]~P79(x93581)+P85(f784(f784(f242(x93581),f784(f84(x93581),f784(f784(f8(x93582,x93581),x93583),x93584))),f784(f784(f8(x93582,x93581),f784(f784(f10(x93581,x93581,x93582),f84(x93581)),x93583)),x93584)))
% 11.41/11.18 [9385]~E(f784(f784(f89(a859),x93851),x93854),f784(f784(f89(a859),x93853),x93852))+P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),f784(f784(f251(a859,a859),x93851),x93852)),f784(f784(f251(a859,a859),x93853),x93854))),a118))
% 11.41/11.18 [9386]~P85(f784(f784(f243(a859),x93861),x93863))+P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),f784(f784(f251(a859,a859),x93861),x93862)),f784(f784(f251(a859,a859),x93863),x93864))),a47))
% 11.41/11.18 [9387]~P85(f784(f784(f243(a859),x93871),x93873))+P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),f784(f784(f251(a859,a859),x93871),x93872)),f784(f784(f251(a859,a859),x93873),x93874))),a79))
% 11.41/11.18 [9528]E(f784(f784(f89(a859),x95281),x95282),f784(f784(f89(a859),x95283),x95284))+~P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),f784(f784(f251(a859,a859),x95281),x95284)),f784(f784(f251(a859,a859),x95283),x95282))),a118))
% 11.41/11.18 [9575]~P85(f784(f784(f347(x95752),x95754),f784(f784(f54(x95751,f869(x95752,a852)),f249(f869(x95751,a852))),x95753)))+P85(f784(f784(f784(f54(x95751,f869(x95752,a852)),f249(f869(x95751,a852))),f784(f784(f10(f869(x95752,a852),f869(x95752,a852),x95751),f784(f9(x95752,f869(x95752,a852),a852),f347(x95752))),x95753)),x95754))
% 11.41/11.18 [9576]~P85(f784(f784(f347(x95762),x95764),f784(f784(f55(x95761,f869(x95762,a852)),f249(f869(x95761,a852))),x95763)))+P85(f784(f784(f784(f55(x95761,f869(x95762,a852)),f249(f869(x95761,a852))),f784(f784(f10(f869(x95762,a852),f869(x95762,a852),x95761),f784(f9(x95762,f869(x95762,a852),a852),f347(x95762))),x95763)),x95764))
% 11.41/11.18 [9647]~P85(f784(f64(x96471,x96472),f784(f784(f251(a1,a1),x96474),x96473)))+P85(f784(f64(f784(f88(a1),x96471),x96472),f784(f784(f251(a1,a1),f784(f784(f784(f105(a1),f784(f784(a343,x96473),f2(a1))),f784(f88(a1),x96474)),f784(f784(f3(a1),f784(f88(a1),x96474)),f87(a1)))),f784(f784(f784(f105(a1),f784(f784(a343,x96473),f2(a1))),f2(a1)),f784(f784(f3(a1),x96472),x96473)))))
% 11.41/11.18 [9656]P85(f784(f784(f347(x96561),x96562),f784(f784(f54(x96563,f869(x96561,a852)),f249(f869(x96563,a852))),x96564)))+~P85(f784(f784(f784(f54(x96563,f869(x96561,a852)),f249(f869(x96563,a852))),f784(f784(f10(f869(x96561,a852),f869(x96561,a852),x96563),f784(f9(x96561,f869(x96561,a852),a852),f347(x96561))),x96564)),x96562))
% 11.41/11.18 [9657]P85(f784(f784(f347(x96571),x96572),f784(f784(f55(x96573,f869(x96571,a852)),f249(f869(x96573,a852))),x96574)))+~P85(f784(f784(f784(f55(x96573,f869(x96571,a852)),f249(f869(x96573,a852))),f784(f784(f10(f869(x96571,a852),f869(x96571,a852),x96573),f784(f9(x96571,f869(x96571,a852),a852),f347(x96571))),x96574)),x96572))
% 11.41/11.18 [9668]E(f784(f784(f54(a859,f869(x96681,a852)),f249(f869(a859,a852))),x96682),f784(f784(f54(a859,f869(x96681,a852)),f249(f869(a859,a852))),x96683))+~E(f784(f784(f54(a859,f869(x96681,a852)),f784(f304(a859,f2(a859)),f412(x96682,x96684,x96683,x96681))),x96683),f784(f784(f54(a859,f869(x96681,a852)),f784(f304(a859,f2(a859)),f784(f784(f89(a859),f412(x96682,x96684,x96683,x96681)),x96684))),x96682))
% 11.41/11.18 [9999]~P85(f784(f784(f242(f869(f868(x99991,x99992),a852)),x99993),x99994))+P85(f784(f784(f242(f869(x99991,f869(x99992,a852))),f784(f784(f9(x99991,f869(f868(x99991,x99992),a852),f869(x99992,a852)),f784(f784(f10(f869(x99992,f869(f869(f868(x99991,x99992),a852),a852)),f869(f869(f868(x99991,x99992),a852),f869(x99992,a852)),x99991),f9(x99992,f869(f868(x99991,x99992),a852),a852)),f784(f784(f10(f869(x99992,f868(x99991,x99992)),f869(x99992,f869(f869(f868(x99991,x99992),a852),a852)),x99991),f784(f10(f868(x99991,x99992),f869(f869(f868(x99991,x99992),a852),a852),x99992),f347(f868(x99991,x99992)))),f251(x99991,x99992)))),x99993)),f784(f784(f9(x99991,f869(f868(x99991,x99992),a852),f869(x99992,a852)),f784(f784(f10(f869(x99992,f869(f869(f868(x99991,x99992),a852),a852)),f869(f869(f868(x99991,x99992),a852),f869(x99992,a852)),x99991),f9(x99992,f869(f868(x99991,x99992),a852),a852)),f784(f784(f10(f869(x99992,f868(x99991,x99992)),f869(x99992,f869(f869(f868(x99991,x99992),a852),a852)),x99991),f784(f10(f868(x99991,x99992),f869(f869(f868(x99991,x99992),a852),a852),x99992),f347(f868(x99991,x99992)))),f251(x99991,x99992)))),x99994)))
% 11.41/11.18 [10014]P85(f784(f784(f242(f869(f868(x100141,x100142),a852)),x100143),x100144))+~P85(f784(f784(f242(f869(x100141,f869(x100142,a852))),f784(f784(f9(x100141,f869(f868(x100141,x100142),a852),f869(x100142,a852)),f784(f784(f10(f869(x100142,f869(f869(f868(x100141,x100142),a852),a852)),f869(f869(f868(x100141,x100142),a852),f869(x100142,a852)),x100141),f9(x100142,f869(f868(x100141,x100142),a852),a852)),f784(f784(f10(f869(x100142,f868(x100141,x100142)),f869(x100142,f869(f869(f868(x100141,x100142),a852),a852)),x100141),f784(f10(f868(x100141,x100142),f869(f869(f868(x100141,x100142),a852),a852),x100142),f347(f868(x100141,x100142)))),f251(x100141,x100142)))),x100143)),f784(f784(f9(x100141,f869(f868(x100141,x100142),a852),f869(x100142,a852)),f784(f784(f10(f869(x100142,f869(f869(f868(x100141,x100142),a852),a852)),f869(f869(f868(x100141,x100142),a852),f869(x100142,a852)),x100141),f9(x100142,f869(f868(x100141,x100142),a852),a852)),f784(f784(f10(f869(x100142,f868(x100141,x100142)),f869(x100142,f869(f869(f868(x100141,x100142),a852),a852)),x100141),f784(f10(f868(x100141,x100142),f869(f869(f868(x100141,x100142),a852),a852),x100142),f347(f868(x100141,x100142)))),f251(x100141,x100142)))),x100144)))
% 11.41/11.18 [9119]~P85(f784(f784(f347(f868(x91191,x91191)),x91192),f310(x91191,x91194)))+P85(f784(f784(f347(f868(x91191,x91191)),x91192),f310(x91191,f784(f784(f110(f869(f868(x91191,x91191),a852)),x91193),x91194))))
% 11.41/11.18 [9120]~P85(f784(f784(f347(f868(x91201,x91201)),x91202),f310(x91201,x91203)))+P85(f784(f784(f347(f868(x91201,x91201)),x91202),f310(x91201,f784(f784(f110(f869(f868(x91201,x91201),a852)),x91203),x91204))))
% 11.41/11.18 [9448]~E(f784(f164(x94481),x94484),f175(x94481,x94482,x94483))+E(f172(x94481,x94482,f784(f784(f146(x94481,f868(x94481,x94482)),f784(f784(f20(x94481,x94482,f868(x94481,x94482)),f251(x94481,x94482)),f784(f784(f10(f864(x94482),x94482,x94481),f241(x94482)),x94483))),x94484)),x94483)
% 11.41/11.18 [9749]~P85(f784(f784(f243(a859),f784(f784(f89(a859),x97491),x97494)),f784(f784(f89(a859),x97493),x97492)))+P85(f784(f784(f243(a1),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x97491),x97492)),f187(f869(f868(a859,a859),a852)))))),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x97493),x97494)),f187(f869(f868(a859,a859),a852)))))))
% 11.41/11.18 [9750]~P85(f784(f784(f242(a859),f784(f784(f89(a859),x97501),x97504)),f784(f784(f89(a859),x97503),x97502)))+P85(f784(f784(f242(a1),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x97501),x97502)),f187(f869(f868(a859,a859),a852)))))),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x97503),x97504)),f187(f869(f868(a859,a859),a852)))))))
% 11.41/11.18 [9841]P85(f784(f784(f243(a859),f784(f784(f89(a859),x98411),x98412)),f784(f784(f89(a859),x98413),x98414)))+~P85(f784(f784(f243(a1),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x98411),x98414)),f187(f869(f868(a859,a859),a852)))))),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x98413),x98412)),f187(f869(f868(a859,a859),a852)))))))
% 11.41/11.18 [9842]P85(f784(f784(f242(a859),f784(f784(f89(a859),x98421),x98422)),f784(f784(f89(a859),x98423),x98424)))+~P85(f784(f784(f242(a1),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x98421),x98424)),f187(f869(f868(a859,a859),a852)))))),f784(a98,f784(f287(f868(a859,a859),f868(a859,a859),a118),f784(f784(f312(f868(a859,a859)),f784(f784(f251(a859,a859),x98423),x98422)),f187(f869(f868(a859,a859),a852)))))))
% 11.41/11.18 [9888]P85(f784(f784(f242(f869(x98881,a852)),f784(f784(f54(a859,f869(x98881,a852)),f249(f869(a859,a852))),x98882)),f784(f784(f54(a859,f869(x98881,a852)),f249(f869(a859,a852))),x98883)))+~P85(f784(f784(f242(f869(x98881,a852)),f784(f784(f54(a859,f869(x98881,a852)),f784(f304(a859,f2(a859)),f410(x98883,x98884,x98882,x98881))),x98882)),f784(f784(f54(a859,f869(x98881,a852)),f784(f304(a859,f2(a859)),f784(f784(f89(a859),f410(x98883,x98884,x98882,x98881)),x98884))),x98883)))
% 11.41/11.18 [9939]P85(f784(f784(f242(a108),x99394),f2(a108)))+E(f784(f784(f263(f868(a108,a108),f868(x99391,f869(a863,a851)),f868(a108,a108),f868(f869(a108,f869(a852,f864(f861(x99391)))),f868(a108,a108))),f784(x99392,x99393)),f784(f784(f10(f869(f869(a108,f869(a852,f864(f861(x99391)))),f869(f868(a108,a108),f868(f869(a108,f869(a852,f864(f861(x99391)))),f868(a108,a108)))),f869(f868(a108,a108),f868(f869(a108,f869(a852,f864(f861(x99391)))),f868(a108,a108))),f868(x99391,f869(a863,a851))),f784(f263(f868(a108,a108),f869(a108,f869(a852,f864(f861(x99391)))),f868(a108,a108),f868(f869(a108,f869(a852,f864(f861(x99391)))),f868(a108,a108))),f282(x99391,x99392,f784(f784(f3(a108),x99394),f87(a108)),x99393))),f784(f784(f10(f869(f869(a108,f869(a852,f864(f861(x99391)))),f869(a108,f869(a852,f864(f861(x99391))))),f869(f869(a108,f869(a852,f864(f861(x99391)))),f869(f868(a108,a108),f868(f869(a108,f869(a852,f864(f861(x99391)))),f868(a108,a108)))),f868(x99391,f869(a863,a851))),f784(f10(f869(a108,f869(a852,f864(f861(x99391)))),f869(f868(a108,a108),f868(f869(a108,f869(a852,f864(f861(x99391)))),f868(a108,a108))),f869(a108,f869(a852,f864(f861(x99391))))),f251(f869(a108,f869(a852,f864(f861(x99391)))),f868(a108,a108)))),f784(f784(f10(f869(a108,f869(a852,f864(f861(x99391)))),f869(f869(a108,f869(a852,f864(f861(x99391)))),f869(a108,f869(a852,f864(f861(x99391))))),f868(x99391,f869(a863,a851))),f59(x99391)),f784(f784(f10(x99391,f869(a108,f869(a852,f864(f861(x99391)))),f868(x99391,f869(a863,a851))),f57(x99391)),f250(x99391,f869(a863,a851))))))),f282(x99391,x99392,x99394,x99393))
% 11.41/11.18 [9990]~P85(f784(f784(f347(x99902),x99904),f784(f269(x99901,x99902),x99903)))+P85(f784(f257(x99901,x99902,f784(f784(f9(x99901,f869(f868(x99901,x99902),a852),f869(x99902,a852)),f784(f784(f10(f869(x99902,f869(f869(f868(x99901,x99902),a852),a852)),f869(f869(f868(x99901,x99902),a852),f869(x99902,a852)),x99901),f9(x99902,f869(f868(x99901,x99902),a852),a852)),f784(f784(f10(f869(x99902,f868(x99901,x99902)),f869(x99902,f869(f869(f868(x99901,x99902),a852),a852)),x99901),f784(f10(f868(x99901,x99902),f869(f869(f868(x99901,x99902),a852),a852),x99902),f347(f868(x99901,x99902)))),f251(x99901,x99902)))),x99903)),x99904))
% 11.41/11.18 [9991]~P85(f784(f784(f347(x99911),x99914),f784(f271(x99911,x99912),x99913)))+P85(f784(f256(x99911,x99912,f784(f784(f9(x99911,f869(f868(x99911,x99912),a852),f869(x99912,a852)),f784(f784(f10(f869(x99912,f869(f869(f868(x99911,x99912),a852),a852)),f869(f869(f868(x99911,x99912),a852),f869(x99912,a852)),x99911),f9(x99912,f869(f868(x99911,x99912),a852),a852)),f784(f784(f10(f869(x99912,f868(x99911,x99912)),f869(x99912,f869(f869(f868(x99911,x99912),a852),a852)),x99911),f784(f10(f868(x99911,x99912),f869(f869(f868(x99911,x99912),a852),a852),x99912),f347(f868(x99911,x99912)))),f251(x99911,x99912)))),x99913)),x99914))
% 11.41/11.18 [10002]P85(f784(f784(f347(x100021),x100022),f784(f269(x100023,x100021),x100024)))+~P85(f784(f257(x100023,x100021,f784(f784(f9(x100023,f869(f868(x100023,x100021),a852),f869(x100021,a852)),f784(f784(f10(f869(x100021,f869(f869(f868(x100023,x100021),a852),a852)),f869(f869(f868(x100023,x100021),a852),f869(x100021,a852)),x100023),f9(x100021,f869(f868(x100023,x100021),a852),a852)),f784(f784(f10(f869(x100021,f868(x100023,x100021)),f869(x100021,f869(f869(f868(x100023,x100021),a852),a852)),x100023),f784(f10(f868(x100023,x100021),f869(f869(f868(x100023,x100021),a852),a852),x100021),f347(f868(x100023,x100021)))),f251(x100023,x100021)))),x100024)),x100022))
% 11.41/11.18 [10003]P85(f784(f784(f347(x100031),x100032),f784(f271(x100031,x100033),x100034)))+~P85(f784(f256(x100031,x100033,f784(f784(f9(x100031,f869(f868(x100031,x100033),a852),f869(x100033,a852)),f784(f784(f10(f869(x100033,f869(f869(f868(x100031,x100033),a852),a852)),f869(f869(f868(x100031,x100033),a852),f869(x100033,a852)),x100031),f9(x100033,f869(f868(x100031,x100033),a852),a852)),f784(f784(f10(f869(x100033,f868(x100031,x100033)),f869(x100033,f869(f869(f868(x100031,x100033),a852),a852)),x100031),f784(f10(f868(x100031,x100033),f869(f869(f868(x100031,x100033),a852),a852),x100033),f347(f868(x100031,x100033)))),f251(x100031,x100033)))),x100034)),x100032))
% 11.41/11.18 [9763]~P86(x97631)+E(f784(f784(f90(x97631),f784(f784(f89(x97631),f87(x97631)),f87(x97631))),f784(f784(f8(a859,x97631),f784(f784(f10(x97631,x97631,a859),f784(f89(x97631),x97632)),f784(f784(f9(a859,x97631,x97631),f784(f784(f10(x97631,f869(x97631,x97631),a859),f90(x97631)),f109(x97631))),x97633))),f784(f267(a859),x97634))),f784(f784(f90(x97631),f784(f109(x97631),x97634)),f784(f784(f89(x97631),x97632),f784(f784(f89(x97631),x97632),f784(f784(f90(x97631),f784(f109(x97631),f784(f784(f3(a859),x97634),f87(a859)))),x97633)))))
% 11.41/11.18 [9909]P85(f784(x99091,f597(x99092,x99093,x99094,x99091)))+P35(x99092,f784(f266(f868(x99092,x99092)),f784(f261(x99092,x99092,a852),f784(f784(f10(f869(x99092,a852),f869(x99092,a852),x99092),f784(f20(x99092,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99092),a344),x99091))),f784(f784(f9(x99092,f869(x99092,x99092),f869(x99092,a852)),f784(f784(f10(f869(x99092,a852),f869(f869(x99092,x99092),f869(x99092,a852)),x99092),f10(x99092,a852,x99092)),a343)),x99093)))))
% 11.41/11.18 [9921]~P85(f784(f784(f243(a859),f784(x99214,f784(x99213,f597(x99211,x99213,x99214,x99212)))),f784(x99214,f597(x99211,x99213,x99214,x99212))))+P35(x99211,f784(f266(f868(x99211,x99211)),f784(f261(x99211,x99211,a852),f784(f784(f10(f869(x99211,a852),f869(x99211,a852),x99211),f784(f20(x99211,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99211),a344),x99212))),f784(f784(f9(x99211,f869(x99211,x99211),f869(x99211,a852)),f784(f784(f10(f869(x99211,a852),f869(f869(x99211,x99211),f869(x99211,a852)),x99211),f10(x99211,a852,x99211)),a343)),x99213)))))
% 11.41/11.18 [10026]~P85(f784(f784(f347(f868(x100261,x100261)),f784(f784(f251(x100261,x100261),x100263),x100264)),f784(f784(f110(f869(f868(x100261,x100261),a852)),x100262),f310(x100261,f187(f869(f868(x100261,x100261),a852))))))+P85(f784(f784(f784(f784(f110(f869(x100261,f869(x100261,a852))),f784(f784(f9(x100261,f869(f868(x100261,x100261),a852),f869(x100261,a852)),f784(f784(f10(f869(x100261,f869(f869(f868(x100261,x100261),a852),a852)),f869(f869(f868(x100261,x100261),a852),f869(x100261,a852)),x100261),f9(x100261,f869(f868(x100261,x100261),a852),a852)),f784(f784(f10(f869(x100261,f868(x100261,x100261)),f869(x100261,f869(f869(f868(x100261,x100261),a852),a852)),x100261),f784(f10(f868(x100261,x100261),f869(f869(f868(x100261,x100261),a852),a852),x100261),f347(f868(x100261,x100261)))),f251(x100261,x100261)))),x100262)),a343),x100263),x100264))
% 11.41/11.18 [10034]P85(f784(f784(f347(f868(x100341,x100341)),f784(f784(f251(x100341,x100341),x100342),x100343)),f784(f784(f110(f869(f868(x100341,x100341),a852)),x100344),f310(x100341,f187(f869(f868(x100341,x100341),a852))))))+~P85(f784(f784(f784(f784(f110(f869(x100341,f869(x100341,a852))),f784(f784(f9(x100341,f869(f868(x100341,x100341),a852),f869(x100341,a852)),f784(f784(f10(f869(x100341,f869(f869(f868(x100341,x100341),a852),a852)),f869(f869(f868(x100341,x100341),a852),f869(x100341,a852)),x100341),f9(x100341,f869(f868(x100341,x100341),a852),a852)),f784(f784(f10(f869(x100341,f868(x100341,x100341)),f869(x100341,f869(f869(f868(x100341,x100341),a852),a852)),x100341),f784(f10(f868(x100341,x100341),f869(f869(f868(x100341,x100341),a852),a852),x100341),f347(f868(x100341,x100341)))),f251(x100341,x100341)))),x100344)),a343),x100342),x100343))
% 11.41/11.18 [9987]E(f784(f784(f144(f860(x99871)),f784(f784(f144(x99871),x99872),f784(f136(f860(x99871),f860(x99871),f130(x99871),f120(x99871)),f784(f784(f146(f860(x99871),f860(x99871)),f148(f860(x99871),x99871,f120(x99871),f784(f784(f10(f860(x99871),f869(f860(x99871),f860(x99871)),x99871),f18(f860(x99871),f860(x99871))),f784(f784(f9(x99871,f860(x99871),f860(x99871)),f144(x99871)),f120(x99871))))),x99873)))),f170(x99871,f784(f784(f144(f860(x99871)),x99874),f784(f136(f860(f860(x99871)),f860(f860(x99871)),f130(f860(x99871)),f120(f860(x99871))),f784(f784(f146(f860(x99871),f860(f860(x99871))),f148(f860(f860(x99871)),x99871,f120(f860(x99871)),f784(f18(f869(f860(x99871),f860(f860(x99871))),x99871),f784(f784(f9(f860(x99871),f860(f860(x99871)),f860(f860(x99871))),f144(f860(x99871))),f120(f860(x99871)))))),x99873))))),f170(x99871,f784(f784(f144(f860(x99871)),f784(f784(f144(x99871),x99872),x99874)),x99873)))+~P85(f784(f334(f860(f860(x99871)),f171(x99871)),f784(f784(f144(f860(x99871)),f784(f784(f144(x99871),x99872),x99874)),x99873)))
% 11.41/11.18 [10025]~P85(f784(f71(x100252),f784(f266(x100252),x100254)))+P85(f784(f71(x100251),f784(f266(x100251),f784(f784(f10(f869(x100252,a852),a852,x100251),f96(x100252)),f784(f784(f9(x100251,f869(x100252,a852),f869(x100252,a852)),f784(f784(f10(f869(x100252,f869(a852,a852)),f869(f869(x100252,a852),f869(x100252,a852)),x100251),f20(x100252,a852,a852)),f784(f784(f10(f869(x100252,a852),f869(x100252,f869(a852,a852)),x100251),f784(f10(a852,f869(a852,a852),x100252),a344)),f784(f784(f9(x100251,f869(x100252,x100251),f869(x100252,a852)),f784(f784(f10(f869(x100251,a852),f869(f869(x100252,x100251),f869(x100252,a852)),x100251),f10(x100251,a852,x100252)),a343)),x100253)))),x100254)))))
% 11.41/11.18 [7182]E(x71821,x71822)+~E(f329(x71823,x71824,x71825,x71821),f329(x71823,x71824,x71825,x71822))
% 11.41/11.18 [7183]E(x71831,x71832)+~E(f330(x71833,x71834,x71835,x71831),f330(x71833,x71834,x71835,x71832))
% 11.41/11.18 [8990]~P38(f38(x89901,x89905),x89902,x89903,x89904)+P38(x89901,x89902,x89903,f796(x89904,x89903,x89902,x89905,x89901))
% 11.41/11.18 [8991]~P38(f38(x89911,x89915),x89912,x89913,x89914)+P38(x89911,x89912,x89913,f821(x89914,x89913,x89912,x89915,x89911))
% 11.41/11.18 [8992]~P38(f38(x89925,x89921),x89924,x89923,x89922)+P38(x89921,f796(x89922,x89923,x89924,x89921,x89925),x89923,x89922)
% 11.41/11.18 [8993]~P38(f38(x89935,x89931),x89934,x89933,x89932)+P38(x89931,f821(x89932,x89933,x89934,x89931,x89935),x89933,x89932)
% 11.41/11.18 [5541]E(f784(f784(f312(x55411),x55412),f175(x55411,x55413,x55414)),f175(x55411,x55413,x55414))+~E(f784(x55414,x55412),f784(f237(x55413),x55415))
% 11.41/11.18 [5953]P85(f784(f257(x59531,x59532,x59533),x59534))+~P85(f784(f784(x59533,x59535),x59534))
% 11.41/11.18 [5954]P85(f784(f257(x59541,x59542,x59543),x59544))+~P85(f784(f784(x59543,x59545),x59544))
% 11.41/11.18 [5955]P85(f784(f256(x59551,x59552,x59553),x59554))+~P85(f784(f784(x59553,x59554),x59555))
% 11.41/11.18 [5956]P85(f784(f256(x59561,x59562,x59563),x59564))+~P85(f784(f784(x59563,x59564),x59565))
% 11.41/11.18 [5959]~E(f784(x59594,x59592),f784(f237(x59593),x59595))+P85(f784(f784(f347(x59591),x59592),f175(x59591,x59593,x59594)))
% 11.41/11.18 [5960]~E(f784(x59604,x59605),f784(f237(x59601),x59602))+P85(f784(f784(f347(x59601),x59602),f177(x59603,x59601,x59604)))
% 11.41/11.18 [6440]~E(x64405,f2(a108))+E(f784(f203(x64401,x64402,x64403,x64404),x64405),f122(x64402))
% 11.41/11.18 [6441]~E(x64415,f2(a108))+E(f784(f201(x64411,x64412,x64413,x64414),x64415),f129(x64412))
% 11.41/11.18 [6536]~P38(f30(x65363,x65364),x65362,x65365,x65361)+E(x65361,f784(f784(f784(a196,x65362),x65363),f784(x65364,x65362)))
% 11.41/11.18 [6581]~E(x65813,f2(a108))+E(f784(f278(x65811,x65812,x65813,x65814),x65815),f784(f251(x65811,x65812),x65815))
% 11.41/11.18 [6658]~E(f784(x66584,x66585),f190(x66582))+E(f784(f239(f864(x66581),x66582,f190(x66581),x66583),f784(x66584,x66585)),f190(x66581))
% 11.41/11.18 [6659]~E(f784(x66594,x66595),f190(x66592))+E(f784(f239(f864(x66591),x66592,f190(x66591),x66593),f784(x66594,x66595)),f190(x66591))
% 11.41/11.18 [7305]E(f784(x73051,x73052),f190(x73053))+~E(f784(f176(x73054,x73053,x73055,x73051),x73052),f190(x73053))
% 11.41/11.18 [7306]E(f784(x73061,x73062),f190(x73063))+~E(f784(f176(x73064,x73063,x73061,x73065),x73062),f190(x73063))
% 11.41/11.18 [7346]E(f784(f176(x73461,x73462,x73463,x73464),x73465),f784(x73463,x73465))+P85(f784(f784(f347(x73461),x73465),f175(x73461,x73462,x73464)))
% 11.41/11.18 [7347]E(f784(f176(x73471,x73472,x73473,x73474),x73475),f784(x73474,x73475))+P85(f784(f784(f347(x73471),x73475),f175(x73471,x73472,x73473)))
% 11.41/11.18 [7672]~P21(x76724,x76721,x76722,x76725)+E(f784(f82(x76721,x76721,x76721,f784(x76722,x76723)),f784(x76722,x76723)),f784(x76722,x76723))
% 11.41/11.18 [7714]E(f784(f176(x77141,x77142,x77143,x77144),x77145),f784(x77144,x77145))+~P85(f784(f784(f347(x77141),x77145),f175(x77141,x77142,x77144)))
% 11.41/11.18 [8059]~P17(x80595,x80591,x80592)+E(f784(f82(x80591,x80591,x80591,f784(x80592,x80593)),f784(x80592,x80594)),f784(f82(x80591,x80591,x80591,f784(x80592,x80594)),f784(x80592,x80593)))
% 11.41/11.18 [8380]P85(f784(f784(f347(f868(x83801,x83801)),f784(f784(f251(x83801,x83801),x83802),x83803)),f340(x83801,x83804,x83805)))+~P85(f784(f784(f243(a859),f784(x83804,x83802)),f784(x83804,x83803)))
% 11.41/11.18 [8478]~P85(f784(f784(f347(x84784),x84783),f292(x84784,x84781,x84782,x84785)))+P85(f784(f784(x84781,x84782),x84783))
% 11.41/11.18 [8479]~P85(f784(f784(f347(x84794),x84793),f301(x84794,x84791,x84792,x84795)))+P85(f784(f784(x84791,x84792),x84793))
% 11.41/11.18 [8480]~P85(f784(f784(f347(x84804),x84802),f292(x84804,x84801,x84805,x84803)))+P85(f784(f784(x84801,x84802),x84803))
% 11.41/11.18 [8481]~P85(f784(f784(f347(x84814),x84812),f301(x84814,x84811,x84815,x84813)))+P85(f784(f784(x84811,x84812),x84813))
% 11.41/11.18 [8604]~P54(x86042,x86041,x86045,x86043,x86044)+E(f784(f313(x86041,x86042,x86043),x86044),f249(f869(x86042,a852)))
% 11.41/11.18 [9376]P85(f784(f784(f347(f868(f860(x93761),f860(x93761))),f784(f784(f251(f860(x93761),f860(x93761)),f784(f784(f144(x93761),x93762),x93763)),f784(f784(f144(x93761),x93762),x93764))),f149(x93761,x93765)))+~P85(f784(f784(f347(f868(f860(x93761),f860(x93761))),f784(f784(f251(f860(x93761),f860(x93761)),x93763),x93764)),f149(x93761,x93765)))
% 11.41/11.18 [9377]P85(f784(f784(f347(f868(f860(x93771),f860(x93771))),f784(f784(f251(f860(x93771),f860(x93771)),f784(f784(f130(x93771),x93772),x93773)),f784(f784(f130(x93771),x93772),x93774))),f141(x93771,x93775)))+~P85(f784(f784(f347(f868(f860(x93771),f860(x93771))),f784(f784(f251(f860(x93771),f860(x93771)),x93773),x93774)),f141(x93771,x93775)))
% 11.41/11.18 [9556]E(f784(f784(f144(x95561),f729(x95562,x95563,x95564,x95565,x95561)),f732(x95562,x95563,x95564,x95565,x95561)),x95565)+~P85(f784(f784(f347(f868(f860(x95561),f860(x95561))),f784(f784(f251(f860(x95561),f860(x95561)),x95565),f784(f784(f144(x95561),x95564),x95563))),f150(x95561,x95562)))
% 11.41/11.18 [9585]E(f784(f784(f144(x95851),f730(x95852,x95853,x95854,x95855,x95851)),f731(x95852,x95853,x95854,x95855,x95851)),x95853)+~P85(f784(f784(f347(f868(f860(x95851),f860(x95851))),f784(f784(f251(f860(x95851),f860(x95851)),f784(f784(f144(x95851),x95855),x95854)),x95853)),f150(x95851,x95852)))
% 11.41/11.18 [9721]~P85(f784(f784(f347(f868(f860(x97211),f860(x97211))),f784(f784(f251(f860(x97211),f860(x97211)),f784(f784(f144(x97211),x97215),x97212)),x97214)),f150(x97211,x97213)))+P85(f784(f784(f347(f868(f860(x97211),f860(x97211))),f784(f784(f251(f860(x97211),f860(x97211)),x97212),f731(x97213,x97214,x97212,x97215,x97211))),f150(x97211,x97213)))
% 11.41/11.18 [9806]~P85(f784(f784(f347(f868(f860(x98061),f860(x98061))),f784(f784(f251(f860(x98061),f860(x98061)),x98065),f784(f784(f144(x98061),x98064),x98063))),f150(x98061,x98062)))+P85(f784(f784(f347(f868(f860(x98061),f860(x98061))),f784(f784(f251(f860(x98061),f860(x98061)),f732(x98062,x98063,x98064,x98065,x98061)),x98063)),f150(x98061,x98062)))
% 11.41/11.18 [9981]P85(f784(f784(f347(f868(x99811,x99811)),f784(f784(f251(x99811,x99811),f784(x99812,f784(f784(f89(a859),x99813),x99814))),f784(x99812,x99813))),f310(x99811,x99815)))+~P85(f784(f784(f347(f868(x99811,x99811)),f784(f784(f251(x99811,x99811),f784(x99812,f784(a160,f648(x99814,x99813,x99815,x99812,x99811)))),f784(x99812,f648(x99814,x99813,x99815,x99812,x99811)))),f310(x99811,x99815)))
% 11.41/11.18 [10005]E(x100051,f2(a108))+E(f784(f239(f868(f860(x100052),x100053),f868(x100052,x100053),f784(f784(f251(f860(x100052),x100053),f120(x100052)),x100054),f784(f261(x100052,x100053,f868(f860(x100052),x100053)),f784(f784(f9(x100052,f869(x100053,f868(f860(x100052),x100053)),f869(x100053,f868(f860(x100052),x100053))),f784(f784(f10(f869(f868(f860(x100052),x100053),f868(f860(x100052),x100053)),f869(f869(x100053,f868(f860(x100052),x100053)),f869(x100053,f868(f860(x100052),x100053))),x100052),f10(f868(f860(x100052),x100053),f868(f860(x100052),x100053),x100053)),f784(f784(f10(f869(f860(x100052),f869(x100053,f868(f860(x100052),x100053))),f869(f868(f860(x100052),x100053),f868(f860(x100052),x100053)),x100052),f261(f860(x100052),x100053,f868(f860(x100052),x100053))),f784(f784(f10(f869(f860(x100052),f860(x100052)),f869(f860(x100052),f869(x100053,f868(f860(x100052),x100053))),x100052),f784(f10(f860(x100052),f869(x100053,f868(f860(x100052),x100053)),f860(x100052)),f251(f860(x100052),x100053))),f144(x100052))))),f124(x100053,x100052,x100055,f784(f784(f3(a108),x100051),f87(a108)))))),f784(x100055,x100054)),f784(f124(x100053,x100052,x100055,x100051),x100054))
% 11.41/11.18 [5145]E(x51451,x51452)+~E(f784(f784(f144(x51453),x51454),x51451),f784(f784(f144(x51453),x51455),x51452))
% 11.41/11.18 [5146]E(x51461,x51462)+~E(f784(f784(f144(x51463),x51461),x51464),f784(f784(f144(x51463),x51462),x51465))
% 11.41/11.18 [5339]~E(f784(f784(f133(x53391),x53393),x53392),f784(f784(f144(x53391),x53394),x53395))+E(f784(f784(f155(x53391),x53392),x53393),x53394)
% 11.41/11.18 [5472]~P16(x54724,x54725,x54721)+E(f784(f784(x54721,x54722),f784(f784(x54721,x54722),x54723)),f784(f784(x54721,x54722),x54723))
% 11.41/11.18 [5837]~E(f784(x58373,x58374),f784(f237(x58372),x58375))+E(f784(f784(f784(f81(x58371,f864(x58372)),x58373),x58374),f784(f237(x58372),x58375)),x58373)
% 11.41/11.18 [6085]~P101(x60852)+~E(f784(f784(f142(x60851,x60852,x60853),x60854),x60855),f120(x60851))
% 11.41/11.18 [6482]E(x64821,x64822)+~E(f784(f784(f130(x64823),x64824),f784(f784(f144(x64823),x64821),f120(x64823))),f784(f784(f130(x64823),x64825),f784(f784(f144(x64823),x64822),f120(x64823))))
% 11.41/11.18 [6483]E(x64831,x64832)+~E(f784(f784(f130(x64833),x64831),f784(f784(f144(x64833),x64834),f120(x64833))),f784(f784(f130(x64833),x64832),f784(f784(f144(x64833),x64835),f120(x64833))))
% 11.41/11.18 [6741]E(f784(f179(x67411,x67412,x67413,x67414),x67415),f190(x67412))+P85(f784(f784(f347(x67411),x67415),x67414))
% 11.41/11.18 [6742]E(f784(f179(x67421,x67422,x67423,x67424),x67425),f190(x67422))+P85(f784(f784(f347(x67421),x67425),x67424))
% 11.41/11.18 [6811]E(f784(f784(f312(x68111),f784(x68112,x68113)),f784(f313(x68114,x68111,x68112),x68115)),f784(f313(x68114,x68111,x68112),x68115))+~P85(f784(f784(f347(x68114),x68113),x68115))
% 11.41/11.18 [6820]~P85(f784(x68204,f784(x68203,x68205)))+P85(f784(f784(f315(x68201,x68202,x68203),x68204),x68205))
% 11.41/11.18 [6825]~E(x68254,f2(a108))+E(f784(f124(x68251,x68252,x68253,x68254),x68255),f784(f784(f251(f860(x68252),x68251),f120(x68252)),x68255))
% 11.41/11.18 [6918]~E(f784(f313(x69181,x69182,x69183),x69184),x69185)+E(f784(f313(f869(x69181,a852),f869(x69182,a852),f313(x69181,x69182,x69183)),f784(f311(x69181),x69184)),f784(f311(x69182),x69185))
% 11.41/11.18 [6947]E(f784(f179(x69471,x69472,x69473,x69474),x69475),f784(x69473,x69475))+~P85(f784(f784(f347(x69471),x69475),x69474))
% 11.41/11.18 [6948]E(f784(f179(x69481,x69482,x69483,x69484),x69485),f784(x69483,x69485))+~P85(f784(f784(f347(x69481),x69485),x69484))
% 11.41/11.18 [7262]P26(x72621,x72622,x72623,x72624)+~P26(x72621,x72622,x72623,f784(f784(f312(x72621),x72625),x72624))
% 11.41/11.18 [7333]P85(f784(x73331,x73332))+~P85(f784(f784(f101(x73333,x73334,x73331),x73335),x73332))
% 11.41/11.18 [7384]~P85(f784(f784(f347(x73844),x73843),x73845))+P85(f784(f784(f347(x73841),f784(x73842,x73843)),f784(f313(x73844,x73841,x73842),x73845)))
% 11.41/11.18 [7435]P85(f784(x74351,f784(x74352,x74353)))+~P85(f784(f784(f315(x74354,x74355,x74352),x74351),x74353))
% 11.41/11.18 [7436]P85(f784(f784(x74361,x74362),x74363))+~P85(f784(f784(f101(x74364,x74361,x74365),x74362),x74363))
% 11.41/11.18 [7504]~P85(f784(f784(f347(x75043),f784(x75044,x75042)),x75045))+P85(f784(f784(f347(x75041),x75042),f784(f315(x75041,x75043,x75044),x75045)))
% 11.41/11.18 [7505]~P85(f784(f784(f347(x75053),f784(x75054,x75052)),x75055))+P85(f784(f784(f347(x75051),x75052),f784(f315(x75051,x75053,x75054),x75055)))
% 11.41/11.18 [7902]~P85(f784(f784(f347(x79025),x79023),f784(f315(x79025,x79021,x79022),x79024)))+P85(f784(f784(f347(x79021),f784(x79022,x79023)),x79024))
% 11.41/11.18 [7903]~P85(f784(f784(f347(x79035),x79033),f784(f315(x79035,x79031,x79032),x79034)))+P85(f784(f784(f347(x79031),f784(x79032,x79033)),x79034))
% 11.41/11.18 [8119]~E(x81193,f784(f784(f784(f81(x81191,f864(x81192)),f784(f18(f864(x81192),x81191),f190(x81192))),x81194),f784(f237(x81192),x81195)))+E(f175(x81191,x81192,x81193),f784(f784(f312(x81191),x81194),f187(f869(x81191,a852))))
% 11.41/11.18 [8213]E(f784(x82131,f427(x82132,x82131,x82133,x82134)),x82134)+~P85(f784(f784(f347(x82135),x82134),f784(f313(x82133,x82135,x82131),x82132)))
% 11.41/11.18 [8465]P85(f784(f784(f347(f870(x84651,x84652)),f784(f326(x84652,x84651),x84653)),f327(x84651,x84652,x84654,x84655)))+~P85(f784(f784(f347(x84652),x84653),x84655))
% 11.41/11.18 [8466]P85(f784(f784(f347(f870(x84661,x84662)),f784(f322(x84661,x84662),x84663)),f327(x84661,x84662,x84664,x84665)))+~P85(f784(f784(f347(x84661),x84663),x84664))
% 11.41/11.18 [8522]~E(x85222,f784(f784(f144(x85221),x85224),x85225))+P85(f784(f784(f347(f868(f860(x85221),f860(x85221))),f784(f784(f251(f860(x85221),f860(x85221)),f120(x85221)),x85222)),f141(x85221,x85223)))
% 11.41/11.18 [8573]P85(f784(f784(f242(f869(x85731,a852)),f784(f784(f55(x85732,f869(x85731,a852)),x85733),x85734)),f784(x85734,x85735)))+~P85(f784(f784(f347(x85732),x85735),x85733))
% 11.41/11.18 [8620]~P54(x86201,x86202,x86203,x86205,x86204)+E(f784(f313(x86201,x86202,x86203),f249(f869(x86201,a852))),x86204)
% 11.41/11.18 [8809]E(f784(f784(f784(f81(x88091,f864(x88092)),f179(x88091,x88092,x88093,x88094)),x88095),f190(x88092)),f179(x88091,x88092,x88093,x88094))+P85(f784(f784(f347(x88091),x88095),x88094))
% 11.41/11.18 [8812]E(f784(x88121,f714(x88122,x88123,x88121,x88124,x88125)),x88122)+~E(f784(f784(f206(x88125,x88124),x88121),x88123),f784(f237(x88124),x88122))
% 11.41/11.18 [8815]E(f784(f237(x88151),f714(x88152,x88153,x88154,x88155,x88151)),x88153)+~E(f784(f784(f206(x88151,x88155),x88154),x88153),f784(f237(x88155),x88152))
% 11.41/11.18 [8901]E(f784(f188(f860(x89011)),x89012),x89013)+~P85(f784(f784(f347(f868(f860(x89011),f860(x89011))),f784(f784(f251(f860(x89011),f860(x89011)),x89014),x89012)),f784(f137(x89011,x89015),x89013)))
% 11.41/11.18 [8902]E(f784(f188(f860(x89021)),x89022),x89023)+~P85(f784(f784(f347(f868(f860(x89021),f860(x89021))),f784(f784(f251(f860(x89021),f860(x89021)),x89022),x89024)),f784(f137(x89021,x89025),x89023)))
% 11.41/11.18 [8962]P85(f784(f784(f347(x89621),f427(x89622,x89623,x89621,x89624)),x89622))+~P85(f784(f784(f347(x89625),x89624),f784(f313(x89621,x89625,x89623),x89622)))
% 11.41/11.18 [9117]E(f784(f313(x91171,x91172,x91173),f376(x91174,x91173,x91171,x91175,x91172)),x91175)+~P85(f784(f784(f242(f869(x91172,a852)),x91175),f784(f313(x91171,x91172,x91173),x91174)))
% 11.41/11.18 [9349]E(f784(x93491,f544(x93492,x93491,x93493,x93494,x93495)),f784(f237(x93495),x93494))+~P85(f784(f784(f347(x93495),x93494),f177(x93493,x93495,f179(x93493,x93495,x93491,x93492))))
% 11.41/11.18 [9392]P85(f784(f784(f347(f868(f860(x93921),f860(x93921))),f784(f784(f251(f860(x93921),f860(x93921)),f784(f784(f144(x93921),x93922),x93923)),f784(f784(f144(x93921),x93922),x93924))),f310(f860(x93921),f149(x93921,x93925))))+~P85(f784(f784(f347(f868(f860(x93921),f860(x93921))),f784(f784(f251(f860(x93921),f860(x93921)),x93923),x93924)),f310(f860(x93921),f149(x93921,x93925))))
% 11.41/11.18 [9422]~E(f784(x94223,f715(x94225,x94224,x94223,x94222,x94221)),f784(x94225,f715(x94225,x94224,x94223,x94222,x94221)))+E(f784(f784(f146(x94221,x94222),x94223),x94224),f784(f784(f146(x94221,x94222),x94225),x94224))
% 11.41/11.18 [9501]E(f784(f784(f146(x95011,x95012),x95013),x95014),f784(f784(f146(x95011,x95012),x95015),x95014))+P85(f784(f784(f347(x95011),f715(x95013,x95014,x95015,x95012,x95011)),f784(f164(x95011),x95014)))
% 11.41/11.18 [9529]~P85(f784(f784(f347(x95295),x95294),f784(f287(x95291,x95295,x95293),x95292)))+P85(f784(f784(f347(x95291),f502(x95292,x95293,x95291,x95294,x95295)),x95292))
% 11.41/11.18 [9530]~P85(f784(f784(f347(x95305),x95304),f784(f287(x95301,x95305,x95303),x95302)))+P85(f784(f784(f347(x95301),f542(x95302,x95303,x95301,x95304,x95305)),x95302))
% 11.41/11.18 [9554]~P85(f784(f784(f242(f869(x95545,a852)),x95544),f784(f313(x95541,x95545,x95543),x95542)))+P85(f784(f784(f242(f869(x95541,a852)),f376(x95542,x95543,x95541,x95544,x95545)),x95542))
% 11.41/11.18 [9603]~P85(f784(f784(f347(x96035),x96034),f177(x96031,x96035,f179(x96031,x96035,x96033,x96032))))+P85(f784(f784(f347(x96031),f544(x96032,x96033,x96031,x96034,x96035)),x96032))
% 11.41/11.18 [5352]~E(f784(x53523,x53524),x53525)+E(f784(f784(f784(f81(x53521,x53522),x53523),x53524),x53525),x53523)
% 11.41/11.18 [5353]~E(f784(x53533,x53534),x53535)+E(f784(f784(f784(f81(x53531,x53532),x53533),x53534),x53535),x53533)
% 11.41/11.18 [5801]E(f784(x58011,x58012),x58013)+~E(f784(f784(f784(f81(x58014,x58015),x58011),x58012),x58013),x58011)
% 11.41/11.18 [5836]~P29(x58365,x58361)+E(f784(f784(x58361,f784(f784(x58361,x58362),x58363)),x58364),f784(f784(x58361,x58362),f784(f784(x58361,x58363),x58364)))
% 11.41/11.18 [5891]E(x58911,x58912)+~E(f784(f260(x58913,x58914),f784(f784(f251(x58913,x58914),x58915),x58911)),x58912)
% 11.41/11.18 [5892]E(x58921,x58922)+~E(f784(f250(x58923,x58924),f784(f784(f251(x58923,x58924),x58921),x58925)),x58922)
% 11.41/11.18 [6569]E(f784(f313(x65691,x65692,f784(f18(x65692,x65691),x65693)),x65694),f784(f784(f312(x65692),x65693),f187(f869(x65692,a852))))+~P85(f784(f784(f347(x65691),x65695),x65694))
% 11.41/11.18 [6642]E(f784(f784(f110(f869(x66421,a852)),f784(f164(x66421),x66422)),f784(f164(x66421),x66423)),f784(f164(x66421),x66424))+~E(f158(x66421,x66425,x66424),f784(f784(f251(f860(x66421),f860(x66421)),x66422),x66423))
% 11.41/11.18 [6748]~P101(x67482)+E(f784(f188(f860(x67481)),f784(f784(f142(x67481,x67482,x67483),x67484),x67485)),f784(a160,f784(f188(f860(x67481)),x67485)))
% 11.41/11.18 [6762]~P101(x67622)+E(f784(f164(x67621),f784(f784(f142(x67621,x67622,x67623),x67624),x67625)),f784(f784(f312(x67621),x67624),f784(f164(x67621),x67625)))
% 11.41/11.18 [7038]~P86(x70381)+E(f784(f784(f89(x70381),f784(f784(f89(x70381),x70382),x70383)),f784(f784(f89(x70381),x70384),x70385)),f784(f784(f89(x70381),f784(f784(f89(x70381),x70382),x70384)),f784(f784(f89(x70381),x70383),x70385)))
% 11.41/11.18 [7039]~P86(x70391)+E(f784(f784(f90(x70391),f784(f784(f90(x70391),x70392),x70393)),f784(f784(f90(x70391),x70394),x70395)),f784(f784(f90(x70391),f784(f784(f90(x70391),x70392),x70394)),f784(f784(f90(x70391),x70393),x70395)))
% 11.41/11.18 [7040]~P59(x70401)+E(f784(f784(f293(x70401),f784(f784(f90(x70401),x70402),x70403)),f784(f784(f90(x70401),x70404),x70405)),f784(f784(f90(x70401),f784(f784(f293(x70401),x70402),x70404)),f784(f784(f293(x70401),x70403),x70405)))
% 11.41/11.18 [7054]~P101(x70541)+E(f305(x70541,f784(f784(f186(x70541),x70542),x70543),f784(f784(f246(x70541),x70544),x70545)),f784(f784(f111(f869(x70541,a852)),f305(x70541,x70542,x70544)),f305(x70541,x70543,x70545)))
% 11.41/11.18 [7055]~P101(x70551)+E(f307(x70551,f784(f784(f186(x70551),x70552),x70553),f784(f784(f246(x70551),x70554),x70555)),f784(f784(f111(f869(x70551,a852)),f307(x70551,x70552,x70554)),f307(x70551,x70553,x70555)))
% 11.41/11.18 [7056]~P101(x70561)+E(f308(x70561,f784(f784(f186(x70561),x70562),x70563),f784(f784(f246(x70561),x70564),x70565)),f784(f784(f111(f869(x70561,a852)),f308(x70561,x70562,x70564)),f308(x70561,x70563,x70565)))
% 11.41/11.18 [7057]~P101(x70571)+E(f784(f784(f111(f869(x70571,a852)),f784(f304(x70571,x70572),x70573)),f784(f304(x70571,x70574),x70575)),f784(f304(x70571,f784(f784(f186(x70571),x70572),x70574)),f784(f784(f246(x70571),x70573),x70575)))
% 11.41/11.18 [7174]~P85(f784(x71741,f832(x71743,x71742,x71741)))+P85(f784(x71741,f784(f784(f251(x71742,x71743),x71744),x71745)))
% 11.41/11.18 [7274]~E(f784(x72743,x72744),f190(x72742))+E(f177(x72741,x72742,f784(f784(f784(f81(x72741,f864(x72742)),x72743),x72744),f784(f237(x72742),x72745))),f784(f784(f312(x72742),x72745),f177(x72741,x72742,x72743)))
% 11.41/11.18 [7297]~E(x72972,f784(x72974,x72975))+P85(f784(f784(f347(x72971),x72972),f784(f313(x72973,x72971,x72974),f249(f869(x72973,a852)))))
% 11.41/11.18 [7358]~E(f784(x73583,x73584),f190(x73582))+E(f784(f784(f3(f869(x73581,a852)),f175(x73581,x73582,x73583)),f784(f784(f312(x73581),x73584),x73585)),f784(f784(f3(f869(x73581,a852)),f175(x73581,x73582,x73583)),x73585))
% 11.41/11.18 [7380]~P16(x73803,x73802,x73804)+P16(x73801,x73802,f784(f784(f10(x73803,f869(x73802,x73802),x73801),x73804),x73805))
% 11.41/11.18 [7381]~P17(x73813,x73812,x73814)+P17(x73811,x73812,f784(f784(f10(x73813,f869(x73812,x73812),x73811),x73814),x73815))
% 11.41/11.18 [7521]~P26(x75211,x75212,x75213,x75214)+P26(x75211,x75212,x75213,f784(f784(f3(f869(x75211,a852)),x75214),x75215))
% 11.41/11.18 [7679]~P85(f784(f784(x76793,x76794),x76795))+P85(f784(f784(f261(x76791,x76792,a852),x76793),f784(f784(f251(x76791,x76792),x76794),x76795)))
% 11.41/11.18 [7680]~P85(f784(f784(x76803,x76804),x76805))+P85(f784(f784(f261(x76801,x76802,a852),x76803),f784(f784(f251(x76801,x76802),x76804),x76805)))
% 11.41/11.18 [7814]P26(x78141,x78142,x78143,x78144)+~P26(x78141,x78142,x78143,f784(f784(f110(f869(x78141,a852)),x78145),x78144))
% 11.41/11.18 [7815]P26(x78151,x78152,x78153,x78154)+~P26(x78151,x78152,x78153,f784(f784(f110(f869(x78151,a852)),x78154),x78155))
% 11.41/11.18 [8173]~P16(x81732,x81731,x81733)+E(f784(f136(x81731,x81732,f784(f9(x81732,x81731,x81731),x81733),x81734),x81735),f784(f784(f74(x81732,x81731,x81733),x81734),f784(f164(x81732),x81735)))
% 11.41/11.18 [8223]P85(f784(f784(x82231,x82232),x82233))+~P85(f784(f784(f261(x82234,x82235,a852),x82231),f784(f784(f251(x82234,x82235),x82232),x82233)))
% 11.41/11.18 [8295]P38(x82954,f465(x82955,x82954,x82953,x82952),x82952,f467(x82955,x82954,x82953,x82952))+P32(x82951,x82952,f784(f784(f784(f100(x82951),x82953),x82954),x82955))
% 11.41/11.18 [8310]~E(f784(f172(x83101,x83102,x83105),x83103),f784(f237(x83102),x83104))+P85(f784(f784(f347(f868(x83101,x83102)),f784(f784(f251(x83101,x83102),x83103),x83104)),f784(f164(f868(x83101,x83102)),x83105)))
% 11.41/11.18 [8311]~E(f784(f172(x83111,x83112,x83115),x83113),f784(f237(x83112),x83114))+P85(f784(f784(f347(f868(x83111,x83112)),f784(f784(f251(x83111,x83112),x83113),x83114)),f784(f164(f868(x83111,x83112)),x83115)))
% 11.41/11.18 [8673]P85(f784(f784(f242(f869(x86731,a852)),f784(f313(x86732,x86731,x86733),x86734)),f784(f313(x86732,x86731,x86733),x86735)))+~P85(f784(f784(f242(f869(x86732,a852)),x86734),x86735))
% 11.41/11.18 [8674]P85(f784(f784(f242(f869(x86741,a852)),f784(f315(x86741,x86742,x86743),x86744)),f784(f315(x86741,x86742,x86743),x86745)))+~P85(f784(f784(f242(f869(x86742,a852)),x86744),x86745))
% 11.41/11.18 [8745]E(x87451,f2(a108))+E(f784(f784(f263(x87452,x87453,x87452,f868(x87453,x87452)),f784(x87454,x87455)),f278(x87453,x87452,f784(f784(f3(a108),x87451),f87(a108)),x87454)),f784(f278(x87453,x87452,x87451,x87454),x87455))
% 11.41/11.18 [8834]P85(f784(f784(f259(x88341,x88342,a852,x88343),x88344),x88345))+~P85(f784(x88343,f784(f784(f251(x88341,x88342),x88344),x88345)))
% 11.41/11.18 [9034]P32(x90341,x90342,f784(f784(f784(f100(x90341),x90343),x90344),x90345))+P85(f784(f784(x90343,f466(x90345,x90344,x90343,x90342)),f465(x90345,x90344,x90343,x90342)))
% 11.41/11.18 [9044]~P85(f784(f784(f194(x90443),f784(f784(f784(a196,x90444),f42(x90441)),f784(x90442,x90444))),x90445))+P85(f784(f784(f194(f34(x90441,x90442,x90443)),x90444),f784(f784(f784(a196,x90445),f42(x90441)),f784(f784(a197,x90444),x90441))))
% 11.41/11.18 [9096]~P85(f784(f784(f259(x90962,x90963,a852,x90961),x90964),x90965))+P85(f784(x90961,f784(f784(f251(x90962,x90963),x90964),x90965)))
% 11.41/11.18 [9097]~P85(f784(f784(f259(x90972,x90973,a852,x90971),x90974),x90975))+P85(f784(x90971,f784(f784(f251(x90972,x90973),x90974),x90975)))
% 11.41/11.18 [9204]E(f784(f237(x92041),f725(x92042,x92043,x92044,x92041,x92045)),f784(f172(x92045,x92041,x92042),x92044))+~P85(f784(f784(f347(f868(x92045,x92041)),f784(f784(f251(x92045,x92041),x92044),x92043)),f784(f164(f868(x92045,x92041)),x92042)))
% 11.41/11.18 [9247]P32(x92471,x92472,f784(f784(f784(f100(x92471),x92473),x92474),x92475))+~P85(f784(f784(x92475,f466(x92475,x92474,x92473,x92472)),f467(x92475,x92474,x92473,x92472)))
% 11.41/11.18 [9341]~P85(f784(f71(x93413),f784(f313(x93412,x93413,x93415),f249(f869(x93412,a852)))))+P85(f784(f71(x93411),f784(f313(x93412,x93411,f784(f784(f10(x93413,x93411,x93412),x93414),x93415)),f249(f869(x93412,a852)))))
% 11.41/11.18 [9362]P85(f784(f784(f242(f869(f869(x93621,a852),a852)),f784(f313(f869(x93622,a852),f869(x93621,a852),f313(x93622,x93621,x93623)),f784(f311(x93622),x93624))),f784(f311(x93621),x93625)))+~P85(f784(f784(f242(f869(x93621,a852)),f784(f313(x93622,x93621,x93623),x93624)),x93625))
% 11.41/11.18 [9372]~P85(f784(f71(f864(x93721)),f784(f313(x93722,f864(x93721),x93723),f249(f869(x93722,a852)))))+P85(f784(f71(f864(x93721)),f784(f313(x93722,f864(x93721),f784(f784(f784(f81(x93722,f864(x93721)),x93723),x93724),f784(f237(x93721),x93725))),f249(f869(x93722,a852)))))
% 11.41/11.18 [9403]P85(f784(f784(f194(x94031),f784(f784(f784(a196,x94032),f42(x94033)),f784(x94034,x94032))),f409(x94035,x94032,x94031,x94034,x94033)))+~P85(f784(f784(f194(f34(x94033,x94034,x94031)),x94032),x94035))
% 11.41/11.18 [9430]E(x94301,x94302)+~P85(f784(f76(x94303,x94304,x94305,x94301,f187(f869(x94303,a852))),x94302))
% 11.41/11.18 [9443]E(f784(f784(f251(x94431,x94432),f558(x94433,x94434,x94435,x94432,x94431)),f567(x94433,x94434,x94435,x94432,x94431)),x94435)+~P85(f784(f784(f347(f868(x94431,x94432)),x94435),f784(f784(f258(x94431,x94432),x94434),x94433)))
% 11.41/11.18 [9454]P85(f784(f784(f194(x94541),f784(f784(f784(a196,x94542),f42(x94543)),f784(x94544,x94542))),f842(x94545,x94542,x94541,x94544,x94543)))+~P85(f784(f784(f194(f34(x94543,x94544,x94541)),x94542),f784(f784(f784(a196,x94545),f42(x94543)),f784(f784(a197,x94542),x94543))))
% 11.41/11.18 [9460]~P85(f784(f784(f194(f784(a29,x94602)),f784(f784(f784(a196,f784(f784(a198,x94604),a199)),f42(a28)),f784(x94603,x94604))),x94605))+P85(f784(f784(f194(f33(x94601,x94602,x94603)),x94604),f784(f784(f784(a196,f784(f784(a198,x94605),f784(a197,x94604))),x94601),f784(f784(a197,x94605),a27))))
% 11.41/11.18 [9494]P85(f784(f784(f194(f784(a29,x94941)),f784(f784(f784(a196,f784(f784(a198,x94942),a199)),f42(a28)),f784(x94943,x94942))),f459(x94944,x94942,x94943,x94941,x94945)))+~P85(f784(f784(f194(f33(x94945,x94941,x94943)),x94942),x94944))
% 11.41/11.18 [9534]P85(f784(f784(f347(x95341),f558(x95342,x95343,x95344,x95345,x95341)),x95343))+~P85(f784(f784(f347(f868(x95341,x95345)),x95344),f784(f784(f258(x95341,x95345),x95343),x95342)))
% 11.41/11.18 [9560]E(f784(f784(f784(a196,f409(x95601,x95602,x95603,x95604,x95605)),f42(x95605)),f784(f784(a197,x95602),x95605)),x95601)+~P85(f784(f784(f194(f34(x95605,x95604,x95603)),x95602),x95601))
% 11.41/11.18 [9586]E(f784(f784(f784(a196,f842(x95861,x95862,x95863,x95864,x95865)),f42(x95865)),f784(f784(a197,x95862),x95865)),f784(f784(f784(a196,x95861),f42(x95865)),f784(f784(a197,x95862),x95865)))+~P85(f784(f784(f194(f34(x95865,x95864,x95863)),x95862),f784(f784(f784(a196,x95861),f42(x95865)),f784(f784(a197,x95862),x95865))))
% 11.41/11.18 [9612]P85(f784(f784(f194(f784(a29,x96121)),f784(f784(f784(a196,f784(f784(a198,x96122),a199)),f42(a28)),f784(x96123,x96122))),f452(x96124,x96122,x96123,x96121,x96125)))+~P85(f784(f784(f194(f33(x96125,x96121,x96123)),x96122),f784(f784(f784(a196,f784(f784(a198,x96124),f784(a197,x96122))),x96125),f784(f784(a197,x96124),a27))))
% 11.41/11.18 [9679]P85(f784(f784(f347(x96791),f567(x96792,x96793,x96794,x96791,x96795)),f784(x96792,f558(x96792,x96793,x96794,x96791,x96795))))+~P85(f784(f784(f347(f868(x96795,x96791)),x96794),f784(f784(f258(x96795,x96791),x96793),x96792)))
% 11.41/11.18 [9698]P85(f784(f784(f347(f868(x96981,x96981)),f784(f784(f251(x96981,x96981),x96982),f671(x96983,x96984,x96985,x96982,x96981))),x96983))+~P85(f784(f784(f347(f868(x96981,x96981)),f784(f784(f251(x96981,x96981),x96982),x96985)),f784(f784(f180(f868(x96981,x96981),a852),f784(a160,x96984)),x96983)))
% 11.41/11.18 [9699]P85(f784(f784(f347(f868(x96991,x96991)),f784(f784(f251(x96991,x96991),x96992),f673(x96993,x96994,x96995,x96992,x96991))),x96993))+~P85(f784(f784(f347(f868(x96991,x96991)),f784(f784(f251(x96991,x96991),x96992),x96995)),f784(f784(f180(f868(x96991,x96991),a852),f784(a160,x96994)),x96993)))
% 11.41/11.18 [9717]~P85(f784(f784(f347(f868(f860(x97171),f860(x97171))),f784(f784(f251(f860(x97171),f860(x97171)),f784(f784(f144(x97171),x97172),x97175)),x97174)),f150(x97171,x97173)))+P85(f784(f784(f347(f868(x97171,x97171)),f784(f784(f251(x97171,x97171),x97172),f730(x97173,x97174,x97175,x97172,x97171))),x97173))
% 11.41/11.18 [9719]~P25(x97191,x97192,f784(f784(f312(f858(x97191)),f784(f784(f784(f100(x97191),f101(x97191,x97193,x97194)),x97195),x97193)),f187(f869(f858(x97191),a852))))+P25(x97191,x97192,f784(f784(f312(f858(x97191)),f784(f784(f784(f100(x97191),x97193),f37(x97194,x97195)),f101(x97191,x97193,f784(f82(a852,a852,a857,a341),x97194)))),f187(f869(f858(x97191),a852))))
% 11.41/11.18 [9838]E(f784(f784(f784(a196,f784(f784(a198,f459(x98381,x98382,x98383,x98384,x98385)),f784(a197,x98382))),x98385),f784(f784(a197,f459(x98381,x98382,x98383,x98384,x98385)),a27)),x98381)+~P85(f784(f784(f194(f33(x98385,x98384,x98383)),x98382),x98381))
% 11.41/11.18 [9850]E(f784(f784(f784(a196,f784(f784(a198,f452(x98501,x98502,x98503,x98504,x98505)),f784(a197,x98502))),x98505),f784(f784(a197,f452(x98501,x98502,x98503,x98504,x98505)),a27)),f784(f784(f784(a196,f784(f784(a198,x98501),f784(a197,x98502))),x98505),f784(f784(a197,x98501),a27)))+~P85(f784(f784(f194(f33(x98505,x98504,x98503)),x98502),f784(f784(f784(a196,f784(f784(a198,x98501),f784(a197,x98502))),x98505),f784(f784(a197,x98501),a27))))
% 11.41/11.18 [6283]~P72(x62832)+E(f784(f784(f784(f3(f869(x62831,x62832)),x62833),x62834),x62835),f784(f784(f3(x62832),f784(x62833,x62835)),f784(x62834,x62835)))
% 11.41/11.18 [6284]~P72(x62842)+E(f784(f784(f784(f3(f869(x62841,x62842)),x62843),x62844),x62845),f784(f784(f3(x62842),f784(x62843,x62845)),f784(x62844,x62845)))
% 11.41/11.18 [6285]~P93(x62852)+E(f784(f784(f784(f110(f869(x62851,x62852)),x62853),x62854),x62855),f784(f784(f110(x62852),f784(x62853,x62855)),f784(x62854,x62855)))
% 11.41/11.18 [6286]~P93(x62862)+E(f784(f784(f784(f110(f869(x62861,x62862)),x62863),x62864),x62865),f784(f784(f110(x62862),f784(x62863,x62865)),f784(x62864,x62865)))
% 11.41/11.18 [6287]~P93(x62872)+E(f784(f784(f784(f111(f869(x62871,x62872)),x62873),x62874),x62875),f784(f784(f111(x62872),f784(x62873,x62875)),f784(x62874,x62875)))
% 11.41/11.18 [6288]~P93(x62882)+E(f784(f784(f784(f111(f869(x62881,x62882)),x62883),x62884),x62885),f784(f784(f111(x62882),f784(x62883,x62885)),f784(x62884,x62885)))
% 11.41/11.18 [6310]E(x63101,x63102)+E(f784(f784(f155(x63103),f784(f784(f151(x63103,x63104),x63101),x63105)),x63102),f784(f784(f155(x63103),x63104),x63102))
% 11.41/11.18 [6586]~E(x65864,f187(f869(x65863,a852)))+E(f784(f784(f3(f869(x65861,a852)),x65862),f784(f784(f54(x65863,f869(x65861,a852)),x65864),x65865)),x65862)
% 11.41/11.18 [6587]~E(x65874,f187(f869(x65873,a852)))+E(f784(f784(f110(f869(x65871,a852)),x65872),f784(f784(f54(x65873,f869(x65871,a852)),x65874),x65875)),x65872)
% 11.41/11.18 [6588]~E(x65884,f187(f869(x65883,a852)))+E(f784(f784(f111(f869(x65881,a852)),x65882),f784(f784(f55(x65883,f869(x65881,a852)),x65884),x65885)),x65882)
% 11.41/11.18 [6601]~E(x66014,f187(f869(x66013,a852)))+E(f784(f784(f312(x66011),x66012),f784(f784(f54(x66013,f869(x66011,a852)),x66014),x66015)),f784(f784(f312(x66011),x66012),f187(f869(x66011,a852))))
% 11.41/11.18 [7037]~P86(x70371)+E(f784(f784(f90(x70371),f784(f784(f90(x70371),x70372),x70373)),f784(f784(f90(x70371),x70374),x70375)),f784(f784(f90(x70371),x70372),f784(f784(f90(x70371),x70373),f784(f784(f90(x70371),x70374),x70375))))
% 11.41/11.18 [7425]E(f784(f784(f155(x74251),f784(f784(f146(x74252,x74251),x74253),x74254)),x74255),f784(x74253,f784(f784(f155(x74252),x74254),x74255)))+~P85(f784(f784(f243(a859),x74255),f784(f188(f860(x74252)),x74254)))
% 11.41/11.18 [7493]E(f784(f784(f110(f869(x74931,a852)),f784(x74932,x74933)),f784(f784(f54(x74934,f869(x74931,a852)),x74935),x74932)),f784(f784(f54(x74934,f869(x74931,a852)),x74935),x74932))+~P85(f784(f784(f347(x74934),x74933),x74935))
% 11.41/11.18 [7494]E(f784(f784(f111(f869(x74941,a852)),f784(x74942,x74943)),f784(f784(f55(x74944,f869(x74941,a852)),x74945),x74942)),f784(f784(f55(x74944,f869(x74941,a852)),x74945),x74942))+~P85(f784(f784(f347(x74944),x74943),x74945))
% 11.41/11.18 [8094]~E(x80943,f187(f869(x80941,a852)))+E(f784(f784(f54(x80941,f869(x80942,a852)),x80943),f784(f784(f10(f869(x80942,a852),f869(x80942,a852),x80941),f784(f312(x80942),x80944)),x80945)),f187(f869(x80942,a852)))
% 11.41/11.18 [8100]~P85(f784(f784(f347(x81004),x81003),x81005))+P85(f784(f784(f242(f869(x81001,a852)),f784(x81002,x81003)),f784(f784(f54(x81004,f869(x81001,a852)),x81005),x81002)))
% 11.41/11.18 [8222]~E(f784(x82224,x82222),x82225)+P85(f784(f784(f347(x82221),x82222),f784(f315(x82221,x82223,x82224),f784(f784(f312(x82223),x82225),f187(f869(x82223,a852))))))
% 11.41/11.18 [8269]~P52(x82691,x82692,f784(f288(x82692,x82691),x82693))+E(f784(f784(f111(f869(x82691,a852)),f784(f287(x82692,x82691,x82693),x82694)),f784(f287(x82692,x82691,x82693),x82695)),f784(f287(x82692,x82691,x82693),f784(f784(f111(f869(x82692,a852)),x82694),x82695)))
% 11.41/11.18 [8294]E(x82941,f2(a108))+E(f123(x82942,x82943,f784(x82944,f784(f784(f3(a108),x82941),f87(a108))),f784(f784(f9(x82942,a108,f861(x82943)),x82945),x82941)),f784(f203(x82942,x82943,x82944,x82945),x82941))
% 11.41/11.18 [8389]E(x83891,f187(f869(x83892,a852)))+E(f784(f784(f54(x83892,f869(x83893,a852)),x83891),f784(f784(f10(f869(x83893,a852),f869(x83893,a852),x83892),f784(f312(x83893),x83894)),x83895)),f784(f784(f312(x83893),x83894),f784(f784(f54(x83892,f869(x83893,a852)),x83891),x83895)))
% 11.41/11.18 [8390]E(x83901,f187(f869(x83902,a852)))+E(f784(f784(f54(x83902,f869(x83903,a852)),x83901),f784(f784(f10(f869(x83903,a852),f869(x83903,a852),x83902),f784(f312(x83903),x83904)),x83905)),f784(f784(f312(x83903),x83904),f784(f784(f54(x83902,f869(x83903,a852)),x83901),x83905)))
% 11.41/11.18 [8443]~P26(x84432,x84431,x84433,f249(f869(x84432,a852)))+E(f784(f784(f3(f869(x84431,a852)),f784(f313(x84432,x84431,x84433),x84434)),f784(f313(x84432,x84431,x84433),x84435)),f784(f313(x84432,x84431,x84433),f784(f784(f3(f869(x84432,a852)),x84434),x84435)))
% 11.41/11.18 [8444]~P26(x84442,x84441,x84443,f249(f869(x84442,a852)))+E(f784(f784(f111(f869(x84441,a852)),f784(f313(x84442,x84441,x84443),x84444)),f784(f313(x84442,x84441,x84443),x84445)),f784(f313(x84442,x84441,x84443),f784(f784(f111(f869(x84442,a852)),x84444),x84445)))
% 11.41/11.18 [8510]~P85(f784(f784(f77(x85101,x85102,x85105),x85103),x85104))+P85(f784(f784(f347(f868(x85101,x85102)),f784(f784(f251(x85101,x85102),x85103),x85104)),x85105))
% 11.41/11.18 [8537]P85(f784(f784(f347(x85371),x85372),f784(f269(x85373,x85371),x85374)))+~P85(f784(f784(f347(f868(x85373,x85371)),f784(f784(f251(x85373,x85371),x85375),x85372)),x85374))
% 11.41/11.18 [8538]P85(f784(f784(f347(x85381),x85382),f784(f269(x85383,x85381),x85384)))+~P85(f784(f784(f347(f868(x85383,x85381)),f784(f784(f251(x85383,x85381),x85385),x85382)),x85384))
% 11.41/11.18 [8539]P85(f784(f784(f347(x85391),x85392),f784(f271(x85391,x85393),x85394)))+~P85(f784(f784(f347(f868(x85391,x85393)),f784(f784(f251(x85391,x85393),x85392),x85395)),x85394))
% 11.41/11.18 [8540]P85(f784(f784(f347(x85401),x85402),f784(f271(x85401,x85403),x85404)))+~P85(f784(f784(f347(f868(x85401,x85403)),f784(f784(f251(x85401,x85403),x85402),x85405)),x85404))
% 11.41/11.18 [8662]P85(f784(f784(f77(x86621,x86622,x86623),x86624),x86625))+~P85(f784(f784(f347(f868(x86621,x86622)),f784(f784(f251(x86621,x86622),x86624),x86625)),x86623))
% 11.41/11.18 [8695]E(f784(x86951,x86952),x86953)+~P85(f784(f784(f347(x86954),x86952),f784(f315(x86954,x86955,x86951),f784(f784(f312(x86955),x86953),f187(f869(x86955,a852))))))
% 11.41/11.18 [8897]P85(f784(f784(f347(f868(x88971,x88972)),f784(f784(f251(x88971,x88972),x88973),x88974)),f784(f288(x88972,x88971),x88975)))+~P85(f784(f784(f347(f868(x88972,x88971)),f784(f784(f251(x88972,x88971),x88974),x88973)),x88975))
% 11.41/11.18 [8898]P85(f784(f784(f347(f868(x88981,x88982)),f784(f784(f251(x88981,x88982),x88983),x88984)),f784(f288(x88982,x88981),x88985)))+~P85(f784(f784(f347(f868(x88982,x88981)),f784(f784(f251(x88982,x88981),x88984),x88983)),x88985))
% 11.41/11.18 [8916]~P85(f784(f784(x89161,x89165),x89164))+P85(f784(f784(x89161,f784(f260(x89162,x89163),f784(f784(f251(x89162,x89163),x89164),x89165))),f784(f250(x89162,x89163),f784(f784(f251(x89162,x89163),x89164),x89165))))
% 11.41/11.18 [8942]~P85(f784(f784(f347(f868(x89422,x89421)),f784(f784(f251(x89422,x89421),x89424),x89423)),f784(f288(x89421,x89422),x89425)))+P85(f784(f784(f347(f868(x89421,x89422)),f784(f784(f251(x89421,x89422),x89423),x89424)),x89425))
% 11.41/11.18 [8943]~P85(f784(f784(f347(f868(x89432,x89431)),f784(f784(f251(x89432,x89431),x89434),x89433)),f784(f288(x89431,x89432),x89435)))+P85(f784(f784(f347(f868(x89431,x89432)),f784(f784(f251(x89431,x89432),x89433),x89434)),x89435))
% 11.41/11.18 [8970]~P85(f784(f784(f347(f868(x89703,x89701)),f784(f784(f251(x89703,x89701),x89705),x89702)),x89704))+P85(f784(f784(f347(x89701),x89702),f784(f287(x89703,x89701,x89704),f784(f784(f312(x89703),x89705),f187(f869(x89703,a852))))))
% 11.41/11.18 [9017]P85(f784(f784(f347(f868(x90171,x90172)),f784(f784(f251(x90171,x90172),x90173),x90174)),x90175))+~P85(f784(f784(f347(x90172),x90174),f784(f287(x90171,x90172,x90175),f784(f784(f312(x90171),x90173),f187(f869(x90171,a852))))))
% 11.41/11.18 [9037]E(f784(f784(f784(f81(x90371,f864(x90372)),f179(x90371,x90372,x90373,x90374)),x90375),f190(x90372)),f179(x90371,x90372,x90373,f784(f784(f3(f869(x90371,a852)),x90374),f784(f784(f312(x90371),x90375),f187(f869(x90371,a852))))))+~P85(f784(f784(f347(x90371),x90375),x90374))
% 11.41/11.18 [9103]~P68(x91031)+E(f784(f784(f8(a859,x91031),x91032),f305(a859,f784(f784(f89(a859),x91033),x91034),f784(f784(f89(a859),x91035),x91034))),f784(f784(f8(a859,x91031),f784(f784(f10(a859,x91031,a859),x91032),f784(f784(f9(a859,a859,a859),f89(a859)),x91034))),f305(a859,x91033,x91035)))
% 11.41/11.18 [9121]~P68(x91211)+E(f784(f784(f8(a859,x91211),x91212),f784(f304(a859,f784(f784(f89(a859),x91213),x91214)),f784(f784(f89(a859),x91215),x91214))),f784(f784(f8(a859,x91211),f784(f784(f10(a859,x91211,a859),x91212),f784(f784(f9(a859,a859,a859),f89(a859)),x91214))),f784(f304(a859,x91213),x91215)))
% 11.41/11.18 [9329]P85(f784(f784(f347(f868(f860(x93291),f860(x93291))),f784(f784(f251(f860(x93291),f860(x93291)),f784(f784(f144(x93291),x93292),x93293)),f784(f784(f144(x93291),x93294),x93293))),f149(x93291,x93295)))+~P85(f784(f784(f347(f868(x93291,x93291)),f784(f784(f251(x93291,x93291),x93292),x93294)),x93295))
% 11.41/11.18 [9439]E(f784(f784(f312(x94391),f548(x94392,x94393,x94394,x94395,x94391)),f549(x94392,x94393,x94394,x94395,x94391)),f784(f784(f312(x94391),x94394),x94393))+~P85(f784(f72(x94391,x94395,f784(f784(f312(x94391),x94394),x94393)),x94392))
% 11.41/11.18 [9440]E(f784(f784(f312(x94401),f550(x94402,x94403,x94404,x94405,x94401)),f551(x94402,x94403,x94404,x94405,x94401)),f784(f784(f312(x94401),x94404),x94403))+~P85(f784(f72(x94401,x94405,f784(f784(f312(x94401),x94404),x94403)),x94402))
% 11.41/11.18 [9520]P85(f784(f784(f347(x95201),f680(x95202,x95203,x95204,x95205,x95201)),x95204))+P85(f784(f784(f784(f55(x95201,f869(x95205,a852)),x95204),x95203),x95202))
% 11.41/11.18 [9525]P85(f784(f784(f347(x95251),f677(x95252,x95253,x95251,x95254,x95255)),x95253))+P85(f784(f784(f347(x95255),x95254),f784(f784(f55(x95251,f869(x95255,a852)),x95253),x95252)))
% 11.41/11.18 [9533]P85(f784(f784(f347(x95331),f678(x95332,x95333,x95331,x95334,x95335)),x95333))+P85(f784(f784(f242(f869(x95335,a852)),x95334),f784(f784(f55(x95331,f869(x95335,a852)),x95333),x95332)))
% 11.41/11.18 [9536]P85(f784(f784(x95361,f400(x95362,x95361,x95363,x95364,x95365)),x95362))+~P85(f784(f784(f784(f54(x95365,f869(x95364,a852)),x95363),x95361),x95362))
% 11.41/11.18 [9538]P85(f784(f784(f347(x95381),f400(x95382,x95383,x95384,x95385,x95381)),x95384))+~P85(f784(f784(f784(f54(x95381,f869(x95385,a852)),x95384),x95383),x95382))
% 11.41/11.18 [9548]P85(f784(f784(f347(x95481),f429(x95482,x95483,x95481,x95484,x95485)),x95483))+~P85(f784(f784(f347(x95485),x95484),f784(f784(f54(x95481,f869(x95485,a852)),x95483),x95482)))
% 11.41/11.18 [9553]P85(f784(f784(f347(x95531),x95532),f784(x95533,f429(x95533,x95534,x95535,x95532,x95531))))+~P85(f784(f784(f347(x95531),x95532),f784(f784(f54(x95535,f869(x95531,a852)),x95534),x95533)))
% 11.41/11.18 [9642]~P85(f784(f784(x96424,f680(x96425,x96424,x96423,x96422,x96421)),x96425))+P85(f784(f784(f784(f55(x96421,f869(x96422,a852)),x96423),x96424),x96425))
% 11.41/11.18 [9645]~P85(f784(f784(f347(x96451),x96452),f784(x96455,f677(x96455,x96454,x96453,x96452,x96451))))+P85(f784(f784(f347(x96451),x96452),f784(f784(f55(x96453,f869(x96451,a852)),x96454),x96455)))
% 11.41/11.18 [9648]~P85(f784(f784(f242(f869(x96481,a852)),x96482),f784(x96485,f678(x96485,x96484,x96483,x96482,x96481))))+P85(f784(f784(f242(f869(x96481,a852)),x96482),f784(f784(f55(x96483,f869(x96481,a852)),x96484),x96485)))
% 11.41/11.18 [9702]~P85(f784(f784(f347(x97021),f548(x97025,x97024,x97023,x97022,x97021)),f549(x97025,x97024,x97023,x97022,x97021)))+~P85(f784(f72(x97021,x97022,f784(f784(f312(x97021),x97023),x97024)),x97025))
% 11.41/11.18 [9703]~P85(f784(f784(f347(x97031),f550(x97035,x97034,x97033,x97032,x97031)),f551(x97035,x97034,x97033,x97032,x97031)))+~P85(f784(f72(x97031,x97032,f784(f784(f312(x97031),x97033),x97034)),x97035))
% 11.41/11.18 [9704]~P85(f784(f784(f347(f868(x97041,x97041)),f784(f784(f251(x97041,x97041),x97042),x97045)),f784(f784(f180(f868(x97041,x97041),a852),f784(a160,x97044)),x97043)))+P85(f784(f784(f347(f868(x97041,x97041)),f784(f784(f251(x97041,x97041),x97042),f672(x97043,x97044,x97045,x97042,x97041))),f784(f784(f180(f868(x97041,x97041),a852),x97044),x97043)))
% 11.41/11.18 [9711]P85(f784(f76(x97111,x97111,x97112,f548(x97113,x97114,x97115,x97112,x97111),f549(x97113,x97114,x97115,x97112,x97111)),x97113))+~P85(f784(f72(x97111,x97112,f784(f784(f312(x97111),x97115),x97114)),x97113))
% 11.41/11.18 [9712]P85(f784(f76(x97121,x97121,x97122,f550(x97123,x97124,x97125,x97122,x97121),f551(x97123,x97124,x97125,x97122,x97121)),x97123))+~P85(f784(f72(x97121,x97122,f784(f784(f312(x97121),x97125),x97124)),x97123))
% 11.41/11.18 [9723]~P101(x97231)+P15(x97231,f784(f784(f146(x97232,x97231),x97233),f784(f131(x97232,f784(f784(f9(x97232,x97231,a852),f784(f784(f10(x97231,f869(x97231,a852),x97232),a343),x97233)),f784(x97234,x97235))),x97235)))
% 11.41/11.18 [9778]~P85(f784(f784(f347(x97782),x97785),f784(f287(x97781,x97782,x97784),x97783)))+P85(f784(f784(f347(f868(x97781,x97782)),f784(f784(f251(x97781,x97782),f502(x97783,x97784,x97781,x97785,x97782)),x97785)),x97784))
% 11.41/11.18 [9779]~P85(f784(f784(f347(x97792),x97795),f784(f287(x97791,x97792,x97794),x97793)))+P85(f784(f784(f347(f868(x97791,x97792)),f784(f784(f251(x97791,x97792),f542(x97793,x97794,x97791,x97795,x97792)),x97795)),x97794))
% 11.41/11.18 [9799]~P85(f784(f784(f347(f868(x97991,x97991)),f784(f784(f251(x97991,x97991),x97995),x97994)),f784(f784(f180(f868(x97991,x97991),a852),f784(a160,x97993)),x97992)))+P85(f784(f784(f347(f868(x97991,x97991)),f784(f784(f251(x97991,x97991),f672(x97992,x97993,x97994,x97995,x97991)),x97994)),x97992))
% 11.41/11.18 [9802]~P85(f784(f784(f347(f868(x98021,x98021)),f784(f784(f251(x98021,x98021),x98025),x98024)),f784(f784(f180(f868(x98021,x98021),a852),f784(a160,x98023)),x98022)))+P85(f784(f784(f347(f868(x98021,x98021)),f784(f784(f251(x98021,x98021),f671(x98022,x98023,x98024,x98025,x98021)),x98024)),f784(f784(f180(f868(x98021,x98021),a852),x98023),x98022)))
% 11.41/11.18 [9803]~P85(f784(f784(f347(f868(x98031,x98031)),f784(f784(f251(x98031,x98031),x98035),x98034)),f784(f784(f180(f868(x98031,x98031),a852),f784(a160,x98033)),x98032)))+P85(f784(f784(f347(f868(x98031,x98031)),f784(f784(f251(x98031,x98031),f673(x98032,x98033,x98034,x98035,x98031)),x98034)),f784(f784(f180(f868(x98031,x98031),a852),x98033),x98032)))
% 11.41/11.18 [9804]~P85(f784(f784(f347(f868(f860(x98041),f860(x98041))),f784(f784(f251(f860(x98041),f860(x98041)),x98045),f784(f784(f144(x98041),x98044),x98043))),f150(x98041,x98042)))+P85(f784(f784(f347(f868(x98041,x98041)),f784(f784(f251(x98041,x98041),f729(x98042,x98043,x98044,x98045,x98041)),x98044)),x98042))
% 11.41/11.18 [6997]E(x69971,f190(x69972))+E(f175(x69973,x69972,f784(f784(f784(f81(x69973,f864(x69972)),x69974),x69975),x69971)),f784(f784(f312(x69973),x69975),f175(x69973,x69972,x69974)))
% 11.41/11.18 [7514]~E(x75143,f187(f869(x75142,a852)))+E(f784(f784(f110(f869(x75141,a852)),f784(f784(f54(x75142,f869(x75141,a852)),x75143),x75144)),x75145),x75145)
% 11.41/11.18 [7515]~E(x75153,f187(f869(x75152,a852)))+E(f784(f784(f111(f869(x75151,a852)),f784(f784(f55(x75152,f869(x75151,a852)),x75153),x75154)),x75155),x75155)
% 11.41/11.18 [7567]~P86(x75671)+E(f784(f784(f90(x75671),f784(f784(f90(x75671),x75672),x75673)),f784(f784(f90(x75671),x75674),x75675)),f784(f784(f90(x75671),x75674),f784(f784(f90(x75671),f784(f784(f90(x75671),x75672),x75673)),x75675)))
% 11.41/11.18 [7876]~E(x78765,f190(x78762))+E(f175(x78761,x78762,f784(f784(f784(f81(x78761,f864(x78762)),x78763),x78764),x78765)),f784(f784(f3(f869(x78761,a852)),f175(x78761,x78762,x78763)),f784(f784(f312(x78761),x78764),f187(f869(x78761,a852)))))
% 11.41/11.18 [7945]~E(x79453,f187(f869(x79452,a852)))+E(f784(f784(f3(f869(x79451,a852)),f784(f784(f55(x79452,f869(x79451,a852)),x79453),x79454)),x79455),f784(f784(f3(f869(x79451,a852)),f249(f869(x79451,a852))),x79455))
% 11.41/11.18 [8071]E(f784(f784(f151(x80711,f784(f784(f130(x80711),x80712),x80713)),x80714),x80715),f784(f784(f130(x80711),f784(f784(f151(x80711,x80712),x80714),x80715)),x80713))+~P85(f784(f784(f243(a859),x80714),f784(f188(f860(x80711)),x80712)))
% 11.41/11.18 [8072]E(f784(f784(f151(x80721,f784(f784(f130(x80721),x80722),x80723)),x80724),x80725),f784(f784(f130(x80721),f784(f784(f151(x80721,x80722),x80724),x80725)),x80723))+~P85(f784(f784(f243(a859),x80724),f784(f188(f860(x80721)),x80722)))
% 11.41/11.18 [8200]P85(f784(f784(f347(x82001),x82005),f784(f164(x82001),x82003)))+E(f784(f172(x82001,x82002,f784(f784(f173(x82001,x82002),x82003),f784(f784(f146(x82001,x82002),x82004),x82003))),x82005),f190(x82002))
% 11.41/11.18 [8309]~P85(f784(f784(f347(x83091),x83095),f784(f164(x83091),x83093)))+E(f784(f172(x83091,x83092,f784(f784(f173(x83091,x83092),x83093),f784(f784(f146(x83091,x83092),x83094),x83093))),x83095),f784(f237(x83092),f784(x83094,x83095)))
% 11.41/11.18 [8340]E(f784(f784(f155(x83401),f784(f784(f146(a859,x83401),x83402),f134(a859,f784(f304(a859,x83403),x83404)))),x83405),f784(x83402,f784(f784(f89(a859),x83403),x83405)))+~P85(f784(f784(f243(a859),x83405),f784(f784(f3(a859),x83404),x83403)))
% 11.41/11.18 [8353]E(x83531,f2(a108))+E(f127(x83532,x83533,f784(x83534,f784(f784(f3(a108),x83531),f87(a108))),f784(f784(f9(x83532,a108,f861(f864(x83533))),x83535),x83531)),f784(f201(x83532,x83533,x83534,x83535),x83531))
% 11.41/11.18 [8377]~E(x83773,f187(f869(x83771,a852)))+E(f784(f784(f54(x83771,f869(x83772,a852)),x83773),f784(f784(f10(f869(x83772,a852),f869(x83772,a852),x83771),f784(f110(f869(x83772,a852)),x83774)),x83775)),f187(f869(x83772,a852)))
% 11.41/11.18 [8378]~E(x83783,f187(f869(x83781,a852)))+E(f784(f784(f55(x83781,f869(x83782,a852)),x83783),f784(f784(f10(f869(x83782,a852),f869(x83782,a852),x83781),f784(f3(f869(x83782,a852)),x83784)),x83785)),f249(f869(x83782,a852)))
% 11.41/11.18 [8379]~E(x83793,f187(f869(x83791,a852)))+E(f784(f784(f55(x83791,f869(x83792,a852)),x83793),f784(f784(f10(f869(x83792,a852),f869(x83792,a852),x83791),f784(f111(f869(x83792,a852)),x83794)),x83795)),f249(f869(x83792,a852)))
% 11.41/11.18 [8384]~P139(x83842)+E(f784(f784(f8(x83841,x83842),f784(f784(f10(x83842,x83842,x83841),f784(f90(x83842),x83843)),x83844)),x83845),f784(f784(f90(x83842),x83843),f784(f784(f8(x83841,x83842),x83844),x83845)))
% 11.41/11.18 [8644]E(x86441,f187(f869(x86442,a852)))+E(f784(f784(f55(x86442,f869(x86443,a852)),x86441),f784(f784(f10(f869(x86443,a852),f869(x86443,a852),x86442),f784(f3(f869(x86443,a852)),x86444)),x86445)),f784(f784(f3(f869(x86443,a852)),x86444),f784(f784(f54(x86442,f869(x86443,a852)),x86441),x86445)))
% 11.41/11.18 [8645]E(x86451,f187(f869(x86452,a852)))+E(f784(f784(f54(x86452,f869(x86453,a852)),x86451),f784(f784(f10(f869(x86453,a852),f869(x86453,a852),x86452),f784(f110(f869(x86453,a852)),x86454)),x86455)),f784(f784(f110(f869(x86453,a852)),x86454),f784(f784(f54(x86452,f869(x86453,a852)),x86451),x86455)))
% 11.41/11.18 [8646]E(x86461,f187(f869(x86462,a852)))+E(f784(f784(f55(x86462,f869(x86463,a852)),x86461),f784(f784(f10(f869(x86463,a852),f869(x86463,a852),x86462),f784(f111(f869(x86463,a852)),x86464)),x86465)),f784(f784(f111(f869(x86463,a852)),x86464),f784(f784(f55(x86462,f869(x86463,a852)),x86461),x86465)))
% 11.41/11.18 [8647]E(x86471,f187(f869(x86472,a852)))+E(f784(f784(f54(x86472,f869(x86473,a852)),x86471),f784(f784(f10(f869(x86473,a852),f869(x86473,a852),x86472),f784(f110(f869(x86473,a852)),x86474)),x86475)),f784(f784(f110(f869(x86473,a852)),x86474),f784(f784(f54(x86472,f869(x86473,a852)),x86471),x86475)))
% 11.41/11.18 [8648]E(x86481,f187(f869(x86482,a852)))+E(f784(f784(f55(x86482,f869(x86483,a852)),x86481),f784(f784(f10(f869(x86483,a852),f869(x86483,a852),x86482),f784(f3(f869(x86483,a852)),x86484)),x86485)),f784(f784(f3(f869(x86483,a852)),x86484),f784(f784(f54(x86482,f869(x86483,a852)),x86481),x86485)))
% 11.41/11.18 [8649]E(x86491,f187(f869(x86492,a852)))+E(f784(f784(f55(x86492,f869(x86493,a852)),x86491),f784(f784(f10(f869(x86493,a852),f869(x86493,a852),x86492),f784(f111(f869(x86493,a852)),x86494)),x86495)),f784(f784(f111(f869(x86493,a852)),x86494),f784(f784(f55(x86492,f869(x86493,a852)),x86491),x86495)))
% 11.41/11.18 [9071]~P26(x90712,x90711,x90713,f784(f784(f110(f869(x90712,a852)),x90714),x90715))+E(f784(f784(f111(f869(x90711,a852)),f784(f313(x90712,x90711,x90713),f784(f784(f3(f869(x90712,a852)),x90714),x90715))),f784(f313(x90712,x90711,x90713),f784(f784(f3(f869(x90712,a852)),x90715),x90714))),f187(f869(x90711,a852)))
% 11.41/11.18 [9325]~P85(f784(f784(f242(f869(x93253,a852)),f784(f287(x93251,x93253,x93254),x93252)),x93255))+P85(f784(f784(f242(f869(x93251,a852)),x93252),f784(f88(f869(x93251,a852)),f784(f287(x93253,x93251,f784(f288(x93251,x93253),x93254)),f784(f88(f869(x93253,a852)),x93255)))))
% 11.41/11.18 [9348]~P26(x93481,x93482,x93483,f784(f784(f312(x93481),x93484),x93485))+~P85(f784(f784(f347(x93482),f784(x93483,x93484)),f784(f313(x93481,x93482,x93483),f784(f784(f3(f869(x93481,a852)),x93485),f784(f784(f312(x93481),x93484),f187(f869(x93481,a852)))))))
% 11.41/11.18 [9396]P85(f784(f784(f242(f869(x93961,a852)),f784(f287(x93962,x93961,x93963),x93964)),x93965))+~P85(f784(f784(f242(f869(x93962,a852)),x93964),f784(f88(f869(x93962,a852)),f784(f287(x93961,x93962,f784(f288(x93962,x93961),x93963)),f784(f88(f869(x93961,a852)),x93965)))))
% 11.41/11.18 [9470]~P79(x94701)+P85(f784(f784(f242(x94701),f784(f84(x94701),f784(f784(f3(x94701),f784(f784(f89(x94701),x94702),x94703)),f784(f784(f89(x94701),x94704),x94705)))),f784(f784(f89(x94701),f784(f84(x94701),f784(f784(f3(x94701),x94702),x94704))),f784(f84(x94701),f784(f784(f3(x94701),x94703),x94705)))))
% 11.41/11.18 [9566]P85(f784(f784(f347(x95661),f405(x95662,x95663,x95664,x95661,x95665)),x95664))+P85(f784(f784(f242(f869(x95665,a852)),f784(f784(f54(x95661,f869(x95665,a852)),x95664),x95663)),x95662))
% 11.41/11.18 [9743]~P85(f784(f784(f242(f869(x97431,a852)),f784(x97434,f405(x97435,x97434,x97433,x97432,x97431))),x97435))+P85(f784(f784(f242(f869(x97431,a852)),f784(f784(f54(x97432,f869(x97431,a852)),x97433),x97434)),x97435))
% 11.41/11.18 [8491]E(f784(f784(f130(x84911),x84912),f784(f784(f151(x84911,x84913),f784(f784(f3(a859),x84914),f784(f188(f860(x84911)),x84912))),x84915)),f784(f784(f151(x84911,f784(f784(f130(x84911),x84912),x84913)),x84914),x84915))+P85(f784(f784(f243(a859),x84914),f784(f188(f860(x84911)),x84912)))
% 11.41/11.18 [8516]~P138(x85161)+E(f784(f784(f89(x85161),f784(f784(f90(x85161),x85162),x85163)),f784(f784(f89(x85161),f784(f784(f90(x85161),x85164),x85163)),x85165)),f784(f784(f89(x85161),f784(f784(f90(x85161),f784(f784(f89(x85161),x85162),x85164)),x85163)),x85165))
% 11.41/11.18 [9027]~P139(x90271)+E(f784(f157(x90271),f784(f784(f146(x90272,x90271),f784(f784(f10(x90271,x90271,x90272),f784(f90(x90271),x90273)),x90274)),x90275)),f784(f784(f90(x90271),x90273),f784(f157(x90271),f784(f784(f146(x90272,x90271),x90274),x90275))))
% 11.41/11.18 [9404]~P139(x94042)+E(f784(f784(f8(x94041,x94042),f784(f784(f9(x94041,x94042,x94042),f784(f784(f10(x94042,f869(x94042,x94042),x94041),f90(x94042)),x94043)),x94044)),x94045),f784(f784(f90(x94042),f784(f784(f8(x94041,x94042),x94043),x94045)),x94044))
% 11.41/11.18 [9405]~P60(x94052)+E(f784(f784(f8(x94051,x94052),f784(f784(f9(x94051,x94052,x94052),f784(f784(f10(x94052,f869(x94052,x94052),x94051),f293(x94052)),x94053)),x94054)),x94055),f784(f784(f293(x94052),f784(f784(f8(x94051,x94052),x94053),x94055)),x94054))
% 11.41/11.18 [9412]~P68(x94122)+E(f784(f784(f8(x94121,x94122),f784(f784(f20(x94121,x94122,x94122),f784(f784(f10(x94122,f869(x94122,x94122),x94121),f89(x94122)),x94123)),x94124)),x94125),f784(f784(f89(x94122),f784(f784(f8(x94121,x94122),x94123),x94125)),f784(f784(f8(x94121,x94122),x94124),x94125)))
% 11.41/11.18 [9413]~P3(x94132)+E(f784(f784(f8(x94131,x94132),f784(f784(f20(x94131,x94132,x94132),f784(f784(f10(x94132,f869(x94132,x94132),x94131),f3(x94132)),x94133)),x94134)),x94135),f784(f784(f3(x94132),f784(f784(f8(x94131,x94132),x94133),x94135)),f784(f784(f8(x94131,x94132),x94134),x94135)))
% 11.41/11.18 [9414]~P71(x94142)+E(f784(f784(f11(x94141,x94142),f784(f784(f20(x94141,x94142,x94142),f784(f784(f10(x94142,f869(x94142,x94142),x94141),f90(x94142)),x94143)),x94144)),x94145),f784(f784(f90(x94142),f784(f784(f11(x94141,x94142),x94143),x94145)),f784(f784(f11(x94141,x94142),x94144),x94145)))
% 11.41/11.18 [9451]~E(x94513,f187(f869(x94511,a852)))+E(f784(f784(f54(x94511,f869(x94512,a852)),x94513),f784(f784(f9(x94511,f869(x94512,a852),f869(x94512,a852)),f784(f784(f10(f869(x94512,a852),f869(f869(x94512,a852),f869(x94512,a852)),x94511),f110(f869(x94512,a852))),x94514)),x94515)),f187(f869(x94512,a852)))
% 11.41/11.18 [9452]~E(x94523,f187(f869(x94521,a852)))+E(f784(f784(f55(x94521,f869(x94522,a852)),x94523),f784(f784(f9(x94521,f869(x94522,a852),f869(x94522,a852)),f784(f784(f10(f869(x94522,a852),f869(f869(x94522,a852),f869(x94522,a852)),x94521),f3(f869(x94522,a852))),x94524)),x94525)),f249(f869(x94522,a852)))
% 11.41/11.18 [9453]~E(x94533,f187(f869(x94531,a852)))+E(f784(f784(f55(x94531,f869(x94532,a852)),x94533),f784(f784(f9(x94531,f869(x94532,a852),f869(x94532,a852)),f784(f784(f10(f869(x94532,a852),f869(f869(x94532,a852),f869(x94532,a852)),x94531),f111(f869(x94532,a852))),x94534)),x94535)),f249(f869(x94532,a852)))
% 11.41/11.18 [9477]E(x94771,f187(f869(x94772,a852)))+E(f784(f784(f55(x94772,f869(x94773,a852)),x94771),f784(f784(f9(x94772,f869(x94773,a852),f869(x94773,a852)),f784(f784(f10(f869(x94773,a852),f869(f869(x94773,a852),f869(x94773,a852)),x94772),f3(f869(x94773,a852))),x94774)),x94775)),f784(f784(f3(f869(x94773,a852)),f784(f784(f55(x94772,f869(x94773,a852)),x94771),x94774)),x94775))
% 11.41/11.18 [9478]E(x94781,f187(f869(x94782,a852)))+E(f784(f784(f54(x94782,f869(x94783,a852)),x94781),f784(f784(f9(x94782,f869(x94783,a852),f869(x94783,a852)),f784(f784(f10(f869(x94783,a852),f869(f869(x94783,a852),f869(x94783,a852)),x94782),f110(f869(x94783,a852))),x94784)),x94785)),f784(f784(f110(f869(x94783,a852)),f784(f784(f54(x94782,f869(x94783,a852)),x94781),x94784)),x94785))
% 11.41/11.18 [9479]E(x94791,f187(f869(x94792,a852)))+E(f784(f784(f55(x94792,f869(x94793,a852)),x94791),f784(f784(f9(x94792,f869(x94793,a852),f869(x94793,a852)),f784(f784(f10(f869(x94793,a852),f869(f869(x94793,a852),f869(x94793,a852)),x94792),f111(f869(x94793,a852))),x94794)),x94795)),f784(f784(f111(f869(x94793,a852)),f784(f784(f55(x94792,f869(x94793,a852)),x94791),x94794)),x94795))
% 11.41/11.18 [9480]E(x94801,f187(f869(x94802,a852)))+E(f784(f784(f54(x94802,f869(x94803,a852)),x94801),f784(f784(f9(x94802,f869(x94803,a852),f869(x94803,a852)),f784(f784(f10(f869(x94803,a852),f869(f869(x94803,a852),f869(x94803,a852)),x94802),f110(f869(x94803,a852))),x94804)),x94805)),f784(f784(f110(f869(x94803,a852)),f784(f784(f54(x94802,f869(x94803,a852)),x94801),x94804)),x94805))
% 11.41/11.18 [9481]E(x94811,f187(f869(x94812,a852)))+E(f784(f784(f55(x94812,f869(x94813,a852)),x94811),f784(f784(f9(x94812,f869(x94813,a852),f869(x94813,a852)),f784(f784(f10(f869(x94813,a852),f869(f869(x94813,a852),f869(x94813,a852)),x94812),f3(f869(x94813,a852))),x94814)),x94815)),f784(f784(f3(f869(x94813,a852)),f784(f784(f55(x94812,f869(x94813,a852)),x94811),x94814)),x94815))
% 11.41/11.18 [9482]E(x94821,f187(f869(x94822,a852)))+E(f784(f784(f55(x94822,f869(x94823,a852)),x94821),f784(f784(f9(x94822,f869(x94823,a852),f869(x94823,a852)),f784(f784(f10(f869(x94823,a852),f869(f869(x94823,a852),f869(x94823,a852)),x94822),f111(f869(x94823,a852))),x94824)),x94825)),f784(f784(f111(f869(x94823,a852)),f784(f784(f55(x94822,f869(x94823,a852)),x94821),x94824)),x94825))
% 11.41/11.18 [9076]~P85(f784(f784(f242(a859),x90761),x90764))+E(f784(f784(f3(a859),f784(f784(f89(a859),f784(f784(f90(a859),x90761),x90762)),x90763)),f784(f784(f89(a859),f784(f784(f90(a859),x90764),x90762)),x90765)),f784(f784(f3(a859),x90763),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x90764),x90761)),x90762)),x90765)))
% 11.41/11.18 [9625]~P139(x96251)+E(f784(f157(x96251),f784(f784(f146(x96252,x96251),f784(f784(f9(x96252,x96251,x96251),f784(f784(f10(x96251,f869(x96251,x96251),x96252),f90(x96251)),x96253)),x96254)),x96255)),f784(f784(f90(x96251),f784(f157(x96251),f784(f784(f146(x96252,x96251),x96253),x96255))),x96254))
% 11.41/11.18 [9631]~P68(x96311)+E(f784(f157(x96311),f784(f784(f146(x96312,x96311),f784(f784(f20(x96312,x96311,x96311),f784(f784(f10(x96311,f869(x96311,x96311),x96312),f89(x96311)),x96313)),x96314)),x96315)),f784(f784(f89(x96311),f784(f157(x96311),f784(f784(f146(x96312,x96311),x96313),x96315))),f784(f157(x96311),f784(f784(f146(x96312,x96311),x96314),x96315))))
% 11.41/11.18 [9632]~P3(x96321)+E(f784(f157(x96321),f784(f784(f146(x96322,x96321),f784(f784(f20(x96322,x96321,x96321),f784(f784(f10(x96321,f869(x96321,x96321),x96322),f3(x96321)),x96323)),x96324)),x96325)),f784(f784(f3(x96321),f784(f157(x96321),f784(f784(f146(x96322,x96321),x96323),x96325))),f784(f157(x96321),f784(f784(f146(x96322,x96321),x96324),x96325))))
% 11.41/11.18 [9292]~P85(f784(f784(f242(a859),x92924),x92921))+E(f784(f784(f3(a859),f784(f784(f89(a859),f784(f784(f90(a859),x92921),x92922)),x92923)),f784(f784(f89(a859),f784(f784(f90(a859),x92924),x92922)),x92925)),f784(f784(f3(a859),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x92921),x92924)),x92922)),x92923)),x92925))
% 11.41/11.18 [10029]P25(x100291,x100292,f784(f313(a855,f858(x100291),f784(f784(f20(a855,f869(x100291,f869(a857,a852)),f858(x100291)),f784(f784(f20(a855,a853,f869(f869(x100291,f869(a857,a852)),f858(x100291))),f784(f784(f10(f869(x100291,f869(a857,a852)),f869(a853,f869(f869(x100291,f869(a857,a852)),f858(x100291))),a855),f100(x100291)),x100293)),a29)),x100294)),x100295))+~P25(x100291,f784(f784(f110(f869(f858(x100291),a852)),x100292),f784(f313(a855,f858(x100291),f784(f784(f20(a855,f869(x100291,f869(a857,a852)),f858(x100291)),f784(f784(f20(a855,a853,f869(f869(x100291,f869(a857,a852)),f858(x100291))),f784(f784(f10(f869(x100291,f869(a857,a852)),f869(a853,f869(f869(x100291,f869(a857,a852)),f858(x100291))),a855),f100(x100291)),x100293)),a29)),x100294)),x100295)),f784(f313(a855,f858(x100291),f784(f784(f20(a855,f869(x100291,f869(a857,a852)),f858(x100291)),f784(f784(f20(a855,a853,f869(f869(x100291,f869(a857,a852)),f858(x100291))),f784(f784(f10(f869(x100291,f869(a857,a852)),f869(a853,f869(f869(x100291,f869(a857,a852)),f858(x100291))),a855),f100(x100291)),x100293)),f784(f784(f10(f864(a853),a853,a855),f241(a853)),a32))),x100294)),x100295))
% 11.41/11.18 [5170]E(x51701,x51702)+~E(f33(x51703,x51704,x51701),f33(x51705,x51706,x51702))
% 11.41/11.18 [5171]E(x51711,x51712)+~E(f33(x51713,x51711,x51714),f33(x51715,x51712,x51716))
% 11.41/11.18 [5172]E(x51721,x51722)+~E(f33(x51721,x51723,x51724),f33(x51722,x51725,x51726))
% 11.41/11.18 [5173]E(x51731,x51732)+~E(f35(x51733,x51734,x51731),f35(x51735,x51736,x51732))
% 11.41/11.18 [5174]E(x51741,x51742)+~E(f35(x51743,x51741,x51744),f35(x51745,x51742,x51746))
% 11.41/11.18 [5175]E(x51751,x51752)+~E(f35(x51751,x51753,x51754),f35(x51752,x51755,x51756))
% 11.41/11.18 [5176]E(x51761,x51762)+~E(f34(x51763,x51764,x51761),f34(x51765,x51766,x51762))
% 11.41/11.18 [5177]E(x51771,x51772)+~E(f34(x51773,x51771,x51774),f34(x51775,x51772,x51776))
% 11.41/11.18 [5178]E(x51781,x51782)+~E(f34(x51781,x51783,x51784),f34(x51782,x51785,x51786))
% 11.41/11.18 [7184]E(x71841,x71842)+~E(f225(x71843,x71844,x71845,x71841),f225(x71843,x71844,x71846,x71842))
% 11.41/11.18 [7185]E(x71851,x71852)+~E(f225(x71853,x71854,x71851,x71855),f225(x71853,x71854,x71852,x71856))
% 11.41/11.18 [6631]E(f784(f176(x66311,x66312,x66313,x66314),x66315),f784(f237(x66312),x66316))+~E(f784(x66314,x66315),f784(f237(x66312),x66316))
% 11.41/11.18 [6632]E(f784(f176(x66321,x66322,x66323,x66324),x66325),f784(f237(x66322),x66326))+~E(f784(x66324,x66325),f784(f237(x66322),x66326))
% 11.41/11.18 [6782]E(f784(f239(f864(x67821),x67822,f190(x67821),x67823),f784(x67824,x67825)),f784(x67823,x67826))+~E(f784(x67824,x67825),f784(f237(x67822),x67826))
% 11.41/11.18 [8320]~P20(x83205,x83201,x83202,x83206)+E(f784(f82(x83201,x83201,x83201,f784(x83202,x83203)),f784(x83202,x83204)),f784(f82(x83201,x83201,x83201,f784(x83202,x83204)),f784(x83202,x83203)))
% 11.41/11.18 [8551]~P54(x85514,x85515,x85512,x85511,x85516)+E(f784(x85511,f784(x85512,x85513)),x85513)
% 11.41/11.18 [8693]P26(x86931,x86932,x86933,x86934)+~P26(x86931,x86935,f784(f82(x86932,x86935,x86931,x86936),x86933),x86934)
% 11.41/11.18 [8770]~P26(x87704,x87702,f784(f82(x87701,x87702,x87704,x87703),x87705),x87706)+P26(x87701,x87702,x87703,f784(f313(x87704,x87701,x87705),x87706))
% 11.41/11.18 [9415]P85(f784(f71(x94151),x94152))+~P85(f784(f76(x94151,x94153,x94154,x94155,x94152),x94156))
% 11.41/11.18 [9425]~P85(f784(f784(f347(x94254),x94253),f302(x94254,x94255,x94251,x94252,x94256)))+P85(f784(f784(x94251,x94252),x94253))
% 11.41/11.18 [9426]~P85(f784(f784(f347(x94264),x94263),f299(x94264,x94261,x94265,x94262,x94266)))+P85(f784(f784(x94261,x94262),x94263))
% 11.41/11.18 [9427]~P85(f784(f784(f347(x94274),x94272),f302(x94274,x94271,x94275,x94276,x94273)))+P85(f784(f784(x94271,x94272),x94273))
% 11.41/11.18 [9428]~P85(f784(f784(f347(x94284),x94282),f299(x94284,x94285,x94281,x94286,x94283)))+P85(f784(f784(x94281,x94282),x94283))
% 11.41/11.18 [9597]~P38(f34(x95973,x95974,x95971),x95972,x95975,x95976)+P38(x95971,f784(f784(f784(a196,x95972),f42(x95973)),f784(x95974,x95972)),x95975,f421(x95976,x95975,x95972,x95971,x95974,x95973))
% 11.41/11.18 [9610]~P38(f33(x96106,x96101,x96103),x96102,x96104,x96105)+P38(f784(a29,x96101),f784(f784(f784(a196,f784(f784(a198,x96102),a199)),f42(a28)),f784(x96103,x96102)),x96104,f472(x96105,x96104,x96102,x96103,x96101,x96106))
% 11.41/11.18 [5655]E(x56551,x56552)+~E(f784(f784(f251(x56553,x56554),x56555),x56551),f784(f784(f251(x56553,x56554),x56556),x56552))
% 11.41/11.18 [5656]E(x56561,x56562)+~E(f784(f784(f251(x56563,x56564),x56565),x56561),f784(f784(f251(x56563,x56564),x56566),x56562))
% 11.41/11.18 [5657]E(x56571,x56572)+~E(f784(f784(f251(x56573,x56574),x56571),x56575),f784(f784(f251(x56573,x56574),x56572),x56576))
% 11.41/11.18 [5658]E(x56581,x56582)+~E(f784(f784(f251(x56583,x56584),x56581),x56585),f784(f784(f251(x56583,x56584),x56582),x56586))
% 11.41/11.18 [5797]~P17(x57975,x57976,x57971)+E(f784(f784(x57971,x57972),f784(f784(x57971,x57973),x57974)),f784(f784(x57971,x57973),f784(f784(x57971,x57972),x57974)))
% 11.41/11.18 [7255]~P33(x72554,x72551,f784(f784(f144(x72554),x72552),x72555),f784(f784(f144(x72554),x72553),x72556))+P85(f784(f784(x72551,x72552),x72553))
% 11.41/11.18 [7633]P33(x76331,x76332,x76333,x76334)+~P33(x76331,x76332,f784(f784(f144(x76331),x76335),x76333),f784(f784(f144(x76331),x76336),x76334))
% 11.41/11.18 [8255]~P38(x82553,f784(f784(f784(a196,x82554),f42(x82551)),f784(x82552,x82554)),x82555,x82556)+P38(f34(x82551,x82552,x82553),x82554,x82555,f784(f784(f784(a196,x82556),f42(x82551)),f784(f784(a197,x82554),x82551)))
% 11.41/11.18 [8638]~P54(x86385,x86381,x86382,x86386,x86384)+P85(f784(f784(f347(x86381),f784(x86382,x86383)),x86384))
% 11.41/11.18 [8791]E(f784(f85(x87911,x87912,x87913,x87914,x87915),x87916),f784(x87913,x87916))+P85(f784(f784(f347(x87911),x87916),x87915))
% 11.41/11.18 [8792]E(f784(f85(x87921,x87922,x87923,x87924,x87925),x87926),f784(x87923,x87926))+P85(f784(f784(f347(x87921),x87926),x87925))
% 11.41/11.18 [8810]~E(x88103,f784(f784(f144(x88101),x88105),x88106))+P85(f784(f784(f347(f868(f860(x88101),f860(x88101))),f784(f784(f251(f860(x88101),f860(x88101)),x88102),f784(f784(f130(x88101),x88102),x88103))),f141(x88101,x88104)))
% 11.41/11.18 [8813]E(f784(f85(x88131,x88132,x88133,x88134,x88135),x88136),f784(x88134,x88136))+~P85(f784(f784(f347(x88131),x88136),x88135))
% 11.41/11.18 [8814]E(f784(f85(x88141,x88142,x88143,x88144,x88145),x88146),f784(x88144,x88146))+~P85(f784(f784(f347(x88141),x88146),x88145))
% 11.41/11.18 [8818]E(f784(f178(x88181,x88182,x88183,x88184,x88185),x88186),f784(x88183,x88186))+P85(f784(f784(f347(x88181),x88186),f784(f164(x88181),x88184)))
% 11.41/11.18 [9018]~P38(f784(a29,x90182),f784(f784(f784(a196,f784(f784(a198,x90184),a199)),f42(a28)),f784(x90183,x90184)),x90185,x90186)+P38(f33(x90181,x90182,x90183),x90184,x90185,f784(f784(f784(a196,f784(f784(a198,x90186),f784(a197,x90184))),x90181),f784(f784(a197,x90186),a27)))
% 11.41/11.18 [9492]~P24(x94924,x94922,x94925,x94923,x94926,x94921)+E(f784(x94921,f187(f869(x94922,a852))),x94923)
% 11.41/11.18 [9608]P38(x96081,f784(f784(f784(a196,x96082),f42(x96083)),f784(x96084,x96082)),x96085,f850(x96086,x96085,x96082,x96081,x96084,x96083))+~P38(f34(x96083,x96084,x96081),x96082,x96085,f784(f784(f784(a196,x96086),f42(x96083)),f784(f784(a197,x96082),x96083)))
% 11.41/11.18 [9636]P38(f784(a29,x96361),f784(f784(f784(a196,f784(f784(a198,x96362),a199)),f42(a28)),f784(x96363,x96362)),x96364,f447(x96365,x96364,x96362,x96363,x96361,x96366))+~P38(f33(x96366,x96361,x96363),x96362,x96364,f784(f784(f784(a196,f784(f784(a198,x96365),f784(a197,x96362))),x96366),f784(f784(a197,x96365),a27)))
% 11.41/11.18 [9705]~E(f784(x97054,f784(f250(x97051,x97053),x97055)),f784(x97056,f784(f250(x97051,x97053),x97055)))+E(f784(f262(x97051,x97052,x97053,x97053,x97054,f41(x97053)),x97055),f784(f262(x97051,x97052,x97053,x97053,x97056,f41(x97053)),x97055))
% 11.41/11.18 [9706]~E(f784(x97064,f784(f260(x97061,x97062),x97065)),f784(x97066,f784(f260(x97061,x97062),x97065)))+E(f784(f262(x97061,x97061,x97062,x97063,f41(x97061),x97064),x97065),f784(f262(x97061,x97061,x97062,x97063,f41(x97061),x97066),x97065))
% 11.41/11.18 [9766]~E(f784(f262(x97662,x97666,x97663,x97663,x97661,f41(x97663)),x97664),f784(f262(x97662,x97666,x97663,x97663,x97665,f41(x97663)),x97664))+E(f784(x97661,f784(f250(x97662,x97663),x97664)),f784(x97665,f784(f250(x97662,x97663),x97664)))
% 11.41/11.18 [9767]~E(f784(f262(x97672,x97672,x97673,x97676,f41(x97672),x97671),x97674),f784(f262(x97672,x97672,x97673,x97676,f41(x97672),x97675),x97674))+E(f784(x97671,f784(f260(x97672,x97673),x97674)),f784(x97675,f784(f260(x97672,x97673),x97674)))
% 11.41/11.18 [9828]~P38(f34(x98286,x98285,x98284),x98283,x98282,x98281)+E(f784(f784(f784(a196,f421(x98281,x98282,x98283,x98284,x98285,x98286)),f42(x98286)),f784(f784(a197,x98283),x98286)),x98281)
% 11.41/11.18 [9835]~P38(f34(x98356,x98355,x98354),x98353,x98352,f784(f784(f784(a196,x98351),f42(x98356)),f784(f784(a197,x98353),x98356)))+E(f784(f784(f784(a196,f850(x98351,x98352,x98353,x98354,x98355,x98356)),f42(x98356)),f784(f784(a197,x98353),x98356)),f784(f784(f784(a196,x98351),f42(x98356)),f784(f784(a197,x98353),x98356)))
% 11.41/11.18 [8725]P85(f784(f784(f347(x87251),x87252),x87253))+~P85(f784(f784(f347(f868(x87251,x87254)),f784(f784(f251(x87251,x87254),x87252),x87255)),f784(f784(f258(x87251,x87254),x87253),x87256)))
% 11.41/11.18 [8726]P85(f784(f784(f347(x87261),x87262),x87263))+~P85(f784(f784(f347(f868(x87261,x87264)),f784(f784(f251(x87261,x87264),x87262),x87265)),f784(f784(f258(x87261,x87264),x87263),x87266)))
% 11.41/11.18 [8727]P85(f784(f784(f347(x87271),x87272),x87273))+~P85(f784(f784(f347(f868(x87271,x87274)),f784(f784(f251(x87271,x87274),x87272),x87275)),f784(f784(f258(x87271,x87274),x87273),x87276)))
% 11.41/11.18 [8740]P85(f784(f784(f347(x87401),x87402),f784(x87403,x87404)))+~P85(f784(f784(f347(f868(x87405,x87401)),f784(f784(f251(x87405,x87401),x87404),x87402)),f784(f784(f258(x87405,x87401),x87406),x87403)))
% 11.41/11.18 [8741]P85(f784(f784(f347(x87411),x87412),f784(x87413,x87414)))+~P85(f784(f784(f347(f868(x87415,x87411)),f784(f784(f251(x87415,x87411),x87414),x87412)),f784(f784(f258(x87415,x87411),x87416),x87413)))
% 11.41/11.18 [8742]P85(f784(f784(f347(x87421),x87422),f784(x87423,x87424)))+~P85(f784(f784(f347(f868(x87425,x87421)),f784(f784(f251(x87425,x87421),x87424),x87422)),f784(f784(f258(x87425,x87421),x87426),x87423)))
% 11.41/11.18 [8816]~E(f784(f188(f860(x88161)),x88164),f784(f188(f860(x88162)),x88165))+E(f178(x88161,x88162,x88163,x88164,f784(f784(f130(x88162),x88165),x88166)),f178(x88161,x88162,x88163,x88164,x88165))
% 11.41/11.18 [8817]~E(f784(f188(f860(x88171)),x88174),f784(f188(f860(x88172)),x88176))+E(f178(x88171,x88172,x88173,f784(f784(f130(x88171),x88174),x88175),x88176),f178(x88171,x88172,x88173,x88174,x88176))
% 11.41/11.18 [9051]P85(f784(f784(f347(x90511),x90514),f175(x90511,x90512,x90516)))+E(f176(x90511,x90512,f784(f784(f784(f81(x90511,f864(x90512)),x90513),x90514),f784(f237(x90512),x90515)),x90516),f784(f784(f784(f81(x90511,f864(x90512)),f176(x90511,x90512,x90513,x90516)),x90514),f784(f237(x90512),x90515)))
% 11.41/11.18 [9142]P85(f784(f784(f347(f868(x91421,x91421)),f784(f784(f251(x91421,x91421),f784(x91422,x91423)),f784(x91422,x91424))),x91425))+~P85(f784(f784(f347(f868(x91426,x91426)),f784(f784(f251(x91426,x91426),x91423),x91424)),f784(f784(f290(x91421,x91426),x91425),x91422)))
% 11.41/11.18 [9155]~P85(f784(f784(f347(f868(x91554,x91554)),f784(f784(f251(x91554,x91554),f784(x91556,x91552)),f784(x91556,x91553))),x91555))+P85(f784(f784(f347(f868(x91551,x91551)),f784(f784(f251(x91551,x91551),x91552),x91553)),f784(f784(f290(x91554,x91551),x91555),x91556)))
% 11.41/11.18 [9769]E(f784(f784(f251(x97691,x97692),f717(x97693,x97694,x97695,x97696,x97692,x97691)),f721(x97693,x97694,x97695,x97696,x97692,x97691)),x97696)+~P85(f784(f784(f347(f868(x97691,x97692)),x97696),f784(f784(f291(x97691,x97695,x97692),x97694),x97693)))
% 11.41/11.18 [9963]~P38(f33(x99636,x99635,x99634),x99633,x99632,x99631)+E(f784(f784(f784(a196,f784(f784(a198,f472(x99631,x99632,x99633,x99634,x99635,x99636)),f784(a197,x99633))),x99636),f784(f784(a197,f472(x99631,x99632,x99633,x99634,x99635,x99636)),a27)),x99631)
% 11.41/11.18 [9968]~P38(f33(x99686,x99685,x99684),x99683,x99682,f784(f784(f784(a196,f784(f784(a198,x99681),f784(a197,x99683))),x99686),f784(f784(a197,x99681),a27)))+E(f784(f784(f784(a196,f784(f784(a198,f447(x99681,x99682,x99683,x99684,x99685,x99686)),f784(a197,x99683))),x99686),f784(f784(a197,f447(x99681,x99682,x99683,x99684,x99685,x99686)),a27)),f784(f784(f784(a196,f784(f784(a198,x99681),f784(a197,x99683))),x99686),f784(f784(a197,x99681),a27)))
% 11.41/11.18 [9979]~P85(f784(f784(f347(f868(x99791,x99796)),x99795),f784(f784(f291(x99791,x99792,x99796),x99794),x99793)))+P85(f784(f784(f347(f868(x99791,x99792)),f784(f784(f251(x99791,x99792),f717(x99793,x99794,x99792,x99795,x99796,x99791)),f718(x99793,x99794,x99792,x99795,x99796,x99791))),x99794))
% 11.41/11.18 [9980]~P85(f784(f784(f347(f868(x99806,x99802)),x99805),f784(f784(f291(x99806,x99801,x99802),x99804),x99803)))+P85(f784(f784(f347(f868(x99801,x99802)),f784(f784(f251(x99801,x99802),f718(x99803,x99804,x99801,x99805,x99802,x99806)),f721(x99803,x99804,x99801,x99805,x99802,x99806))),x99803))
% 11.41/11.18 [6071]~E(x60716,x60714)+E(f784(f784(f784(f784(f81(x60711,x60712),x60713),x60714),x60715),x60716),x60715)
% 11.41/11.18 [6072]~E(x60726,x60724)+E(f784(f784(f784(f784(f81(x60721,x60722),x60723),x60724),x60725),x60726),x60725)
% 11.41/11.18 [6119]E(x61191,x61192)+E(f784(f784(f784(f784(f81(x61193,x61194),x61195),x61192),x61196),x61191),f784(x61195,x61191))
% 11.41/11.18 [6120]E(x61201,x61202)+E(f784(f784(f784(f784(f81(x61203,x61204),x61205),x61202),x61206),x61201),f784(x61205,x61201))
% 11.41/11.18 [6121]E(x61211,x61212)+E(f784(f784(f784(f784(f81(x61213,x61214),x61215),x61212),x61216),x61211),f784(x61215,x61211))
% 11.41/11.18 [7698]~P6(x76982)+E(f784(f784(f54(x76981,x76982),x76983),f784(f784(f9(x76981,x76984,x76982),x76985),x76986)),f784(f784(f784(f54(x76981,f869(x76984,x76982)),x76983),x76985),x76986))
% 11.41/11.18 [7699]~P6(x76992)+E(f784(f784(f55(x76991,x76992),x76993),f784(f784(f9(x76991,x76994,x76992),x76995),x76996)),f784(f784(f784(f55(x76991,f869(x76994,x76992)),x76993),x76995),x76996))
% 11.41/11.18 [8284]E(f784(f313(x82841,f864(x82842),f784(f784(f784(f81(x82841,f864(x82842)),x82843),x82844),f784(f237(x82842),x82845))),x82846),f784(f313(x82841,f864(x82842),x82843),x82846))+P85(f784(f784(f347(x82841),x82844),x82846))
% 11.41/11.18 [8473]E(f784(f784(f54(x84731,f869(x84732,a852)),x84733),f784(f784(f10(f869(x84732,a852),f869(x84732,a852),x84731),f784(f312(x84732),x84734)),x84735)),f784(f784(f312(x84732),x84734),f784(f784(f54(x84731,f869(x84732,a852)),x84733),x84735)))+~P85(f784(f784(f347(x84731),x84736),x84733))
% 11.41/11.18 [8474]E(f784(f784(f55(x84741,f869(x84742,a852)),x84743),f784(f784(f10(f869(x84742,a852),f869(x84742,a852),x84741),f784(f312(x84742),x84744)),x84745)),f784(f784(f312(x84742),x84744),f784(f784(f55(x84741,f869(x84742,a852)),x84743),x84745)))+~P85(f784(f784(f347(x84741),x84746),x84743))
% 11.41/11.18 [8856]~P6(x88562)+E(f784(f784(f54(x88561,x88562),x88563),f784(f784(f10(f869(x88564,x88562),x88562,x88561),f784(f54(x88564,x88562),x88565)),f784(f9(x88564,x88561,x88562),x88566))),f784(f784(f54(x88564,x88562),x88565),f784(f784(f10(f869(x88561,x88562),x88562,x88564),f784(f54(x88561,x88562),x88563)),x88566)))
% 11.41/11.18 [8857]~P6(x88572)+E(f784(f784(f55(x88571,x88572),x88573),f784(f784(f10(f869(x88574,x88572),x88572,x88571),f784(f55(x88574,x88572),x88575)),f784(f9(x88574,x88571,x88572),x88576))),f784(f784(f55(x88574,x88572),x88575),f784(f784(f10(f869(x88571,x88572),x88572,x88574),f784(f55(x88571,x88572),x88573)),x88576)))
% 11.41/11.18 [9057]P85(f784(f784(f347(x90571),x90572),f784(f164(x90571),x90573)))+~P85(f784(f784(f347(f868(x90574,x90571)),f784(f784(f251(x90574,x90571),x90575),x90572)),f784(f164(f868(x90574,x90571)),f784(f784(f173(x90574,x90571),x90576),x90573))))
% 11.41/11.18 [9058]P85(f784(f784(f347(x90581),x90582),f784(f164(x90581),x90583)))+~P85(f784(f784(f347(f868(x90581,x90584)),f784(f784(f251(x90581,x90584),x90582),x90585)),f784(f164(f868(x90581,x90584)),f784(f784(f173(x90581,x90584),x90583),x90586))))
% 11.41/11.18 [9059]P85(f784(f784(f347(x90591),x90592),f784(f164(x90591),x90593)))+~P85(f784(f784(f347(f868(x90594,x90591)),f784(f784(f251(x90594,x90591),x90595),x90592)),f784(f164(f868(x90594,x90591)),f784(f784(f173(x90594,x90591),x90596),x90593))))
% 11.41/11.18 [9060]P85(f784(f784(f347(x90601),x90602),f784(f164(x90601),x90603)))+~P85(f784(f784(f347(f868(x90601,x90604)),f784(f784(f251(x90601,x90604),x90602),x90605)),f784(f164(f868(x90601,x90604)),f784(f784(f173(x90601,x90604),x90603),x90606))))
% 11.41/11.18 [9153]P85(f784(f784(f242(f869(x91531,a852)),f784(f287(x91532,x91531,x91533),x91534)),x91535))+~P85(f784(f784(f242(f869(f868(x91532,x91531),a852)),x91533),f784(f784(f258(x91532,x91531),x91536),f784(f18(f869(x91531,a852),x91532),x91535))))
% 11.41/11.18 [9328]P85(f784(f784(f347(f868(f860(x93281),f860(x93281))),f784(f784(f251(f860(x93281),f860(x93281)),f784(f784(f144(x93281),x93282),x93283)),f784(f784(f144(x93281),x93284),x93285))),f141(x93281,x93286)))+~P85(f784(f784(f347(f868(x93281,x93281)),f784(f784(f251(x93281,x93281),x93282),x93284)),x93286))
% 11.41/11.18 [9765]E(f784(f784(f251(x97651,x97652),f624(x97653,x97654,x97655,x97652,x97651,x97656)),f625(x97653,x97654,x97655,x97652,x97651,x97656)),x97656)+P85(f784(f784(f347(x97655),x97654),f784(f784(f261(x97651,x97652,f869(x97655,a852)),x97653),x97656)))
% 11.41/11.18 [9770]E(f784(f784(f251(x97701,x97702),f626(x97703,x97704,x97702,x97701,x97705,x97706)),f627(x97703,x97704,x97702,x97701,x97705,x97706)),x97703)+~P85(f784(f784(f347(x97706),x97705),f784(f784(f261(x97701,x97702,f869(x97706,a852)),x97704),x97703)))
% 11.41/11.18 [9932]P85(f784(f784(f347(x99321),x99322),f784(f784(x99323,f626(x99324,x99323,x99325,x99326,x99322,x99321)),f627(x99324,x99323,x99325,x99326,x99322,x99321))))+~P85(f784(f784(f347(x99321),x99322),f784(f784(f261(x99326,x99325,f869(x99321,a852)),x99323),x99324)))
% 11.41/11.18 [9956]~P85(f784(f784(f347(x99561),x99562),f784(f784(x99565,f624(x99565,x99562,x99561,x99564,x99563,x99566)),f625(x99565,x99562,x99561,x99564,x99563,x99566))))+P85(f784(f784(f347(x99561),x99562),f784(f784(f261(x99563,x99564,f869(x99561,a852)),x99565),x99566)))
% 11.41/11.18 [7823]P85(f784(f784(f347(x78231),x78234),x78236))+E(f179(x78231,x78232,f784(f784(f784(f81(x78231,f864(x78232)),x78233),x78234),x78235),x78236),f179(x78231,x78232,x78233,x78236))
% 11.41/11.18 [7898]P85(f784(f784(f347(x78981),x78984),x78986))+E(f784(f313(x78981,x78982,f784(f784(f784(f81(x78981,x78982),x78983),x78984),x78985)),x78986),f784(f313(x78981,x78982,x78983),x78986))
% 11.41/11.18 [7925]P85(f784(f784(f347(x79251),x79254),f784(f164(x79251),x79256)))+E(f784(f784(f146(x79251,x79252),f784(f784(f784(f81(x79251,x79252),x79253),x79254),x79255)),x79256),f784(f784(f146(x79251,x79252),x79253),x79256))
% 11.41/11.18 [8370]E(x83701,x83702)+E(f784(f784(f151(x83703,f784(f784(f151(x83703,x83704),x83701),x83705)),x83702),x83706),f784(f784(f151(x83703,f784(f784(f151(x83703,x83704),x83702),x83706)),x83701),x83705))
% 11.41/11.18 [8862]~P85(f784(f784(f347(x88623),x88626),x88625))+E(f784(f784(f312(x88621),x88622),f784(f313(x88623,x88621,x88624),f784(f784(f3(f869(x88623,a852)),x88625),f784(f784(f312(x88623),x88626),f187(f869(x88623,a852)))))),f784(f313(x88623,x88621,f784(f784(f784(f81(x88623,x88621),x88624),x88626),x88622)),x88625))
% 11.41/11.18 [9590]E(f178(x95901,x95902,x95903,f784(f784(f130(x95901),x95904),f784(f784(f144(x95901),x95905),f120(x95901))),x95906),f784(f784(f784(f81(x95901,f864(x95902)),f178(x95901,x95902,x95903,x95904,x95906)),x95905),f784(f237(x95902),f784(f784(f155(x95902),x95906),f784(f188(f860(x95901)),x95904)))))+~P85(f784(f784(f243(a859),f784(f188(f860(x95901)),x95904)),f784(f188(f860(x95902)),x95906)))
% 11.41/11.18 [8688]~E(x86883,x86886)+E(f784(f172(x86881,x86882,f784(f784(f144(f868(x86881,x86882)),f784(f784(f251(x86881,x86882),x86883),x86884)),x86885)),x86886),f784(f237(x86882),x86884))
% 11.41/11.18 [8729]E(x87291,x87292)+E(f784(f172(x87293,x87294,f784(f784(f144(f868(x87293,x87294)),f784(f784(f251(x87293,x87294),x87291),x87295)),x87296)),x87292),f784(f172(x87293,x87294,x87296),x87292))
% 11.41/11.18 [8936]~P85(f784(f784(x89364,x89365),x89366))+P85(f784(f784(f784(f784(f110(f869(x89361,f869(x89362,a852))),x89363),x89364),x89365),x89366))
% 11.41/11.18 [8937]~P85(f784(f784(x89374,x89375),x89376))+P85(f784(f784(f784(f784(f110(f869(x89371,f869(x89372,a852))),x89373),x89374),x89375),x89376))
% 11.41/11.18 [8938]~P85(f784(f784(x89383,x89385),x89386))+P85(f784(f784(f784(f784(f110(f869(x89381,f869(x89382,a852))),x89383),x89384),x89385),x89386))
% 11.41/11.18 [8939]~P85(f784(f784(x89393,x89395),x89396))+P85(f784(f784(f784(f784(f110(f869(x89391,f869(x89392,a852))),x89393),x89394),x89395),x89396))
% 11.41/11.18 [9190]P85(f784(f784(x91901,x91902),x91903))+~P85(f784(f784(f784(f784(f111(f869(x91904,f869(x91905,a852))),x91906),x91901),x91902),x91903))
% 11.41/11.18 [9191]P85(f784(f784(x91911,x91912),x91913))+~P85(f784(f784(f784(f784(f111(f869(x91914,f869(x91915,a852))),x91911),x91916),x91912),x91913))
% 11.41/11.18 [9192]P85(f784(f784(x91921,x91922),x91923))+~P85(f784(f784(f784(f784(f111(f869(x91924,f869(x91925,a852))),x91926),x91921),x91922),x91923))
% 11.41/11.18 [9193]P85(f784(f784(x91931,x91932),x91933))+~P85(f784(f784(f784(f784(f111(f869(x91934,f869(x91935,a852))),x91931),x91936),x91932),x91933))
% 11.41/11.18 [9615]~P68(x96152)+E(f784(f784(f8(x96151,x96152),f784(f784(f9(x96151,f869(x96153,a852),x96152),f784(f784(f10(f869(x96153,x96152),f869(f869(x96153,a852),x96152),x96151),f8(x96153,x96152)),x96154)),x96155)),x96156),f784(f784(f8(f868(x96151,x96153),x96152),f784(f261(x96151,x96153,x96152),x96154)),f784(f784(f258(x96151,x96153),x96156),f784(f18(f869(x96153,a852),x96151),x96155))))
% 11.41/11.18 [9616]~P71(x96162)+E(f784(f784(f11(x96161,x96162),f784(f784(f9(x96161,f869(x96163,a852),x96162),f784(f784(f10(f869(x96163,x96162),f869(f869(x96163,a852),x96162),x96161),f11(x96163,x96162)),x96164)),x96165)),x96166),f784(f784(f11(f868(x96161,x96163),x96162),f784(f261(x96161,x96163,x96162),x96164)),f784(f784(f258(x96161,x96163),x96166),f784(f18(f869(x96163,a852),x96161),x96165))))
% 11.41/11.18 [9732]~P68(x97322)+E(f784(f784(f8(x97321,x97322),f784(f784(f9(x97321,f869(x97323,a852),x97322),f784(f784(f10(f869(x97323,x97322),f869(f869(x97323,a852),x97322),x97321),f8(x97323,x97322)),f784(f9(x97323,x97321,x97322),x97324))),x97325)),x97326),f784(f784(f8(x97323,x97322),f784(f784(f9(x97323,f869(x97321,a852),x97322),f784(f784(f10(f869(x97321,x97322),f869(f869(x97321,a852),x97322),x97323),f8(x97321,x97322)),x97324)),x97326)),x97325))
% 11.41/11.18 [9456]~P85(f784(f784(f347(x94561),x94565),x94564))+E(f784(f784(f784(f81(x94561,f864(x94562)),f179(x94561,x94562,x94563,f784(f784(f3(f869(x94561,a852)),x94564),f784(f784(f312(x94561),x94565),f187(f869(x94561,a852)))))),x94565),x94566),f179(x94561,x94562,f784(f784(f784(f81(x94561,f864(x94562)),x94563),x94565),x94566),x94564))
% 11.41/11.18 [9510]~P85(f784(f784(f347(x95101),x95105),x95104))+E(f784(f784(f784(f81(x95101,f864(x95102)),f179(x95101,x95102,x95103,f784(f784(f3(f869(x95101,a852)),x95104),f784(f784(f312(x95101),x95105),f187(f869(x95101,a852)))))),x95105),x95106),f784(f784(f784(f81(x95101,f864(x95102)),f179(x95101,x95102,x95103,x95104)),x95105),x95106))
% 11.41/11.18 [10032]~P85(f784(f784(f347(f868(x100321,x100322)),f784(f784(f251(x100321,x100322),x100325),x100326)),f784(f784(f110(f869(f868(x100321,x100322),a852)),x100323),x100324)))+P85(f784(f784(f784(f784(f110(f869(x100321,f869(x100322,a852))),f784(f784(f9(x100321,f869(f868(x100321,x100322),a852),f869(x100322,a852)),f784(f784(f10(f869(x100322,f869(f869(f868(x100321,x100322),a852),a852)),f869(f869(f868(x100321,x100322),a852),f869(x100322,a852)),x100321),f9(x100322,f869(f868(x100321,x100322),a852),a852)),f784(f784(f10(f869(x100322,f868(x100321,x100322)),f869(x100322,f869(f869(f868(x100321,x100322),a852),a852)),x100321),f784(f10(f868(x100321,x100322),f869(f869(f868(x100321,x100322),a852),a852),x100322),f347(f868(x100321,x100322)))),f251(x100321,x100322)))),x100323)),f784(f784(f9(x100321,f869(f868(x100321,x100322),a852),f869(x100322,a852)),f784(f784(f10(f869(x100322,f869(f869(f868(x100321,x100322),a852),a852)),f869(f869(f868(x100321,x100322),a852),f869(x100322,a852)),x100321),f9(x100322,f869(f868(x100321,x100322),a852),a852)),f784(f784(f10(f869(x100322,f868(x100321,x100322)),f869(x100322,f869(f869(f868(x100321,x100322),a852),a852)),x100321),f784(f10(f868(x100321,x100322),f869(f869(f868(x100321,x100322),a852),a852),x100322),f347(f868(x100321,x100322)))),f251(x100321,x100322)))),x100324)),x100325),x100326))
% 11.41/11.18 [10033]~P85(f784(f784(f347(f868(x100331,x100332)),f784(f784(f251(x100331,x100332),x100335),x100336)),f784(f784(f111(f869(f868(x100331,x100332),a852)),x100333),x100334)))+P85(f784(f784(f784(f784(f111(f869(x100331,f869(x100332,a852))),f784(f784(f9(x100331,f869(f868(x100331,x100332),a852),f869(x100332,a852)),f784(f784(f10(f869(x100332,f869(f869(f868(x100331,x100332),a852),a852)),f869(f869(f868(x100331,x100332),a852),f869(x100332,a852)),x100331),f9(x100332,f869(f868(x100331,x100332),a852),a852)),f784(f784(f10(f869(x100332,f868(x100331,x100332)),f869(x100332,f869(f869(f868(x100331,x100332),a852),a852)),x100331),f784(f10(f868(x100331,x100332),f869(f869(f868(x100331,x100332),a852),a852),x100332),f347(f868(x100331,x100332)))),f251(x100331,x100332)))),x100333)),f784(f784(f9(x100331,f869(f868(x100331,x100332),a852),f869(x100332,a852)),f784(f784(f10(f869(x100332,f869(f869(f868(x100331,x100332),a852),a852)),f869(f869(f868(x100331,x100332),a852),f869(x100332,a852)),x100331),f9(x100332,f869(f868(x100331,x100332),a852),a852)),f784(f784(f10(f869(x100332,f868(x100331,x100332)),f869(x100332,f869(f869(f868(x100331,x100332),a852),a852)),x100331),f784(f10(f868(x100331,x100332),f869(f869(f868(x100331,x100332),a852),a852),x100332),f347(f868(x100331,x100332)))),f251(x100331,x100332)))),x100334)),x100335),x100336))
% 11.41/11.18 [10037]P85(f784(f784(f347(f868(x100371,x100372)),f784(f784(f251(x100371,x100372),x100373),x100374)),f784(f784(f110(f869(f868(x100371,x100372),a852)),x100375),x100376)))+~P85(f784(f784(f784(f784(f110(f869(x100371,f869(x100372,a852))),f784(f784(f9(x100371,f869(f868(x100371,x100372),a852),f869(x100372,a852)),f784(f784(f10(f869(x100372,f869(f869(f868(x100371,x100372),a852),a852)),f869(f869(f868(x100371,x100372),a852),f869(x100372,a852)),x100371),f9(x100372,f869(f868(x100371,x100372),a852),a852)),f784(f784(f10(f869(x100372,f868(x100371,x100372)),f869(x100372,f869(f869(f868(x100371,x100372),a852),a852)),x100371),f784(f10(f868(x100371,x100372),f869(f869(f868(x100371,x100372),a852),a852),x100372),f347(f868(x100371,x100372)))),f251(x100371,x100372)))),x100375)),f784(f784(f9(x100371,f869(f868(x100371,x100372),a852),f869(x100372,a852)),f784(f784(f10(f869(x100372,f869(f869(f868(x100371,x100372),a852),a852)),f869(f869(f868(x100371,x100372),a852),f869(x100372,a852)),x100371),f9(x100372,f869(f868(x100371,x100372),a852),a852)),f784(f784(f10(f869(x100372,f868(x100371,x100372)),f869(x100372,f869(f869(f868(x100371,x100372),a852),a852)),x100371),f784(f10(f868(x100371,x100372),f869(f869(f868(x100371,x100372),a852),a852),x100372),f347(f868(x100371,x100372)))),f251(x100371,x100372)))),x100376)),x100373),x100374))
% 11.41/11.18 [10038]P85(f784(f784(f347(f868(x100381,x100382)),f784(f784(f251(x100381,x100382),x100383),x100384)),f784(f784(f111(f869(f868(x100381,x100382),a852)),x100385),x100386)))+~P85(f784(f784(f784(f784(f111(f869(x100381,f869(x100382,a852))),f784(f784(f9(x100381,f869(f868(x100381,x100382),a852),f869(x100382,a852)),f784(f784(f10(f869(x100382,f869(f869(f868(x100381,x100382),a852),a852)),f869(f869(f868(x100381,x100382),a852),f869(x100382,a852)),x100381),f9(x100382,f869(f868(x100381,x100382),a852),a852)),f784(f784(f10(f869(x100382,f868(x100381,x100382)),f869(x100382,f869(f869(f868(x100381,x100382),a852),a852)),x100381),f784(f10(f868(x100381,x100382),f869(f869(f868(x100381,x100382),a852),a852),x100382),f347(f868(x100381,x100382)))),f251(x100381,x100382)))),x100385)),f784(f784(f9(x100381,f869(f868(x100381,x100382),a852),f869(x100382,a852)),f784(f784(f10(f869(x100382,f869(f869(f868(x100381,x100382),a852),a852)),f869(f869(f868(x100381,x100382),a852),f869(x100382,a852)),x100381),f9(x100382,f869(f868(x100381,x100382),a852),a852)),f784(f784(f10(f869(x100382,f868(x100381,x100382)),f869(x100382,f869(f869(f868(x100381,x100382),a852),a852)),x100381),f784(f10(f868(x100381,x100382),f869(f869(f868(x100381,x100382),a852),a852),x100382),f347(f868(x100381,x100382)))),f251(x100381,x100382)))),x100386)),x100383),x100384))
% 11.41/11.18 [10027]~P85(f784(f784(f347(f868(x100272,x100273)),f784(f784(f251(x100272,x100273),x100275),x100276)),f784(f784(f54(x100271,f869(f868(x100272,x100273),a852)),f249(f869(x100271,a852))),x100274)))+P85(f784(f784(f784(f784(f54(x100271,f869(x100272,f869(x100273,a852))),f249(f869(x100271,a852))),f784(f784(f10(f869(f868(x100272,x100273),a852),f869(x100272,f869(x100273,a852)),x100271),f784(f9(x100272,f869(f868(x100272,x100273),a852),f869(x100273,a852)),f784(f784(f10(f869(x100273,f869(f869(f868(x100272,x100273),a852),a852)),f869(f869(f868(x100272,x100273),a852),f869(x100273,a852)),x100272),f9(x100273,f869(f868(x100272,x100273),a852),a852)),f784(f784(f10(f869(x100273,f868(x100272,x100273)),f869(x100273,f869(f869(f868(x100272,x100273),a852),a852)),x100272),f784(f10(f868(x100272,x100273),f869(f869(f868(x100272,x100273),a852),a852),x100273),f347(f868(x100272,x100273)))),f251(x100272,x100273))))),x100274)),x100275),x100276))
% 11.41/11.18 [10028]~P85(f784(f784(f347(f868(x100282,x100283)),f784(f784(f251(x100282,x100283),x100285),x100286)),f784(f784(f55(x100281,f869(f868(x100282,x100283),a852)),f249(f869(x100281,a852))),x100284)))+P85(f784(f784(f784(f784(f55(x100281,f869(x100282,f869(x100283,a852))),f249(f869(x100281,a852))),f784(f784(f10(f869(f868(x100282,x100283),a852),f869(x100282,f869(x100283,a852)),x100281),f784(f9(x100282,f869(f868(x100282,x100283),a852),f869(x100283,a852)),f784(f784(f10(f869(x100283,f869(f869(f868(x100282,x100283),a852),a852)),f869(f869(f868(x100282,x100283),a852),f869(x100283,a852)),x100282),f9(x100283,f869(f868(x100282,x100283),a852),a852)),f784(f784(f10(f869(x100283,f868(x100282,x100283)),f869(x100283,f869(f869(f868(x100282,x100283),a852),a852)),x100282),f784(f10(f868(x100282,x100283),f869(f869(f868(x100282,x100283),a852),a852),x100283),f347(f868(x100282,x100283)))),f251(x100282,x100283))))),x100284)),x100285),x100286))
% 11.41/11.18 [10035]P85(f784(f784(f347(f868(x100351,x100352)),f784(f784(f251(x100351,x100352),x100353),x100354)),f784(f784(f54(x100355,f869(f868(x100351,x100352),a852)),f249(f869(x100355,a852))),x100356)))+~P85(f784(f784(f784(f784(f54(x100355,f869(x100351,f869(x100352,a852))),f249(f869(x100355,a852))),f784(f784(f10(f869(f868(x100351,x100352),a852),f869(x100351,f869(x100352,a852)),x100355),f784(f9(x100351,f869(f868(x100351,x100352),a852),f869(x100352,a852)),f784(f784(f10(f869(x100352,f869(f869(f868(x100351,x100352),a852),a852)),f869(f869(f868(x100351,x100352),a852),f869(x100352,a852)),x100351),f9(x100352,f869(f868(x100351,x100352),a852),a852)),f784(f784(f10(f869(x100352,f868(x100351,x100352)),f869(x100352,f869(f869(f868(x100351,x100352),a852),a852)),x100351),f784(f10(f868(x100351,x100352),f869(f869(f868(x100351,x100352),a852),a852),x100352),f347(f868(x100351,x100352)))),f251(x100351,x100352))))),x100356)),x100353),x100354))
% 11.41/11.18 [10036]P85(f784(f784(f347(f868(x100361,x100362)),f784(f784(f251(x100361,x100362),x100363),x100364)),f784(f784(f55(x100365,f869(f868(x100361,x100362),a852)),f249(f869(x100365,a852))),x100366)))+~P85(f784(f784(f784(f784(f55(x100365,f869(x100361,f869(x100362,a852))),f249(f869(x100365,a852))),f784(f784(f10(f869(f868(x100361,x100362),a852),f869(x100361,f869(x100362,a852)),x100365),f784(f9(x100361,f869(f868(x100361,x100362),a852),f869(x100362,a852)),f784(f784(f10(f869(x100362,f869(f869(f868(x100361,x100362),a852),a852)),f869(f869(f868(x100361,x100362),a852),f869(x100362,a852)),x100361),f9(x100362,f869(f868(x100361,x100362),a852),a852)),f784(f784(f10(f869(x100362,f868(x100361,x100362)),f869(x100362,f869(f869(f868(x100361,x100362),a852),a852)),x100361),f784(f10(f868(x100361,x100362),f869(f869(f868(x100361,x100362),a852),a852),x100362),f347(f868(x100361,x100362)))),f251(x100361,x100362))))),x100366)),x100363),x100364))
% 11.41/11.18 [9127]E(x91271,x91272)+~E(f332(x91273,x91274,x91275,x91276,x91271),f332(x91273,x91274,x91275,x91277,x91272))
% 11.41/11.18 [9128]E(x91281,x91282)+~E(f332(x91283,x91284,x91285,x91281,x91286),f332(x91283,x91284,x91285,x91282,x91287))
% 11.41/11.18 [7373]E(f784(x73731,f784(x73732,x73733)),f784(x73734,x73733))+~E(f784(f82(x73735,x73736,x73737,x73731),x73732),x73734)
% 11.41/11.18 [9491]~P23(x94913,x94914,x94911,x94915,x94916,x94917)+E(f784(f784(x94911,x94912),x94912),x94912)
% 11.41/11.18 [9825]~P50(x98255,x98256,x98257,x98251,x98254,x98252,x98253)+P85(f784(f784(x98251,x98252),f593(x98253,x98252,x98254,x98251)))
% 11.41/11.18 [9854]~E(f784(f239(f864(x98547),x98541,f190(x98547),x98545),f784(x98544,x98543)),f784(f237(x98547),x98542))+E(f784(f237(x98541),f724(x98542,x98543,x98544,x98545,x98546,x98547,x98541)),f784(x98544,x98543))
% 11.41/11.18 [9855]~E(f784(f239(f864(x98556),x98557,f190(x98556),x98551),f784(x98554,x98553)),f784(f237(x98556),x98552))+E(f784(x98551,f724(x98552,x98553,x98554,x98551,x98555,x98556,x98557)),f784(f237(x98556),x98552))
% 11.41/11.18 [5893]~E(f784(f784(f146(x58931,x58935),x58936),x58932),f784(f784(f146(x58933,x58935),x58937),x58934))+E(f784(f188(f860(x58931)),x58932),f784(f188(f860(x58933)),x58934))
% 11.41/11.18 [7448]E(x74481,x74482)+~E(f784(f784(f784(f81(x74483,f864(x74484)),x74485),x74486),f784(f237(x74484),x74481)),f784(f784(f784(f81(x74483,f864(x74484)),x74487),x74486),f784(f237(x74484),x74482)))
% 11.41/11.18 [8405]E(f784(x84051,f784(x84052,x84053)),f784(x84054,x84053))+~E(f784(f82(x84055,x84056,x84057,x84051),x84052),f784(f82(x84056,x84056,x84057,f41(x84056)),x84054))
% 11.41/11.18 [9831]~P50(x98315,x98316,x98317,x98314,x98311,x98313,x98312)+P85(f784(f784(x98311,f593(x98312,x98313,x98311,x98314)),x98312))
% 11.41/11.18 [5939]E(x59391,x59392)+~E(f784(f784(f784(f100(x59393),x59394),x59395),x59391),f784(f784(f784(f100(x59393),x59396),x59397),x59392))
% 11.41/11.18 [5940]E(x59401,x59402)+~E(f784(f784(f784(f100(x59403),x59404),x59401),x59405),f784(f784(f784(f100(x59403),x59406),x59402),x59407))
% 11.41/11.18 [5941]E(x59411,x59412)+~E(f784(f784(f784(f100(x59413),x59411),x59414),x59415),f784(f784(f784(f100(x59413),x59412),x59416),x59417))
% 11.41/11.18 [8820]~P21(x88206,x88201,x88203,x88207)+E(f784(f82(x88201,x88201,x88202,f784(x88203,x88204)),f784(f82(x88201,x88201,x88202,f784(x88203,x88204)),x88205)),f784(f82(x88201,x88201,x88202,f784(x88203,x88204)),x88205))
% 11.41/11.18 [9572]E(f178(x95721,x95722,f784(f784(f784(f81(x95721,f864(x95722)),x95723),x95724),f784(f237(x95722),x95725)),x95726,x95727),f784(f784(f784(f81(x95721,f864(x95722)),f178(x95721,x95722,x95723,x95726,x95727)),x95724),f784(f237(x95722),x95725)))+P85(f784(f784(f347(x95721),x95724),f784(f164(x95721),x95726)))
% 11.41/11.18 [8819]~P85(f784(f784(f347(x88191),x88192),f784(f784(x88195,x88196),x88197)))+P85(f784(f784(f347(x88191),x88192),f784(f784(f261(x88193,x88194,f869(x88191,a852)),x88195),f784(f784(f251(x88193,x88194),x88196),x88197))))
% 11.41/11.18 [9087]P85(f784(f784(f784(x90871,x90872),x90873),x90874))+~P85(f784(f784(f784(f261(x90875,x90876,f869(x90877,a852)),x90871),f784(f784(f251(x90875,x90876),x90872),x90873)),x90874))
% 11.41/11.18 [9205]P85(f784(f784(f347(x92051),f784(f784(x92052,x92053),x92054)),f784(f313(f868(x92055,x92056),x92051,f784(f261(x92055,x92056,x92051),x92052)),x92057)))+~P85(f784(f784(f347(f868(x92055,x92056)),f784(f784(f251(x92055,x92056),x92053),x92054)),x92057))
% 11.41/11.18 [9531]P85(f784(f784(f347(f868(f860(x95311),f860(x95311))),f784(f784(f251(f860(x95311),f860(x95311)),f784(f784(f130(x95311),x95312),f784(f784(f144(x95311),x95313),x95314))),f784(f784(f130(x95311),x95312),f784(f784(f144(x95311),x95315),x95316)))),f141(x95311,x95317)))+~P85(f784(f784(f347(f868(x95311,x95311)),f784(f784(f251(x95311,x95311),x95313),x95315)),x95317))
% 11.41/11.18 [9955]P50(x99551,x99552,x99553,f784(f784(f9(x99551,f869(f868(x99551,x99552),a852),f869(x99552,a852)),f784(f784(f10(f869(x99552,f869(f869(f868(x99551,x99552),a852),a852)),f869(f869(f868(x99551,x99552),a852),f869(x99552,a852)),x99551),f9(x99552,f869(f868(x99551,x99552),a852),a852)),f784(f784(f10(f869(x99552,f868(x99551,x99552)),f869(x99552,f869(f869(f868(x99551,x99552),a852),a852)),x99551),f784(f10(f868(x99551,x99552),f869(f869(f868(x99551,x99552),a852),a852),x99552),f347(f868(x99551,x99552)))),f251(x99551,x99552)))),x99554),f784(f784(f9(x99552,f869(f868(x99552,x99553),a852),f869(x99553,a852)),f784(f784(f10(f869(x99553,f869(f869(f868(x99552,x99553),a852),a852)),f869(f869(f868(x99552,x99553),a852),f869(x99553,a852)),x99552),f9(x99553,f869(f868(x99552,x99553),a852),a852)),f784(f784(f10(f869(x99553,f868(x99552,x99553)),f869(x99553,f869(f869(f868(x99552,x99553),a852),a852)),x99552),f784(f10(f868(x99552,x99553),f869(f869(f868(x99552,x99553),a852),a852),x99553),f347(f868(x99552,x99553)))),f251(x99552,x99553)))),x99555),x99556,x99557)+~P85(f784(f784(f347(f868(x99551,x99553)),f784(f784(f251(x99551,x99553),x99556),x99557)),f784(f784(f291(x99551,x99552,x99553),x99554),x99555)))
% 11.41/11.18 [9986]~P50(x99861,x99865,x99862,f784(f784(f9(x99861,f869(f868(x99861,x99865),a852),f869(x99865,a852)),f784(f784(f10(f869(x99865,f869(f869(f868(x99861,x99865),a852),a852)),f869(f869(f868(x99861,x99865),a852),f869(x99865,a852)),x99861),f9(x99865,f869(f868(x99861,x99865),a852),a852)),f784(f784(f10(f869(x99865,f868(x99861,x99865)),f869(x99865,f869(f869(f868(x99861,x99865),a852),a852)),x99861),f784(f10(f868(x99861,x99865),f869(f869(f868(x99861,x99865),a852),a852),x99865),f347(f868(x99861,x99865)))),f251(x99861,x99865)))),x99866),f784(f784(f9(x99865,f869(f868(x99865,x99862),a852),f869(x99862,a852)),f784(f784(f10(f869(x99862,f869(f869(f868(x99865,x99862),a852),a852)),f869(f869(f868(x99865,x99862),a852),f869(x99862,a852)),x99865),f9(x99862,f869(f868(x99865,x99862),a852),a852)),f784(f784(f10(f869(x99862,f868(x99865,x99862)),f869(x99862,f869(f869(f868(x99865,x99862),a852),a852)),x99865),f784(f10(f868(x99865,x99862),f869(f869(f868(x99865,x99862),a852),a852),x99862),f347(f868(x99865,x99862)))),f251(x99865,x99862)))),x99867),x99863,x99864)+P85(f784(f784(f347(f868(x99861,x99862)),f784(f784(f251(x99861,x99862),x99863),x99864)),f784(f784(f291(x99861,x99865,x99862),x99866),x99867)))
% 11.41/11.18 [9082]E(x90821,x90822)+E(f784(f784(f784(f81(x90823,x90824),f784(f784(f784(f81(x90823,x90824),x90825),x90821),x90826)),x90822),x90827),f784(f784(f784(f81(x90823,x90824),f784(f784(f784(f81(x90823,x90824),x90825),x90822),x90827)),x90821),x90826))
% 11.41/11.18 [9302]E(f178(x93021,x93022,f784(f784(f784(f81(x93021,f864(x93022)),x93023),x93024),f784(f237(x93022),x93025)),x93026,x93027),f178(x93021,x93022,x93023,x93026,x93027))+~P85(f784(f784(f347(x93021),x93024),f784(f164(x93021),f784(f784(f165(x93021),f784(f188(f860(x93022)),x93027)),x93026))))
% 11.41/11.18 [9600]E(f178(x96001,x96002,f784(f784(f784(f81(x96001,f864(x96002)),x96003),x96004),f784(f237(x96002),x96005)),x96006,x96007),f784(f784(f784(f81(x96001,f864(x96002)),f178(x96001,x96002,x96003,x96006,x96007)),x96004),f784(f237(x96002),x96005)))+P85(f784(f784(f347(x96001),x96004),f784(f164(x96001),f784(f784(f165(x96001),f784(f188(f860(x96002)),x96007)),x96006))))
% 11.41/11.18 [9967]P85(f784(f784(f347(x99671),f681(x99672,x99673,x99674,x99675,x99676,x99677,x99671)),x99675))+P85(f784(f784(f784(f784(f55(x99671,f869(x99677,f869(x99676,a852))),x99675),x99674),x99673),x99672))
% 11.41/11.18 [9969]P85(f784(f784(f347(x99691),f440(x99692,x99693,x99694,x99695,x99696,x99697,x99691)),x99695))+~P85(f784(f784(f784(f784(f54(x99691,f869(x99697,f869(x99696,a852))),x99695),x99694),x99693),x99692))
% 11.41/11.18 [9996]P85(f784(f784(f784(x99961,f440(x99962,x99963,x99961,x99964,x99965,x99966,x99967)),x99963),x99962))+~P85(f784(f784(f784(f784(f54(x99967,f869(x99966,f869(x99965,a852))),x99964),x99961),x99963),x99962))
% 11.41/11.18 [10012]~P85(f784(f784(f784(x100125,f681(x100127,x100126,x100125,x100124,x100123,x100122,x100121)),x100126),x100127))+P85(f784(f784(f784(f784(f55(x100121,f869(x100122,f869(x100123,a852))),x100124),x100125),x100126),x100127))
% 11.41/11.18 [9978]~P139(x99782)+E(f784(f784(f8(x99781,x99782),f784(f784(f9(x99781,f869(x99783,a852),x99782),f784(f784(f10(f869(x99783,x99782),f869(f869(x99783,a852),x99782),x99781),f8(x99783,x99782)),f784(f784(f9(x99781,f869(x99783,x99782),f869(x99783,x99782)),f784(f784(f10(f869(x99782,x99782),f869(f869(x99783,x99782),f869(x99783,x99782)),x99781),f10(x99782,x99782,x99783)),f784(f784(f10(x99782,f869(x99782,x99782),x99781),f90(x99782)),x99784))),x99785))),x99786)),x99787),f784(f784(f90(x99782),f784(f784(f8(x99781,x99782),x99784),x99787)),f784(f784(f8(x99783,x99782),x99785),x99786)))
% 11.41/11.18 [9118]~P20(x91187,x91181,x91183,x91188)+E(f784(f82(x91181,x91181,x91182,f784(x91183,x91184)),f784(f82(x91181,x91181,x91182,f784(x91183,x91185)),x91186)),f784(f82(x91181,x91181,x91182,f784(x91183,x91185)),f784(f82(x91181,x91181,x91182,f784(x91183,x91184)),x91186)))
% 11.41/11.18 [10023]P25(x100231,x100232,f784(f784(f312(f858(x100231)),f784(f784(f784(f100(x100231),f784(f784(f10(f869(a857,a852),f869(a857,a852),x100231),f784(f20(a857,a852,a852),f784(f784(f10(a852,f869(a852,a852),a857),a344),f784(a343,x100233)))),f784(f784(f9(x100231,f869(a857,a857),f869(a857,a852)),f784(f784(f10(f869(a857,a852),f869(f869(a857,a857),f869(a857,a852)),x100231),f10(a857,a852,a857)),x100234)),f784(f784(f20(a857,a859,a857),f784(f784(f9(a857,a854,f869(a859,a857)),a196),f42(x100235))),x100236)))),f34(x100235,x100236,x100237)),x100238)),f187(f869(f858(x100231),a852))))+~P25(x100231,x100232,f784(f784(f312(f858(x100231)),f784(f784(f784(f100(x100231),x100234),x100237),f784(f784(f9(x100231,f869(a857,a857),f869(a857,a852)),f784(f784(f10(f869(a857,a852),f869(f869(a857,a857),f869(a857,a852)),x100231),f10(a857,a852,a857)),x100238)),f784(f784(f9(a857,a859,a857),f784(f784(f9(a857,a854,f869(a859,a857)),a196),f42(x100235))),f784(f784(a197,x100233),x100235))))),f187(f869(f858(x100231),a852))))
% 11.41/11.18 [10030]E(f784(f784(f251(x100301,x100302),f784(x100303,f568(x100304,x100305,x100303,x100306,x100307,x100308,x100302,x100301))),f784(x100305,f569(x100304,x100305,x100303,x100306,x100307,x100308,x100302,x100301))),x100308)+~P85(f784(f784(f347(f868(x100301,x100302)),x100308),f784(f313(f868(x100307,x100306),f868(x100301,x100302),f262(x100307,x100301,x100306,x100302,x100303,x100305)),x100304)))
% 11.41/11.18 [10042]P25(x100421,x100422,f784(f784(f312(f858(x100421)),f784(f784(f784(f100(x100421),f784(f784(f10(f869(a857,a852),f869(a857,a852),x100421),f784(f20(a857,a852,a852),f784(f784(f10(a852,f869(a852,a852),a857),a344),f784(a343,x100423)))),f784(f784(f9(x100421,f869(a857,a857),f869(a857,a852)),f784(f784(f10(f869(a857,a852),f869(f869(a857,a857),f869(a857,a852)),x100421),f10(a857,a852,a857)),x100424)),f784(f784(f20(a857,a859,a857),f784(f784(f9(a857,a854,f869(a859,a857)),f784(f784(f10(a857,f869(a854,f869(a859,a857)),a857),a196),f784(f784(f9(a857,f869(a856,a859),a857),a198),a199))),f42(a28))),x100425)))),f33(x100426,x100427,x100425)),x100428)),f187(f869(f858(x100421),a852))))+~P25(x100421,x100422,f784(f784(f312(f858(x100421)),f784(f784(f784(f100(x100421),x100424),f784(a29,x100427)),f784(f784(f9(x100421,f869(a857,a857),f869(a857,a852)),f784(f784(f10(f869(a857,a852),f869(f869(a857,a857),f869(a857,a852)),x100421),f10(a857,a852,a857)),x100428)),f784(f784(f20(a857,a859,a857),f784(f784(f9(a857,a854,f869(a859,a857)),f784(f784(f10(a857,f869(a854,f869(a859,a857)),a857),a196),f784(f784(f9(a857,f869(a856,a859),a857),a198),f784(a197,x100423)))),x100426)),f784(f784(f9(a857,a856,a859),a197),a27))))),f187(f869(f858(x100421),a852))))
% 11.41/11.18 [10043]~P85(f784(f784(f347(f868(x100438,x100437)),x100436),f784(f313(f868(x100431,x100432),f868(x100438,x100437),f262(x100431,x100438,x100432,x100437,x100435,x100434)),x100433)))+P85(f784(f784(f347(f868(x100431,x100432)),f784(f784(f251(x100431,x100432),f568(x100433,x100434,x100435,x100432,x100431,x100436,x100437,x100438)),f569(x100433,x100434,x100435,x100432,x100431,x100436,x100437,x100438))),x100433))
% 11.41/11.18 [9521]P85(f784(f784(f347(f868(f868(x95211,x95212),f868(x95211,x95212))),f784(f784(f251(f868(x95211,x95212),f868(x95211,x95212)),f784(f784(f251(x95211,x95212),x95213),x95214)),f784(f784(f251(x95211,x95212),x95215),x95216))),f339(x95211,x95212,x95217,x95218)))+~P85(f784(f784(f347(f868(x95211,x95211)),f784(f784(f251(x95211,x95211),x95213),x95215)),x95217))
% 11.41/11.18 [8410]E(f784(x84101,f784(x84102,x84103)),f784(x84104,f784(x84105,x84103)))+~E(f784(f82(x84106,x84107,x84108,x84101),x84102),f784(f82(x84109,x84107,x84108,x84104),x84105))
% 11.41/11.18 [8411]E(f784(x84111,f784(x84112,x84113)),f784(x84114,f784(x84115,x84113)))+~E(f784(f82(x84116,x84117,x84118,x84111),x84112),f784(f82(x84119,x84117,x84118,x84114),x84115))
% 11.41/11.18 [9903]P85(f784(f784(f347(f868(x99031,x99032)),f784(f784(f251(x99031,x99032),f784(x99033,x99034)),f784(x99035,x99036))),f784(f313(f868(x99037,x99038),f868(x99031,x99032),f262(x99037,x99031,x99038,x99032,x99033,x99035)),x99039)))+~P85(f784(f784(f347(f868(x99037,x99038)),f784(f784(f251(x99037,x99038),x99034),x99036)),x99039))
% 11.41/11.18 [8669]~E(f784(x86694,f784(x86695,x86696)),f784(x86699,f784(x866910,x866911)))+E(f784(f784(f82(x86691,x86692,x86693,x86694),x86695),x86696),f784(f784(f82(x86697,x86692,x86698,x86699),x866910),x866911))
% 11.41/11.18 [9179]~P20(x91798,x91799,x917910,x917911)+E(f784(f82(x91791,x91792,x91793,x91794),f784(f82(x91795,x91791,x91793,x91796),x91797)),f784(f82(x91795,x91792,x91793,f784(f82(x91791,x91792,x91795,x91794),x91796)),x91797))
% 11.41/11.18 [4516]~P101(x45161)+~P98(x45161)+E(f186(x45161),f110(x45161))
% 11.41/11.18 [4517]~P101(x45171)+~P99(x45171)+E(f246(x45171),f111(x45171))
% 11.41/11.18 [4750]~P113(x47501)+~P89(x47501)+E(f784(f84(x47501),f784(f113(x47501),a106)),f87(x47501))
% 11.41/11.18 [5028]E(x50281,f2(a1))+E(f91(a1,x50281),f784(f88(a1),f87(a1)))+P85(f784(f784(f243(a1),f2(a1)),x50281))
% 11.41/11.18 [5227]E(x52271,f2(a1))+E(f91(a1,x52271),f87(a1))+~P85(f784(f784(f243(a1),f2(a1)),x52271))
% 11.41/11.18 [6539]~P37(x65391)+~P85(f784(f71(a1),x65391))+P85(f784(f71(a859),f784(f313(a1,a859,a114),x65391)))
% 11.41/11.18 [6915]E(f62(f87(a1),f784(f113(a1),x69151)),f784(f784(f251(a1,a1),f2(a1)),f87(a1)))+~P85(f784(f784(f243(a1),f2(a1)),f784(f113(a1),x69151)))+~P85(f784(f784(f243(a1),f87(a1)),f784(f113(a1),x69151)))
% 11.41/11.18 [7260]~P37(x72601)+P85(f784(f71(a1),x72601))+~P85(f784(f71(a859),f784(f313(a1,a859,a114),x72601)))
% 11.41/11.18 [8110]E(f784(f784(f251(a1,a1),f784(f113(a1),a106)),f784(f784(f89(a1),f87(a1)),f784(f113(a1),x81101))),f65(f87(a1),f784(f113(a1),x81101)))+~P85(f784(f784(f243(a1),f2(a1)),f784(f113(a1),x81101)))+~P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),f87(a1)),f784(f113(a1),x81101))))
% 11.41/11.18 [8515]~P10(a500)+~P85(f784(f784(f347(f868(a855,a853)),x85151),f784(f164(f868(a855,a853)),a31)))+P85(f784(f784(f261(a855,a853,a852),f784(f18(f869(a853,a852),a855),a26)),x85151))
% 11.41/11.18 [9788]E(f784(f58(f784(f113(a1),x97881)),f62(f87(a1),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f113(a1),x97881)))),f62(f87(a1),f784(f113(a1),x97881)))+~P85(f784(f784(f243(a1),f2(a1)),f784(f113(a1),x97881)))+P85(f784(f784(f243(a1),f87(a1)),f784(f113(a1),x97881)))
% 11.41/11.18 [9794]E(f784(f58(f784(f113(a1),x97941)),f65(f87(a1),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f113(a1),x97941)))),f65(f87(a1),f784(f113(a1),x97941)))+~P85(f784(f784(f243(a1),f2(a1)),f784(f113(a1),x97941)))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),f87(a1)),f784(f113(a1),x97941))))
% 11.41/11.18 [9490]E(x94901,f187(f869(f868(a859,a859),a852)))+~P85(f784(f71(f868(a859,a859)),x94901))+P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),f187(f869(f868(a859,a859),a852))),x94901)),a49))
% 11.41/11.18 [9646]E(x96461,f2(a859))+E(x96461,f784(a160,f2(a859)))+~P85(f784(f784(f243(a859),x96461),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.18 [9927]E(x99271,f2(a108))+E(f784(f784(f89(a1),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(a23,f784(f784(f51(a108),x99271),f784(f113(a108),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))),f87(a1)),f784(a23,x99271))+E(f60(a108,x99271,f784(f113(a108),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f2(a108))
% 11.41/11.18 [9774]E(x97741,f2(a108))+~E(f60(a108,x97741,f784(f113(a108),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f2(a108))+E(f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(a23,f784(f784(f51(a108),x97741),f784(f113(a108),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))),f784(a23,x97741))
% 11.41/11.18 [4587]~P55(x45871,x45872)+P41(x45871,x45872)+~P42(a852)
% 11.41/11.18 [4527]~P112(x45271)+P30(x45271,x45272)+~E(x45272,f2(x45271))
% 11.41/11.18 [4536]~P113(x45361)+~E(x45362,f2(x45361))+E(f91(x45361,x45362),f2(x45361))
% 11.41/11.18 [4537]~P82(x45371)+~E(x45372,f2(x45371))+E(f91(x45371,x45372),f2(x45371))
% 11.41/11.18 [4543]~P112(x45432)+~P30(x45432,x45431)+E(x45431,f2(x45432))
% 11.41/11.18 [4577]~P113(x45772)+~E(f91(x45772,x45771),f2(x45772))+E(x45771,f2(x45772))
% 11.41/11.18 [4594]~P7(x45942)+~P7(x45941)+P7(f195(x45941,x45942))
% 11.41/11.18 [4595]~P58(x45952)+~P58(x45951)+P58(f870(x45951,x45952))
% 11.41/11.18 [4596]~P58(x45962)+~P58(x45961)+P58(f869(x45961,x45962))
% 11.41/11.18 [4597]~P58(x45972)+~P58(x45971)+P58(f868(x45971,x45972))
% 11.41/11.18 [4598]~P141(x45982)+~P141(x45981)+P141(f868(x45981,x45982))
% 11.41/11.18 [4955]~P7(x49552)+~P7(x49551)+P7(f60(a1,x49551,x49552))
% 11.41/11.18 [4544]~P69(x45441)+~E(x45442,f2(x45441))+E(f784(f88(x45441),x45442),x45442)
% 11.41/11.18 [4545]~P69(x45451)+~E(x45452,f2(x45451))+E(f784(f88(x45451),x45452),x45452)
% 11.41/11.18 [4548]~P88(x45481)+~E(x45482,f2(a1))+E(f784(f112(x45481),x45482),f2(x45481))
% 11.41/11.18 [4549]~P136(x45491)+~E(x45492,f2(a1))+E(f784(f112(x45491),x45492),f2(x45491))
% 11.41/11.18 [4550]~P88(x45501)+~E(x45502,f2(a1))+E(f784(f112(x45501),x45502),f2(x45501))
% 11.41/11.18 [4574]~P70(x45741)+~E(f2(x45741),x45742)+E(f784(f88(x45741),x45742),f2(x45741))
% 11.41/11.18 [4575]~P70(x45751)+~E(x45752,f2(x45751))+E(f784(f88(x45751),x45752),f2(x45751))
% 11.41/11.18 [4576]~P79(x45761)+~E(x45762,f2(x45761))+E(f784(f84(x45761),x45762),f2(x45761))
% 11.41/11.18 [4599]~P69(x45992)+E(x45991,f2(x45992))+~E(f784(f88(x45992),x45991),x45991)
% 11.41/11.18 [4600]~P69(x46002)+E(x46001,f2(x46002))+~E(f784(f88(x46002),x46001),x46001)
% 11.41/11.18 [4608]E(x46081,f784(a114,x46082))+~E(x46081,f2(a859))+~E(x46082,f784(f109(a1),x46081))
% 11.41/11.18 [4609]E(f784(a114,x46091),x46092)+~E(x46092,f2(a859))+~E(x46091,f784(f109(a1),x46092))
% 11.41/11.18 [4612]~P88(x46122)+E(x46121,f2(a1))+~E(f784(f112(x46122),x46121),f2(x46122))
% 11.41/11.18 [4613]~P88(x46132)+E(x46131,f2(a1))+~E(f784(f112(x46132),x46131),f2(x46132))
% 11.41/11.18 [4618]~P70(x46182)+E(x46181,f2(x46182))+~E(f784(f88(x46182),x46181),f2(x46182))
% 11.41/11.18 [4619]~P79(x46192)+E(x46191,f2(x46192))+~E(f784(f84(x46192),x46191),f2(x46192))
% 11.41/11.18 [4620]~P70(x46201)+E(f2(x46201),x46202)+~E(f784(f88(x46201),x46202),f2(x46201))
% 11.41/11.18 [4754]~P10(a500)+~E(f784(a32,x47542),f784(f237(a853),x47541))+P85(f784(a26,x47541))
% 11.41/11.18 [4793]~P101(x47931)+~P15(x47931,x47932)+P15(x47931,f784(f163(x47931),x47932))
% 11.41/11.18 [4819]~P85(x48192)+~P85(x48191)+P85(f784(f784(a344,x48191),x48192))
% 11.41/11.18 [4853]~E(f87(a859),f2(a859))+E(f784(f50(x48531),x48532),f2(a859))+~P85(f784(f71(x48531),x48532))
% 11.41/11.18 [4884]~P106(x48841)+~P139(x48841)+E(f784(f784(f252(x48841),f2(x48841)),f784(a160,x48842)),f2(x48841))
% 11.41/11.18 [4924]~P101(x49241)+P15(x49241,f134(x49241,x49242))+~P85(f784(f71(x49241),x49242))
% 11.41/11.18 [4946]~P101(x49461)+E(f784(f164(x49461),f134(x49461,x49462)),x49462)+~P85(f784(f71(x49461),x49462))
% 11.41/11.18 [4981]P85(x49811)+P85(x49812)+~P85(f784(f784(a345,x49812),x49811))
% 11.41/11.18 [4993]E(x49931,f187(f869(x49932,a852)))+~E(f784(f50(x49932),x49931),f2(a859))+~P85(f784(f71(x49932),x49931))
% 11.41/11.18 [4998]P85(x49981)+~P85(x49982)+~P85(f784(f784(a348,x49982),x49981))
% 11.41/11.18 [5046]~P66(x50461)+E(f784(f84(x50461),x50462),x50462)+P85(f784(f784(f243(x50461),x50462),f2(x50461)))
% 11.41/11.18 [5140]~P85(f784(a26,x51402))+~P85(f784(a26,x51401))+P85(f784(a26,f38(x51401,x51402)))
% 11.41/11.18 [5141]~P85(f784(a26,x51412))+~P85(f784(a26,x51411))+P85(f784(a26,f38(x51411,x51412)))
% 11.41/11.18 [5148]E(x51481,f120(x51482))+P85(f784(f132(x51482),f121(x51482,x51481)))+~P85(f784(f132(x51482),x51481))
% 11.41/11.18 [5153]~P101(x51531)+~P85(f784(f71(x51531),x51532))+P85(f784(f132(x51531),f134(x51531,x51532)))
% 11.41/11.18 [5159]~P136(x51591)+E(f784(f109(x51591),f784(a114,x51592)),f784(f112(x51591),x51592))+P85(f784(f784(f243(a1),x51592),f2(a1)))
% 11.41/11.18 [5185]P8(x51852,x51851)+E(f784(x51851,f517(x51851)),f784(x51851,f527(x51851)))+P85(f784(f784(x51851,f517(x51851)),f527(x51851)))
% 11.41/11.18 [5197]E(f784(f109(a1),f628(x51971,x51972)),x51971)+P85(f784(x51972,f784(a114,x51971)))+~P85(f784(x51972,f2(a859)))
% 11.41/11.18 [5237]~P113(x52371)+~E(f91(x52371,x52372),f784(f88(x52371),f87(x52371)))+P85(f784(f784(f243(x52371),x52372),f2(x52371)))
% 11.41/11.18 [5309]~E(x53092,f2(a1))+E(f220(x53091,x53092),f784(f784(f251(a1,a1),f2(a1)),f87(a1)))+P85(f784(f784(f243(a1),x53092),f2(a1)))
% 11.41/11.18 [5310]~E(x53101,f2(a1))+E(f220(x53101,x53102),f784(f784(f251(a1,a1),f2(a1)),f87(a1)))+P85(f784(f784(f243(a1),x53102),f2(a1)))
% 11.41/11.18 [5333]~P85(f784(x53331,x53332))+~P85(f784(x53331,f562(x53332,x53331)))+P85(f784(x53331,f2(a859)))
% 11.41/11.18 [5362]E(f784(f109(a1),f628(x53621,x53622)),x53621)+P85(f784(x53622,f784(a114,x53621)))+P85(f784(f784(f243(a1),x53621),f2(a1)))
% 11.41/11.18 [5427]~P113(x54271)+E(f91(x54271,x54272),f784(f88(x54271),f87(x54271)))+~P85(f784(f784(f243(x54271),x54272),f2(x54271)))
% 11.41/11.18 [5428]~P113(x54281)+E(f91(x54281,x54282),f784(f88(x54281),f87(x54281)))+~P85(f784(f784(f243(x54281),x54282),f2(x54281)))
% 11.41/11.18 [5429]~P79(x54291)+E(f784(f84(x54291),x54292),f784(f88(x54291),x54292))+~P85(f784(f784(f243(x54291),x54292),f2(x54291)))
% 11.41/11.18 [5430]~P79(x54301)+E(f784(f84(x54301),x54302),f784(f88(x54301),x54302))+~P85(f784(f784(f242(x54301),x54302),f2(x54301)))
% 11.41/11.18 [5431]~P66(x54311)+E(f784(f84(x54311),x54312),f784(f88(x54311),x54312))+~P85(f784(f784(f243(x54311),x54312),f2(x54311)))
% 11.41/11.18 [5522]~P85(f784(x55221,f628(x55222,x55221)))+P85(f784(x55221,f784(a114,x55222)))+~P85(f784(x55221,f2(a859)))
% 11.41/11.18 [5529]E(x55291,f2(a859))+E(f784(a160,f585(x55292,x55291)),x55291)+~P85(f784(f784(f243(a859),x55291),f784(a160,x55292)))
% 11.41/11.18 [5533]P8(x55331,x55332)+~E(f784(x55332,f517(x55332)),f784(x55332,f527(x55332)))+~P85(f784(f784(x55332,f517(x55332)),f527(x55332)))
% 11.41/11.18 [5552]~P101(x55521)+P15(x55521,x55522)+P85(f784(f784(f242(a859),f772(x55522,x55521)),f773(x55522,x55521)))
% 11.41/11.18 [5638]~P79(x56381)+~E(x56382,f2(x56381))+P85(f784(f784(f242(x56381),f784(f84(x56381),x56382)),f2(x56381)))
% 11.41/11.18 [5727]~P85(f784(x57271,f628(x57272,x57271)))+P85(f784(x57271,f784(a114,x57272)))+P85(f784(f784(f243(a1),x57272),f2(a1)))
% 11.41/11.18 [5753]~P85(f784(x57531,f784(a114,x57532)))+P85(f784(x57531,f2(a859)))+~P85(f784(f784(f243(a1),x57532),f2(a1)))
% 11.41/11.18 [6094]~P113(x60941)+~P85(f784(f784(f243(x60941),x60942),f2(x60941)))+P85(f784(f784(f243(x60941),f91(x60941,x60942)),f2(x60941)))
% 11.41/11.18 [6211]~P113(x62111)+P85(f784(f784(f243(x62111),f784(f112(x62111),x62112)),f2(x62111)))+~P85(f784(f784(f243(a1),x62112),f2(a1)))
% 11.41/11.18 [6212]~P113(x62121)+P85(f784(f784(f242(x62121),f784(f112(x62121),x62122)),f2(x62121)))+~P85(f784(f784(f242(a1),x62122),f2(a1)))
% 11.41/11.18 [6216]~P79(x62162)+E(x62161,f2(x62162))+~P85(f784(f784(f242(x62162),f784(f84(x62162),x62161)),f2(x62162)))
% 11.41/11.18 [6300]~P136(x63001)+~P85(f784(f784(f347(x63001),x63002),f119(x63001)))+P85(f784(f784(f347(x63001),f784(f88(x63001),x63002)),f119(x63001)))
% 11.41/11.18 [6332]~P113(x63321)+~P85(f784(f784(f243(x63321),f91(x63321,x63322)),f2(x63321)))+P85(f784(f784(f243(x63321),x63322),f2(x63321)))
% 11.41/11.18 [6413]~P100(x64131)+P49(a859,x64131,f289(a859),x64132)+P85(f784(f784(f289(a859),f390(x64132,x64131)),f406(x64132,x64131)))
% 11.41/11.18 [6510]~P113(x65102)+~P85(f784(f784(f243(x65102),f784(f112(x65102),x65101)),f2(x65102)))+P85(f784(f784(f243(a1),x65101),f2(a1)))
% 11.41/11.18 [6511]~P113(x65112)+~P85(f784(f784(f242(x65112),f784(f112(x65112),x65111)),f2(x65112)))+P85(f784(f784(f242(a1),x65111),f2(a1)))
% 11.41/11.18 [7030]~P69(x70301)+~P85(f784(f784(f243(x70301),x70302),f2(x70301)))+P85(f784(f784(f243(x70301),f784(f784(f89(x70301),x70302),x70302)),f2(x70301)))
% 11.41/11.18 [7031]~P113(x70311)+~P85(f784(f784(f243(x70311),x70312),f2(x70311)))+P85(f784(f784(f243(x70311),f784(f784(f89(x70311),x70312),x70312)),f2(x70311)))
% 11.41/11.18 [7032]~P69(x70321)+~P85(f784(f784(f242(x70321),x70322),f2(x70321)))+P85(f784(f784(f242(x70321),f784(f784(f89(x70321),x70322),x70322)),f2(x70321)))
% 11.41/11.18 [7626]~P69(x76261)+~P85(f784(f784(f243(x76261),f784(f784(f89(x76261),x76262),x76262)),f2(x76261)))+P85(f784(f784(f243(x76261),x76262),f2(x76261)))
% 11.41/11.18 [7627]~P113(x76271)+~P85(f784(f784(f243(x76271),f784(f784(f89(x76271),x76272),x76272)),f2(x76271)))+P85(f784(f784(f243(x76271),x76272),f2(x76271)))
% 11.41/11.18 [7628]~P69(x76281)+~P85(f784(f784(f242(x76281),f784(f784(f89(x76281),x76282),x76282)),f2(x76281)))+P85(f784(f784(f242(x76281),x76282),f2(x76281)))
% 11.41/11.18 [4656]~E(x46562,f87(a859))+~E(x46561,f87(a859))+E(f784(f784(f90(a859),x46561),x46562),f87(a859))
% 11.41/11.18 [4657]~E(x46572,f2(a859))+~E(x46571,f2(a859))+E(f784(f784(f89(a859),x46571),x46572),f2(a859))
% 11.41/11.18 [4658]~E(x46582,f87(a859))+~E(x46581,f87(a859))+E(f784(f784(f90(a859),x46581),x46582),f87(a859))
% 11.41/11.18 [4659]~E(x46592,f87(a1))+~E(x46591,f87(a1))+E(f784(f784(f90(a1),x46591),x46592),f87(a1))
% 11.41/11.18 [4709]~P4(x47092)+E(x47091,f2(x47092))+E(f784(f784(f51(x47092),x47091),x47091),f87(x47092))
% 11.41/11.18 [4710]~P116(x47102)+E(x47101,f2(x47102))+E(f784(f784(f293(x47102),x47101),x47101),f87(x47102))
% 11.41/11.18 [4711]~P117(x47112)+E(x47111,f2(x47112))+E(f784(f784(f293(x47112),x47111),x47111),f87(x47112))
% 11.41/11.18 [4725]~P69(x47251)+~E(x47252,f2(x47251))+E(f784(f784(f89(x47251),x47252),x47252),f2(x47251))
% 11.41/11.18 [4726]~P69(x47261)+~E(x47262,f2(x47261))+E(f784(f784(f89(x47261),x47262),x47262),f2(x47261))
% 11.41/11.18 [4729]~P135(x47291)+~E(x47292,f87(x47291))+E(f784(f784(f90(x47291),x47292),x47292),f87(x47291))
% 11.41/11.18 [4730]~P117(x47301)+~E(x47302,f2(x47301))+E(f784(f784(f293(x47301),x47302),x47302),f2(x47301))
% 11.41/11.18 [4774]~E(x47742,f2(a859))+~E(x47741,f2(a859))+E(f784(f88(a1),f784(f109(a1),x47741)),f784(f109(a1),x47742))
% 11.41/11.18 [4792]E(x47921,f87(a859))+E(x47922,f2(a859))+~E(f784(f784(f90(a859),x47922),x47921),x47922)
% 11.41/11.18 [4800]E(x48001,f2(a859))+E(x48002,f2(a859))+~E(f784(f784(f90(a859),x48002),x48001),f2(a859))
% 11.41/11.18 [4826]~E(x48262,f2(a859))+~E(x48261,f784(a160,f2(a859)))+E(f784(f784(f89(a859),x48261),x48262),f784(a160,f2(a859)))
% 11.41/11.18 [4827]~E(x48271,f2(a859))+~E(x48272,f784(a160,f2(a859)))+E(f784(f784(f89(a859),x48271),x48272),f784(a160,f2(a859)))
% 11.41/11.18 [4828]~E(x48282,f2(a859))+~E(x48281,f784(a160,f2(a859)))+E(f784(f784(f89(a859),x48281),x48282),f784(a160,f2(a859)))
% 11.41/11.18 [4829]~E(x48291,f2(a859))+~E(x48292,f784(a160,f2(a859)))+E(f784(f784(f89(a859),x48291),x48292),f784(a160,f2(a859)))
% 11.41/11.18 [4834]E(x48341,f87(a1))+E(x48342,f784(f113(a1),a106))+~E(f784(f784(f90(a1),x48341),x48342),f87(a1))
% 11.41/11.18 [4835]E(x48351,f87(a1))+E(x48352,f784(f113(a1),a106))+~E(f784(f784(f90(a1),x48352),x48351),f87(a1))
% 11.41/11.18 [4836]E(x48361,f87(a1))+E(x48361,f784(f113(a1),a106))+~E(f784(f784(f90(a1),x48362),x48361),f87(a1))
% 11.41/11.18 [4837]E(x48371,f87(a1))+E(x48371,f784(f113(a1),a106))+~E(f784(f784(f90(a1),x48371),x48372),f87(a1))
% 11.41/11.18 [4838]E(x48381,f87(a1))+E(x48381,f784(f113(a1),a106))+~E(f784(f784(f90(a1),x48381),x48382),f87(a1))
% 11.41/11.18 [4856]~P69(x48562)+E(x48561,f2(x48562))+~E(f784(f784(f89(x48562),x48561),x48561),f2(x48562))
% 11.41/11.18 [4857]~P69(x48572)+E(x48571,f2(x48572))+~E(f784(f784(f89(x48572),x48571),x48571),f2(x48572))
% 11.41/11.18 [4863]~E(x48631,f784(f113(a1),a106))+~E(x48632,f784(f113(a1),a106))+E(f784(f784(f90(a1),x48631),x48632),f87(a1))
% 11.41/11.18 [4874]E(x48741,f2(a859))+E(x48742,f2(a859))+~E(f784(f784(f89(a859),x48742),x48741),f784(a160,f2(a859)))
% 11.41/11.18 [4875]E(x48751,f2(a859))+E(x48752,f2(a859))+~E(f784(f784(f89(a859),x48752),x48751),f784(a160,f2(a859)))
% 11.41/11.18 [4883]~P89(x48831)+~P59(x48831)+E(f784(f784(f293(x48831),x48832),f784(f113(x48831),a92)),f2(x48831))
% 11.41/11.18 [4890]~P135(x48901)+~E(x48902,f784(f88(x48901),f87(x48901)))+E(f784(f784(f90(x48901),x48902),x48902),f87(x48901))
% 11.41/11.18 [4895]~P7(x48952)+~P7(x48951)+P7(f784(f784(f89(a1),x48951),x48952))
% 11.41/11.18 [4896]~P7(x48962)+~P7(x48961)+P7(f784(f784(f90(a1),x48961),x48962))
% 11.41/11.18 [4897]~P7(x48972)+~P7(x48971)+P7(f784(f784(f51(a1),x48971),x48972))
% 11.41/11.18 [4898]~E(x48982,f2(a1))+E(x48981,f2(a1))+E(f61(x48981,x48982),f784(f784(f251(a1,a1),f2(a1)),x48981))
% 11.41/11.18 [4899]~E(x48992,f2(a1))+E(x48991,f2(a1))+E(f61(x48991,x48992),f784(f784(f251(a1,a1),f2(a1)),x48991))
% 11.41/11.18 [4922]~E(x49222,f784(a160,f2(a859)))+~E(x49221,f784(a160,f2(a859)))+E(f784(f784(f90(a859),x49221),x49222),f784(a160,f2(a859)))
% 11.41/11.18 [4933]E(x49331,f2(a859))+E(x49331,f784(a160,f2(a859)))+~E(f784(f784(f89(a859),x49332),x49331),f784(a160,f2(a859)))
% 11.41/11.18 [4934]E(x49341,f2(a859))+E(x49341,f784(a160,f2(a859)))+~E(f784(f784(f89(a859),x49341),x49342),f784(a160,f2(a859)))
% 11.41/11.18 [4935]E(x49351,f2(a859))+E(x49352,f784(a160,f2(a859)))+~E(f784(f784(f252(a859),x49352),x49351),f784(a160,f2(a859)))
% 11.41/11.18 [4936]E(x49361,f2(a859))+E(x49361,f784(a160,f2(a859)))+~E(f784(f784(f89(a859),x49362),x49361),f784(a160,f2(a859)))
% 11.41/11.18 [4937]E(x49371,f2(a859))+E(x49371,f784(a160,f2(a859)))+~E(f784(f784(f89(a859),x49371),x49372),f784(a160,f2(a859)))
% 11.41/11.18 [4947]~P89(x49471)+~P59(x49471)+E(f784(f784(f293(x49471),x49472),f784(f113(x49471),a106)),f784(f88(x49471),x49472))
% 11.41/11.18 [4968]E(x49681,f784(a114,x49682))+~E(x49681,f2(a859))+P85(f784(f784(f242(a1),f2(a1)),x49682))
% 11.41/11.18 [4969]E(f784(a114,x49691),x49692)+~E(x49692,f2(a859))+P85(f784(f784(f242(a1),f2(a1)),x49691))
% 11.41/11.18 [4988]E(x49881,f784(a160,f2(a859)))+E(x49882,f784(a160,f2(a859)))+~E(f784(f784(f89(a859),x49881),x49882),f784(a160,f2(a859)))
% 11.41/11.18 [4989]E(x49891,f784(a160,f2(a859)))+E(x49892,f784(a160,f2(a859)))+~E(f784(f784(f89(a859),x49891),x49892),f784(a160,f2(a859)))
% 11.41/11.18 [5000]~E(x50001,f784(a114,x50002))+E(x50001,f2(a859))+P85(f784(f784(f242(a1),f2(a1)),x50002))
% 11.41/11.18 [5001]~E(f784(a114,x50012),x50011)+E(x50011,f2(a859))+P85(f784(f784(f242(a1),f2(a1)),x50012))
% 11.41/11.18 [5024]~P93(x50241)+E(f784(f73(x50241,f110(x50241)),x50242),f15(x50241,x50242))+~P85(f784(f71(x50241),x50242))
% 11.41/11.18 [5025]~P101(x50251)+E(f784(f73(x50251,f186(x50251)),x50252),f16(x50251,x50252))+~P85(f784(f71(x50251),x50252))
% 11.41/11.18 [5026]~P101(x50261)+E(f784(f73(x50261,f246(x50261)),x50262),f17(x50261,x50262))+~P85(f784(f71(x50261),x50262))
% 11.41/11.18 [5027]~P93(x50271)+E(f784(f73(x50271,f111(x50271)),x50272),f12(x50271,x50272))+~P85(f784(f71(x50271),x50272))
% 11.41/11.18 [5109]E(x51091,x51092)+~E(f784(f784(f3(a859),x51092),x51091),f2(a859))+~E(f784(f784(f3(a859),x51091),x51092),f2(a859))
% 11.41/11.18 [5119]P7(x51191)+~P37(x51192)+~P85(f784(f784(f347(a1),x51191),x51192))
% 11.41/11.18 [5149]~P113(x51491)+~E(f91(x51491,x51492),f87(x51491))+P85(f784(f784(f243(x51491),f2(x51491)),x51492))
% 11.41/11.18 [5160]~P89(x51601)+E(f784(f109(x51601),f784(f113(a859),x51602)),f784(f113(x51601),x51602))+P85(f784(a193,f784(f113(a1),x51602)))
% 11.41/11.18 [5165]~P41(x51651,x51652)+P42(a852)+P85(f784(f71(f868(x51651,x51651)),x51652))
% 11.41/11.18 [5229]~P101(x52291)+E(f784(f73(x52291,f186(x52291)),x52292),f13(x52291,f186(x52291),x52292))+~P85(f784(f71(x52291),x52292))
% 11.41/11.18 [5230]~P101(x52301)+E(f784(f73(x52301,f246(x52301)),x52302),f14(x52301,f246(x52301),x52302))+~P85(f784(f71(x52301),x52302))
% 11.41/11.18 [5242]E(x52421,x52422)+P85(f784(f784(f243(a859),x52422),x52421))+P85(f784(f784(f243(a859),x52421),x52422))
% 11.41/11.18 [5243]E(x52431,x52432)+P85(f784(f784(f243(a859),x52432),x52431))+P85(f784(f784(f243(a859),x52431),x52432))
% 11.41/11.18 [5244]E(x52441,x52442)+P85(f784(f784(f243(a1),x52442),x52441))+P85(f784(f784(f243(a1),x52441),x52442))
% 11.41/11.18 [5296]~P89(x52961)+E(f784(f109(x52961),f784(f113(a859),x52962)),f2(x52961))+~P85(f784(a193,f784(f113(a1),x52962)))
% 11.41/11.18 [5299]~E(x52992,f784(a114,x52991))+E(x52991,f784(f109(a1),x52992))+~P85(f784(f784(f242(a1),f2(a1)),x52991))
% 11.41/11.18 [5300]~E(f784(a114,x53001),x53002)+E(x53001,f784(f109(a1),x53002))+~P85(f784(f784(f242(a1),f2(a1)),x53001))
% 11.41/11.18 [5301]~E(x53011,f784(a114,x53012))+E(f784(f109(a1),x53011),x53012)+~P85(f784(f784(f242(a1),f2(a1)),x53012))
% 11.41/11.18 [5311]E(x53111,f784(a114,x53112))+~E(x53112,f784(f109(a1),x53111))+~P85(f784(f784(f242(a1),f2(a1)),x53112))
% 11.41/11.18 [5312]E(f784(a114,x53121),x53122)+~E(x53121,f784(f109(a1),x53122))+~P85(f784(f784(f242(a1),f2(a1)),x53121))
% 11.41/11.18 [5342]~P86(x53422)+E(x53421,f2(x53422))+~P85(f784(f784(f289(x53422),f2(x53422)),x53421))
% 11.41/11.18 [5351]~P79(x53512)+E(x53511,f2(x53512))+P85(f784(f784(f243(x53512),f2(x53512)),f784(f84(x53512),x53511)))
% 11.41/11.18 [5418]~P113(x54181)+E(f91(x54181,x54182),f87(x54181))+~P85(f784(f784(f243(x54181),f2(x54181)),x54182))
% 11.41/11.18 [5419]~P113(x54191)+E(f91(x54191,x54192),f87(x54191))+~P85(f784(f784(f243(x54191),f2(x54191)),x54192))
% 11.41/11.18 [5425]~P89(x54251)+E(f784(f109(x54251),f784(f113(a859),x54252)),f2(x54251))+P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x54252)))
% 11.41/11.18 [5432]~P79(x54321)+E(f784(f84(x54321),x54322),x54322)+~P85(f784(f784(f243(x54321),f2(x54321)),x54322))
% 11.41/11.18 [5433]~P79(x54331)+E(f784(f84(x54331),x54332),x54332)+~P85(f784(f784(f242(x54331),f2(x54331)),x54332))
% 11.41/11.18 [5440]E(x54401,f2(a859))+~E(f134(a859,f784(f304(a859,x54402),x54401)),f120(a859))+P85(f784(f784(f242(a859),x54401),x54402))
% 11.41/11.18 [5450]~P68(x54501)+E(f784(f784(f8(x54501,x54501),f7(x54501)),f784(f164(x54501),x54502)),f784(f157(x54501),x54502))+~P85(f784(f132(x54501),x54502))
% 11.41/11.18 [5453]~P136(x54531)+E(f784(f109(x54531),f784(a114,x54532)),f784(f112(x54531),x54532))+~P85(f784(f784(f242(a1),f2(a1)),x54532))
% 11.41/11.18 [5455]~E(x54551,x54552)+P85(f784(f784(f243(a859),x54551),f784(a160,x54552)))+P85(f784(f784(f243(a859),x54551),x54552))
% 11.41/11.18 [5474]E(x54741,x54742)+P85(f784(f784(f243(a859),x54741),x54742))+~P85(f784(f784(f242(a859),x54741),x54742))
% 11.41/11.18 [5475]E(x54751,x54752)+P85(f784(f784(f243(a859),x54751),x54752))+~P85(f784(f784(f242(a859),x54751),x54752))
% 11.41/11.18 [5476]E(x54761,x54762)+P85(f784(f784(f243(a859),x54761),x54762))+~P85(f784(f784(f242(a859),x54761),x54762))
% 11.41/11.18 [5477]E(x54771,x54772)+P85(f784(f784(f243(a1),x54771),x54772))+~P85(f784(f784(f242(a1),x54771),x54772))
% 11.41/11.18 [5480]E(x54801,f87(a1))+~E(f784(f784(f90(a1),x54802),x54801),f87(a1))+~P85(f784(f784(f243(a1),f2(a1)),x54802))
% 11.41/11.18 [5481]E(x54811,f87(a1))+~E(f784(f784(f90(a1),x54811),x54812),f87(a1))+~P85(f784(f784(f243(a1),f2(a1)),x54811))
% 11.41/11.18 [5518]~P37(x55182)+P85(f784(f784(f242(a1),f2(a1)),x55181))+~P85(f784(f784(f347(a1),x55181),x55182))
% 11.41/11.18 [5519]~P37(x55192)+P85(f784(f784(f242(a1),f2(a1)),x55191))+~P85(f784(f784(f347(a1),x55191),x55192))
% 11.41/11.18 [5530]~P85(f784(x55301,x55302))+P85(f784(x55301,f2(a859)))+P85(f784(x55301,f784(a160,f562(x55302,x55301))))
% 11.41/11.18 [5537]~P55(x55371,x55372)+P35(x55371,x55372)+~P85(f784(f71(f868(x55371,x55371)),x55372))
% 11.41/11.18 [5538]~P55(x55381,x55382)+P35(x55381,x55382)+~P85(f784(f71(f868(x55381,x55381)),x55382))
% 11.41/11.18 [5539]~P35(x55391,x55392)+P55(x55391,x55392)+~P85(f784(f71(f868(x55391,x55391)),x55392))
% 11.41/11.18 [5540]~P55(x55401,x55402)+P41(x55401,x55402)+~P85(f784(f71(f868(x55401,x55401)),x55402))
% 11.41/11.18 [5580]E(x55801,f187(f869(x55802,a852)))+~P85(f784(f71(x55802),x55801))+P85(f784(f784(f243(a859),f2(a859)),f784(f50(x55802),x55801)))
% 11.41/11.18 [5606]~P85(f784(x56061,x56062))+P85(f784(x56061,f2(a859)))+P85(f784(f784(f243(a859),f801(x56062,x56061)),x56062))
% 11.41/11.18 [5631]E(x56311,f2(a859))+~E(f784(f157(a859),x56312),f2(a859))+~P85(f784(f784(f347(a859),x56311),f784(f164(a859),x56312)))
% 11.41/11.18 [5664]~E(x56641,x56642)+P85(f784(f784(f243(a859),x56641),f784(a160,x56642)))+~P85(f784(f784(f242(a859),x56642),x56641))
% 11.41/11.18 [5693]~E(x56932,f2(a859))+P85(f784(f784(f242(a1),f2(a1)),x56931))+P85(f784(f784(f289(a859),f784(a114,x56931)),x56932))
% 11.41/11.18 [5696]E(x56961,x56962)+~P85(f784(f784(f242(a859),x56962),x56961))+~P85(f784(f784(f242(a859),x56961),x56962))
% 11.41/11.18 [5697]E(x56971,x56972)+~P85(f784(f784(f242(a1),x56972),x56971))+~P85(f784(f784(f242(a1),x56971),x56972))
% 11.41/11.18 [5698]E(x56981,x56982)+~P85(f784(f784(f289(a859),x56982),x56981))+~P85(f784(f784(f289(a859),x56981),x56982))
% 11.41/11.18 [5699]E(x56991,x56992)+~P85(f784(f784(f289(a859),x56992),x56991))+~P85(f784(f784(f289(a859),x56991),x56992))
% 11.41/11.18 [5700]E(x57001,x57002)+~P85(f784(f784(f289(a859),x57002),x57001))+~P85(f784(f784(f289(a859),x57001),x57002))
% 11.41/11.18 [5701]E(x57011,x57012)+~P85(f784(f784(f289(a859),x57012),x57011))+~P85(f784(f784(f289(a859),x57011),x57012))
% 11.41/11.18 [5702]E(x57021,x57022)+~P85(f784(f784(f289(a859),x57022),x57021))+~P85(f784(f784(f289(a859),x57021),x57022))
% 11.41/11.18 [5703]E(x57031,x57032)+~P85(f784(f784(f289(a859),x57032),x57031))+~P85(f784(f784(f289(a859),x57031),x57032))
% 11.41/11.18 [5704]E(x57041,x57042)+~P85(f784(f784(f289(a859),x57042),x57041))+~P85(f784(f784(f289(a859),x57041),x57042))
% 11.41/11.18 [5705]E(x57051,x57052)+~P85(f784(f784(f289(a859),x57052),x57051))+~P85(f784(f784(f289(a859),x57051),x57052))
% 11.41/11.18 [5706]E(x57061,x57062)+~P85(f784(f784(f289(a859),x57062),x57061))+~P85(f784(f784(f289(a859),x57061),x57062))
% 11.41/11.18 [5707]E(f784(f50(x57071),x57072),f2(a859))+~P85(f784(f71(x57071),x57072))+P85(f784(f784(f347(x57071),f630(x57072,x57071)),x57072))
% 11.41/11.18 [5713]E(f65(x57131,x57132),f61(x57131,x57132))+P85(f784(f784(f242(a1),f2(a1)),x57131))+~P85(f784(f784(f243(a1),f2(a1)),x57132))
% 11.41/11.18 [5742]~P85(f784(x57421,f787(x57421)))+P85(f784(x57421,f784(a114,x57422)))+~P85(f784(f784(f242(a1),f2(a1)),x57422))
% 11.41/11.18 [5744]P85(f784(f784(f243(a859),x57441),f414(x57442)))+~P85(f784(f71(a859),x57442))+~P85(f784(f784(f347(a859),x57441),x57442))
% 11.41/11.18 [5745]P85(f784(f784(f242(a859),x57451),f389(x57452)))+~P85(f784(f71(a859),x57452))+~P85(f784(f784(f347(a859),x57451),x57452))
% 11.41/11.18 [5771]E(x57711,x57712)+~P85(f784(f784(f243(a859),x57711),f784(a160,x57712)))+P85(f784(f784(f243(a859),x57711),x57712))
% 11.41/11.18 [5772]E(x57721,x57722)+~P85(f784(f784(f243(a859),x57721),f784(a160,x57722)))+P85(f784(f784(f243(a859),x57721),x57722))
% 11.41/11.18 [5773]E(x57731,x57732)+~P85(f784(f784(f243(a859),x57731),f784(a160,x57732)))+P85(f784(f784(f243(a859),x57731),x57732))
% 11.41/11.18 [5774]E(x57741,x57742)+~P85(f784(f784(f243(a859),x57741),f784(a160,x57742)))+P85(f784(f784(f243(a859),x57741),x57742))
% 11.41/11.18 [5810]E(x58101,f784(a160,x58102))+~P85(f784(f784(f242(a859),x58101),f784(a160,x58102)))+P85(f784(f784(f242(a859),x58101),x58102))
% 11.41/11.18 [5811]E(x58111,f784(a160,x58112))+~P85(f784(f784(f242(a859),x58111),f784(a160,x58112)))+P85(f784(f784(f242(a859),x58111),x58112))
% 11.41/11.18 [5821]P85(f784(x58211,f788(x58211)))+~P85(f784(x58211,f784(a114,x58212)))+~P85(f784(f784(f242(a1),f2(a1)),x58212))
% 11.41/11.18 [5823]E(f784(f84(a1),x58231),f784(f84(a1),x58232))+~P85(f784(f784(f289(a1),x58232),x58231))+~P85(f784(f784(f289(a1),x58231),x58232))
% 11.41/11.18 [5835]~P85(f784(x58351,x58352))+~P85(f784(f784(f242(a1),f2(a1)),x58352))+P85(f784(x58351,f784(f109(a1),f735(x58351))))
% 11.41/11.18 [5848]~P79(x58482)+~E(x58481,f2(x58482))+~P85(f784(f784(f243(x58482),f2(x58482)),f784(f84(x58482),x58481)))
% 11.41/11.18 [5873]~P55(x58731,x58732)+P35(x58731,f784(f288(x58731,x58731),x58732))+~P85(f784(f71(f868(x58731,x58731)),x58732))
% 11.41/11.18 [5881]~P89(x58811)+E(f784(f109(x58811),f784(f113(a859),x58812)),f784(f113(x58811),x58812))+~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x58812)))
% 11.41/11.18 [5885]E(f784(a160,x58851),x58852)+~P85(f784(f784(f243(a859),x58851),x58852))+P85(f784(f784(f243(a859),f784(a160,x58851)),x58852))
% 11.41/11.18 [5897]E(f784(f784(f51(a1),x58971),x58972),f2(a1))+~P85(f784(f784(f242(a1),x58971),f2(a1)))+~P85(f784(f784(f243(a1),x58972),x58971))
% 11.41/11.18 [5898]E(f784(f784(f51(a1),x58981),x58982),f2(a1))+~P85(f784(f784(f242(a1),x58981),f2(a1)))+~P85(f784(f784(f243(a1),x58982),x58981))
% 11.41/11.18 [5911]E(f60(a1,x59111,x59112),x59111)+~P85(f784(f784(f242(a1),x59111),f2(a1)))+~P85(f784(f784(f243(a1),x59112),x59111))
% 11.41/11.18 [5923]E(f62(x59231,x59232),f61(x59231,x59232))+~P85(f784(f784(f242(a1),f2(a1)),x59231))+~P85(f784(f784(f242(a1),f2(a1)),x59232))
% 11.41/11.18 [5929]E(f784(f784(f51(a859),x59291),x59292),f2(a859))+~P85(f784(f784(f243(a859),f2(a859)),x59292))+~P85(f784(f784(f243(a859),x59291),x59292))
% 11.41/11.18 [5930]E(f784(f784(f51(a1),x59301),x59302),f2(a1))+~P85(f784(f784(f242(a1),f2(a1)),x59301))+~P85(f784(f784(f243(a1),x59301),x59302))
% 11.41/11.18 [5931]E(f784(f784(f51(a1),x59311),x59312),f2(a1))+~P85(f784(f784(f242(a1),f2(a1)),x59311))+~P85(f784(f784(f243(a1),x59311),x59312))
% 11.41/11.18 [5945]E(f60(a859,f784(f113(a859),x59451),f784(f113(a859),x59452)),f784(f113(a859),x59451))+P85(f784(a193,f784(f113(a1),x59451)))+~P85(f784(a193,f784(f113(a1),x59452)))
% 11.41/11.18 [5947]E(f60(a1,x59471,x59472),x59471)+~P85(f784(f784(f242(a1),f2(a1)),x59471))+~P85(f784(f784(f243(a1),x59471),x59472))
% 11.41/11.18 [5949]E(x59491,x59492)+~P85(f784(f784(f243(a859),x59491),f784(a160,x59492)))+~P85(f784(f784(f242(a859),x59492),x59491))
% 11.41/11.18 [5961]E(f784(f113(a1),x59611),f784(f109(a1),x59612))+~E(x59612,f784(a114,f784(f113(a1),x59611)))+~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x59611)))
% 11.41/11.18 [5965]~P113(x59651)+~P85(f784(f784(f243(x59651),x59652),f2(x59651)))+P85(f784(f784(f243(x59651),x59652),f784(f88(x59651),x59652)))
% 11.41/11.18 [5966]~P69(x59661)+~P85(f784(f784(f242(x59661),x59662),f2(x59661)))+P85(f784(f784(f242(x59661),x59662),f784(f88(x59661),x59662)))
% 11.41/11.18 [5974]~P6(x59741)+E(f784(f784(f74(x59741,x59741,f111(x59741)),f249(x59741)),x59742),f53(x59741,x59742))+~P85(f784(f71(x59741),x59742))
% 11.41/11.18 [5975]~P6(x59751)+E(f784(f784(f74(x59751,x59751,f110(x59751)),f187(x59751)),x59752),f52(x59751,x59752))+~P85(f784(f71(x59751),x59752))
% 11.41/11.18 [5989]~P120(x59891)+~P85(f784(f784(f243(a859),f2(a859)),x59892))+P85(f784(f784(f243(x59891),f2(x59891)),f784(f109(x59891),x59892)))
% 11.41/11.18 [5990]~P113(x59901)+~P85(f784(f784(f243(a1),f2(a1)),x59902))+P85(f784(f784(f243(x59901),f2(x59901)),f784(f112(x59901),x59902)))
% 11.41/11.18 [5991]~P113(x59911)+~P85(f784(f784(f242(a1),f2(a1)),x59912))+P85(f784(f784(f242(x59911),f2(x59911)),f784(f112(x59911),x59912)))
% 11.41/11.18 [5994]~P7(x59942)+~P7(x59941)+E(f784(f313(a859,a1,f109(a1)),f305(a859,f784(a114,x59941),f784(a114,x59942))),f305(a1,x59941,x59942))
% 11.41/11.18 [6000]P85(f784(x60001,x60002))+~P85(f784(f784(f242(a1),f2(a1)),x60002))+~P85(f784(x60001,f784(f109(a1),f760(x60001))))
% 11.41/11.18 [6027]E(f784(f784(f89(a859),f784(f113(a859),x60271)),f784(f113(a859),x60272)),f784(f113(a859),x60271))+P85(f784(f784(f243(a1),x60271),a92))+~P85(f784(f784(f243(a1),x60272),a92))
% 11.41/11.18 [6031]~P113(x60311)+P85(f784(f784(f243(x60311),f2(x60311)),f91(x60311,x60312)))+~P85(f784(f784(f243(x60311),f2(x60311)),x60312))
% 11.41/11.18 [6045]~P77(x60451)+~P85(f784(f784(f243(x60451),x60452),f2(x60451)))+P85(f784(f784(f243(x60451),f2(x60451)),f784(f88(x60451),x60452)))
% 11.41/11.18 [6046]~P77(x60461)+~P85(f784(f784(f242(x60461),x60462),f2(x60461)))+P85(f784(f784(f242(x60461),f2(x60461)),f784(f88(x60461),x60462)))
% 11.41/11.18 [6049]E(x60491,f2(a859))+P85(f784(f784(f242(a1),f2(a1)),x60492))+~P85(f784(f784(f289(a859),f784(a114,x60492)),x60491))
% 11.41/11.18 [6050]E(x60501,f249(f869(x60502,a852)))+~E(f784(f50(x60502),x60501),f784(f50(x60502),f249(f869(x60502,a852))))+~P85(f784(f71(x60502),f249(f869(x60502,a852))))
% 11.41/11.18 [6080]~P85(f784(f784(f243(a859),f2(a859)),x60802))+~P85(f784(f784(f289(a859),x60801),x60802))+P85(f784(f784(f242(a859),x60801),x60802))
% 11.41/11.18 [6081]~P85(f784(f784(f243(a1),f2(a1)),x60812))+~P85(f784(f784(f289(a1),x60811),x60812))+P85(f784(f784(f242(a1),x60811),x60812))
% 11.41/11.18 [6087]~P113(x60871)+P85(f784(f784(f243(x60871),x60872),f2(x60871)))+~P85(f784(f784(f243(x60871),x60872),f784(f88(x60871),x60872)))
% 11.41/11.18 [6088]~P69(x60881)+P85(f784(f784(f242(x60881),x60882),f2(x60881)))+~P85(f784(f784(f242(x60881),x60882),f784(f88(x60881),x60882)))
% 11.41/11.18 [6093]E(f62(x60931,x60932),f784(f784(f251(a1,a1),f2(a1)),x60931))+~P85(f784(f784(f243(a1),f2(a1)),x60932))+~P85(f784(f784(f243(a1),x60931),x60932))
% 11.41/11.18 [6096]~P89(x60961)+P85(f784(f784(f347(x60961),f784(f113(x60961),x60962)),f183(x60961)))+~P85(f784(f784(f242(a1),a92),x60962))
% 11.41/11.18 [6126]E(x61261,f2(a859))+~P85(f784(f784(f243(a859),x61261),f784(a160,x61262)))+P85(f784(f784(f243(a859),f585(x61262,x61261)),x61262))
% 11.41/11.18 [6150]~P113(x61501)+~P85(f784(f784(f243(x61501),f2(x61501)),f91(x61501,x61502)))+P85(f784(f784(f243(x61501),f2(x61501)),x61502))
% 11.41/11.18 [6152]~E(f784(f113(a859),x61522),f784(f113(a859),x61521))+P85(f784(f784(f242(a1),f784(f113(a1),x61521)),f2(a1)))+~P85(f784(a193,f784(f113(a1),x61522)))
% 11.41/11.18 [6180]E(f784(f250(a1,a1),f65(x61801,x61802)),f784(f784(f51(a1),x61801),x61802))+~P85(f784(f784(f243(a1),x61801),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x61802))
% 11.41/11.18 [6214]E(f784(f260(a1,a1),f65(x62141,x62142)),f60(a1,x62141,x62142))+~P85(f784(f784(f243(a1),x62141),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x62142))
% 11.41/11.18 [6215]E(x62151,f2(a1))+~P85(f784(f784(f289(a1),x62152),x62151))+P85(f784(f784(f242(a1),f784(f84(a1),x62152)),f784(f84(a1),x62151)))
% 11.41/11.18 [6217]~P120(x62172)+~P85(f784(f784(f243(x62172),f2(x62172)),f784(f109(x62172),x62171)))+P85(f784(f784(f243(a859),f2(a859)),x62171))
% 11.41/11.18 [6218]~P113(x62182)+~P85(f784(f784(f243(x62182),f2(x62182)),f784(f112(x62182),x62181)))+P85(f784(f784(f243(a1),f2(a1)),x62181))
% 11.41/11.18 [6219]~P113(x62192)+~P85(f784(f784(f242(x62192),f2(x62192)),f784(f112(x62192),x62191)))+P85(f784(f784(f242(a1),f2(a1)),x62191))
% 11.41/11.18 [6223]~E(x62232,f2(a859))+P85(f784(f784(f289(a859),f784(a114,x62231)),x62232))+~P85(f784(f784(f289(a1),x62231),f784(f109(a1),x62232)))
% 11.41/11.18 [6224]E(f784(f250(a1,a1),f62(x62241,x62242)),f784(f784(f51(a1),x62241),x62242))+~P85(f784(f784(f243(a1),f2(a1)),x62241))+~P85(f784(f784(f242(a1),f2(a1)),x62242))
% 11.41/11.18 [6237]E(f784(f260(a1,a1),f62(x62371,x62372)),f60(a1,x62371,x62372))+~P85(f784(f784(f243(a1),f2(a1)),x62371))+~P85(f784(f784(f242(a1),f2(a1)),x62372))
% 11.41/11.18 [6255]~P77(x62551)+P85(f784(f784(f243(x62551),x62552),f2(x62551)))+~P85(f784(f784(f243(x62551),f2(x62551)),f784(f88(x62551),x62552)))
% 11.41/11.18 [6256]~P77(x62561)+P85(f784(f784(f242(x62561),x62562),f2(x62561)))+~P85(f784(f784(f242(x62561),f2(x62561)),f784(f88(x62561),x62562)))
% 11.41/11.18 [6282]P85(f784(f64(x62821,x62822),f65(x62821,x62822)))+~P85(f784(f784(f243(a1),x62821),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x62822))
% 11.41/11.18 [6298]~P85(f784(f784(f243(a859),f2(a859)),x62981))+~P85(f784(f784(f289(a859),x62982),x62981))+~P85(f784(f784(f243(a859),x62981),x62982))
% 11.41/11.18 [6299]~P85(f784(f784(f243(a1),f2(a1)),x62991))+~P85(f784(f784(f289(a1),x62992),x62991))+~P85(f784(f784(f243(a1),x62991),x62992))
% 11.41/11.18 [6311]P85(f784(f64(x63111,x63112),f62(x63111,x63112)))+~P85(f784(f784(f243(a1),f2(a1)),x63112))+~P85(f784(f784(f242(a1),f2(a1)),x63111))
% 11.41/11.18 [6353]~P77(x63531)+P85(f784(f784(f243(x63531),f784(f88(x63531),x63532)),f2(x63531)))+~P85(f784(f784(f243(x63531),f2(x63531)),x63532))
% 11.41/11.18 [6354]~P77(x63541)+P85(f784(f784(f242(x63541),f784(f88(x63541),x63542)),f2(x63541)))+~P85(f784(f784(f242(x63541),f2(x63541)),x63542))
% 11.41/11.18 [6376]E(f784(f784(f3(a859),f784(a114,x63761)),f784(a114,x63762)),f784(a114,f195(x63761,x63762)))+~P85(f784(f784(f242(a1),f2(a1)),x63762))+~P85(f784(f784(f242(a1),f2(a1)),x63761))
% 11.41/11.18 [6394]P85(f784(f784(f242(a1),f2(a1)),f195(x63941,x63942)))+~P85(f784(f784(f242(a1),f2(a1)),x63942))+~P85(f784(f784(f242(a1),f2(a1)),x63941))
% 11.41/11.18 [6433]~P85(f784(x64331,x64332))+P85(f784(x64331,f2(a859)))+P85(f784(x64331,f784(f784(f89(a859),f801(x64332,x64331)),f87(a859))))
% 11.41/11.18 [6439]E(f292(a859,f289(a859),x64391,x64392),f187(f869(a859,a852)))+P85(f784(f784(f289(a859),x64391),x64392))+~P85(f784(f784(f289(a859),x64392),x64391))
% 11.41/11.18 [6518]E(f784(f113(a859),x65181),f784(f113(a859),x65182))+~P85(f784(f784(f242(a1),f784(f113(a1),x65182)),f2(a1)))+~P85(f784(a193,f784(f113(a1),x65181)))
% 11.41/11.18 [6531]~E(x65311,f2(a859))+~E(f749(x65312,x65311),f2(a859))+E(f784(f136(a859,a859,f89(a859),x65311),x65312),f2(a859))
% 11.41/11.18 [6557]~P85(f784(f71(x65571),f683(x65572,x65571)))+~P85(f784(f71(f869(x65571,a852)),x65572))+P85(f784(f71(x65571),f52(f869(x65571,a852),x65572)))
% 11.41/11.18 [6563]E(x65631,x65632)+P85(f784(f784(f243(a1),x65631),x65632))+~P85(f784(f784(f243(a1),x65631),f784(f784(f89(a1),x65632),f87(a1))))
% 11.41/11.18 [6564]P85(f784(f784(f243(a859),f784(a114,x65641)),f784(a114,x65642)))+~P85(f784(f784(f243(a1),f2(a1)),x65642))+~P85(f784(f784(f243(a1),x65641),x65642))
% 11.41/11.18 [6565]P85(f784(f784(f243(a859),f784(a114,x65651)),f784(a114,x65652)))+~P85(f784(f784(f243(a1),f2(a1)),x65652))+~P85(f784(f784(f243(a1),x65651),x65652))
% 11.41/11.18 [6566]P85(f784(f784(f243(a859),f784(a114,x65661)),f784(a114,x65662)))+~P85(f784(f784(f242(a1),f2(a1)),x65661))+~P85(f784(f784(f243(a1),x65661),x65662))
% 11.41/11.18 [6567]P85(f784(f784(f242(a859),f784(a114,x65671)),f784(a114,x65672)))+~P85(f784(f784(f243(a1),f2(a1)),x65671))+~P85(f784(f784(f242(a1),x65671),x65672))
% 11.41/11.18 [6568]P85(f784(f784(f242(a859),f784(a114,x65681)),f784(a114,x65682)))+~P85(f784(f784(f242(a1),f2(a1)),x65682))+~P85(f784(f784(f242(a1),x65681),x65682))
% 11.41/11.18 [6578]E(f60(a859,f784(a114,x65781),f784(a114,x65782)),f784(a114,f60(a1,x65781,x65782)))+~P85(f784(f784(f242(a1),f2(a1)),x65782))+~P85(f784(f784(f242(a1),f2(a1)),x65781))
% 11.41/11.18 [6579]E(f60(a859,f784(a114,x65791),f784(a114,x65792)),f784(a114,f60(a1,x65791,x65792)))+~P85(f784(f784(f242(a1),f2(a1)),x65792))+~P85(f784(f784(f242(a1),f2(a1)),x65791))
% 11.41/11.18 [6599]~P77(x65991)+~P85(f784(f784(f243(x65991),f784(f88(x65991),x65992)),f2(x65991)))+P85(f784(f784(f243(x65991),f2(x65991)),x65992))
% 11.41/11.18 [6600]~P77(x66001)+~P85(f784(f784(f242(x66001),f784(f88(x66001),x66002)),f2(x66001)))+P85(f784(f784(f242(x66001),f2(x66001)),x66002))
% 11.41/11.18 [6617]~P85(f784(f784(f243(a1),a92),x66172))+~P85(f784(f784(f243(a1),x66171),x66172))+P85(f784(f784(f243(a859),f784(f113(a859),x66171)),f784(f113(a859),x66172)))
% 11.41/11.18 [6713]~P85(f784(f784(f242(a1),f2(a1)),x67131))+P85(f784(f784(f243(a859),f784(a114,x67131)),x67132))+~P85(f784(f784(f243(a1),x67131),f784(f109(a1),x67132)))
% 11.41/11.18 [6714]~P85(f784(f784(f242(a1),f2(a1)),x67141))+P85(f784(f784(f289(a859),f784(a114,x67141)),x67142))+~P85(f784(f784(f289(a1),x67141),f784(f109(a1),x67142)))
% 11.41/11.18 [6730]E(x67301,f2(a1))+E(f60(a1,x67302,x67301),f2(a1))+E(f784(f784(f3(a1),f784(f88(a1),f784(f784(f51(a1),x67302),x67301))),f87(a1)),f784(f784(f51(a1),x67302),f784(f88(a1),x67301)))
% 11.41/11.18 [6746]~P85(f784(f784(f242(a1),f2(a1)),x67461))+~P85(f784(f784(f243(a859),f784(a114,x67461)),x67462))+P85(f784(f784(f243(a1),x67461),f784(f109(a1),x67462)))
% 11.41/11.18 [6747]~P85(f784(f784(f242(a1),f2(a1)),x67471))+~P85(f784(f784(f289(a859),f784(a114,x67471)),x67472))+P85(f784(f784(f289(a1),x67471),f784(f109(a1),x67472)))
% 11.41/11.18 [6784]~P85(f784(f784(f243(a859),f784(a114,x67841)),f784(a114,x67842)))+~P85(f784(f784(f243(a1),f2(a1)),x67842))+P85(f784(f784(f243(a1),x67841),x67842))
% 11.41/11.18 [6785]~P85(f784(f784(f243(a859),f784(a114,x67851)),f784(a114,x67852)))+~P85(f784(f784(f242(a1),f2(a1)),x67851))+P85(f784(f784(f243(a1),x67851),x67852))
% 11.41/11.18 [6786]~P85(f784(f784(f242(a859),f784(a114,x67861)),f784(a114,x67862)))+~P85(f784(f784(f243(a1),f2(a1)),x67861))+P85(f784(f784(f242(a1),x67861),x67862))
% 11.41/11.18 [6787]~P85(f784(f784(f242(a859),f784(a114,x67871)),f784(a114,x67872)))+~P85(f784(f784(f242(a1),f2(a1)),x67872))+P85(f784(f784(f242(a1),x67871),x67872))
% 11.41/11.18 [6818]P85(f784(f784(f242(a1),x68181),x68182))+~P85(f784(f784(f242(a859),f784(f113(a859),x68181)),f784(f113(a859),x68182)))+P85(f784(f784(f242(a1),x68181),a92))
% 11.41/11.18 [6845]P85(f784(f784(f242(a1),f2(a1)),f60(a1,x68451,x68452)))+~P85(f784(f784(f242(a1),f2(a1)),x68452))+~P85(f784(f784(f242(a1),f2(a1)),x68451))
% 11.41/11.18 [6942]P85(f784(f784(f243(a1),a92),x69421))+~P85(f784(f784(f243(a1),x69422),x69421))+~P85(f784(f784(f243(a859),f784(f113(a859),x69422)),f784(f113(a859),x69421)))
% 11.41/11.18 [6990]E(f784(f784(f251(a1,a1),f784(f784(f51(a1),x69901),x69902)),f60(a1,x69901,x69902)),f65(x69901,x69902))+~P85(f784(f784(f243(a1),x69901),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x69902))
% 11.41/11.18 [7011]E(f784(f784(f251(a1,a1),f784(f784(f51(a1),x70111),x70112)),f60(a1,x70111,x70112)),f62(x70111,x70112))+~P85(f784(f784(f242(a1),f2(a1)),x70112))+~P85(f784(f784(f242(a1),f2(a1)),x70111))
% 11.41/11.18 [7066]~P92(x70662)+E(x70661,f120(x70662))+E(f784(f136(x70662,x70662,f90(x70662),f784(f135(x70662),x70661)),f784(f163(x70662),x70661)),f784(f73(x70662,f90(x70662)),f784(f164(x70662),x70661)))
% 11.41/11.18 [7179]~E(x71791,f2(a859))+E(f784(f136(a859,a859,f89(a859),x71791),x71792),f2(a859))+P85(f784(f784(f347(a859),f749(x71792,x71791)),f784(f164(a859),x71792)))
% 11.41/11.18 [7233]~P85(f784(f784(f243(a1),x72332),f2(a1)))+P85(f784(f784(f243(a1),f784(f784(f51(a1),x72331),x72332)),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x72331))
% 11.41/11.18 [7234]~P85(f784(f784(f243(a1),x72341),f2(a1)))+P85(f784(f784(f243(a1),f784(f784(f51(a1),x72341),x72342)),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x72342))
% 11.41/11.18 [7235]~P85(f784(f784(f243(a1),x72351),f2(a1)))+P85(f784(f784(f243(a1),f784(f784(f51(a1),x72351),x72352)),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x72352))
% 11.41/11.18 [7236]~P85(f784(f784(f243(a1),x72362),f2(a1)))+P85(f784(f784(f242(a1),f784(f784(f51(a1),x72361),x72362)),f2(a1)))+~P85(f784(f784(f242(a1),f2(a1)),x72361))
% 11.41/11.18 [7237]~P85(f784(f784(f242(a1),x72371),f2(a1)))+P85(f784(f784(f242(a1),f784(f784(f51(a1),x72371),x72372)),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x72372))
% 11.41/11.18 [7246]P85(f784(f784(f347(f869(x72461,a852)),f683(x72462,x72461)),x72462))+~P85(f784(f71(f869(x72461,a852)),x72462))+P85(f784(f71(x72461),f52(f869(x72461,a852),x72462)))
% 11.41/11.18 [7351]P26(x73511,x73511,x73512,f249(f869(x73511,a852)))+~E(f784(f313(x73511,x73511,x73512),f249(f869(x73511,a852))),f249(f869(x73511,a852)))+~P85(f784(f71(x73511),f249(f869(x73511,a852))))
% 11.41/11.18 [7479]~P26(x74791,x74791,x74792,f249(f869(x74791,a852)))+E(f784(f313(x74791,x74791,x74792),f249(f869(x74791,a852))),f249(f869(x74791,a852)))+~P85(f784(f71(x74791),f249(f869(x74791,a852))))
% 11.41/11.18 [7502]E(f62(f784(f113(a1),x75021),f784(f113(a1),x75022)),f784(f784(f251(a1,a1),f2(a1)),f784(f113(a1),x75021)))+~P85(f784(f784(f243(a1),f2(a1)),f784(f113(a1),x75022)))+~P85(f784(f784(f243(a1),f784(f113(a1),x75021)),f784(f113(a1),x75022)))
% 11.41/11.18 [7620]E(f784(f784(f51(a1),x76201),x76202),f784(f113(a1),a106))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),x76201),x76202)),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x76201))
% 11.41/11.18 [7678]~P85(f784(f784(f243(a1),x76782),f2(a1)))+~P85(f784(f784(f243(a1),f784(f784(f51(a1),x76781),x76782)),f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x76781))
% 11.41/11.18 [7682]E(f784(f784(f89(a1),x76821),x76822),f60(a1,x76821,x76822))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),x76821),x76822)),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x76821))
% 11.41/11.18 [7684]P85(f784(f784(f243(a1),x76841),f2(a1)))+~P85(f784(f784(f243(a1),f784(f784(f51(a1),x76841),x76842)),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x76842))
% 11.41/11.18 [7935]~P100(x79351)+P49(a859,x79351,f289(a859),x79352)+~P85(f784(f784(f242(x79351),f784(x79352,f390(x79352,x79351))),f784(x79352,f406(x79352,x79351))))
% 11.41/11.18 [8375]~P101(x83751)+P15(x83751,x83752)+~P85(f784(f784(f242(x83751),f784(f784(f155(x83751),x83752),f772(x83752,x83751))),f784(f784(f155(x83751),x83752),f773(x83752,x83751))))
% 11.41/11.18 [5574]E(x55741,f2(a1))+~E(f60(a1,x55742,x55741),f2(a1))+E(f784(f784(f51(a1),x55742),f784(f88(a1),x55741)),f784(f88(a1),f784(f784(f51(a1),x55742),x55741)))
% 11.41/11.18 [5591]~P37(x55912)+~P37(x55911)+P37(f784(f784(f110(f869(a1,a852)),x55911),x55912))
% 11.41/11.18 [5592]~P37(x55922)+~P37(x55921)+P37(f784(f784(f111(f869(a1,a852)),x55921),x55922))
% 11.41/11.18 [5609]~P89(x56091)+~P59(x56091)+E(f784(f88(x56091),f784(f784(f293(x56091),f87(x56091)),x56092)),f784(f784(f293(x56091),f784(f113(x56091),a106)),x56092))
% 11.41/11.18 [5734]E(x57341,f2(a1))+~E(f60(a1,x57342,x57341),f2(a1))+E(f784(f784(f51(a1),f784(f88(a1),x57342)),x57341),f784(f88(a1),f784(f784(f51(a1),x57342),x57341)))
% 11.41/11.18 [5868]~P101(x58681)+P15(x58681,x58682)+P85(f784(f784(f243(a859),f773(x58682,x58681)),f784(f188(f860(x58681)),x58682)))
% 11.41/11.18 [6023]~P89(x60231)+~E(f784(f113(x60231),x60232),f2(x60231))+P30(x60231,f784(f113(x60231),f784(f784(f89(a1),x60232),f784(f88(a1),a92))))
% 11.41/11.18 [6024]~P89(x60241)+~E(f784(f113(x60241),x60242),f2(x60241))+P30(x60241,f784(f113(x60241),f784(f784(f89(a1),a92),f784(f88(a1),x60242))))
% 11.41/11.18 [6026]E(f784(a66,f62(f784(f88(a1),x60261),f784(f88(a1),x60262))),f61(x60261,x60262))+P85(f784(f784(f243(a1),f2(a1)),x60262))+P85(f784(f784(f242(a1),f2(a1)),x60261))
% 11.41/11.18 [6158]~E(x61582,f2(a859))+~E(x61581,f2(a859))+P85(f784(f784(f242(a1),f784(f109(a1),x61581)),f784(f88(a1),f784(f109(a1),x61582))))
% 11.41/11.18 [6184]E(f784(f784(f89(a859),f784(f113(a859),x61841)),f784(f113(a859),x61842)),f784(f113(a859),f784(f784(f89(a1),x61841),x61842)))+P85(f784(f784(f243(a1),x61841),a92))+P85(f784(f784(f243(a1),x61842),a92))
% 11.41/11.18 [6320]~P69(x63201)+~P85(f784(f784(f243(x63201),f2(x63201)),x63202))+P85(f784(f784(f243(x63201),f784(f88(x63201),x63202)),x63202))
% 11.41/11.18 [6321]~P69(x63211)+~P85(f784(f784(f242(x63211),f2(x63211)),x63212))+P85(f784(f784(f242(x63211),f784(f88(x63211),x63212)),x63212))
% 11.41/11.18 [6503]E(f784(f784(f3(a859),f784(a114,x65031)),f784(a114,x65032)),f784(a114,f784(f784(f3(a1),x65031),x65032)))+~P85(f784(f784(f242(a1),f2(a1)),x65032))+~P85(f784(f784(f242(a1),x65032),x65031))
% 11.41/11.18 [6540]E(f784(a114,f60(a1,f784(f113(a1),x65401),f784(f113(a1),x65402))),f60(a859,f784(f113(a859),x65401),f784(f113(a859),x65402)))+P85(f784(a193,f784(f113(a1),x65401)))+P85(f784(a193,f784(f113(a1),x65402)))
% 11.41/11.18 [6558]~P69(x65581)+P85(f784(f784(f243(x65581),f2(x65581)),x65582))+~P85(f784(f784(f243(x65581),f784(f88(x65581),x65582)),x65582))
% 11.41/11.18 [6559]~P69(x65591)+P85(f784(f784(f242(x65591),f2(x65591)),x65592))+~P85(f784(f784(f242(x65591),f784(f88(x65591),x65592)),x65592))
% 11.41/11.18 [6570]~P69(x65701)+~P85(f784(f784(f243(x65701),f2(x65701)),x65702))+P85(f784(f784(f243(x65701),f2(x65701)),f784(f784(f89(x65701),x65702),x65702)))
% 11.41/11.18 [6572]~P69(x65721)+~P85(f784(f784(f242(x65721),f2(x65721)),x65722))+P85(f784(f784(f242(x65721),f2(x65721)),f784(f784(f89(x65721),x65722),x65722)))
% 11.41/11.18 [6582]E(f784(f784(f89(a859),f784(a114,x65821)),f784(a114,x65822)),f784(a114,f784(f784(f89(a1),x65821),x65822)))+~P85(f784(f784(f242(a1),f2(a1)),x65822))+~P85(f784(f784(f242(a1),f2(a1)),x65821))
% 11.41/11.18 [6583]E(f784(f784(f89(a859),f784(a114,x65831)),f784(a114,x65832)),f784(a114,f784(f784(f89(a1),x65831),x65832)))+~P85(f784(f784(f242(a1),f2(a1)),x65832))+~P85(f784(f784(f242(a1),f2(a1)),x65831))
% 11.41/11.18 [6584]E(f784(f784(f90(a859),f784(a114,x65841)),f784(a114,x65842)),f784(a114,f784(f784(f90(a1),x65841),x65842)))+~P85(f784(f784(f242(a1),f2(a1)),x65842))+~P85(f784(f784(f242(a1),f2(a1)),x65841))
% 11.41/11.18 [6585]E(f784(f784(f51(a859),f784(a114,x65851)),f784(a114,x65852)),f784(a114,f784(f784(f51(a1),x65851),x65852)))+~P85(f784(f784(f242(a1),f2(a1)),x65852))+~P85(f784(f784(f242(a1),f2(a1)),x65851))
% 11.41/11.18 [6595]E(x65951,f2(a859))+P85(f784(f784(f243(a859),f2(a859)),x65952))+~P85(f784(f784(f243(a859),f2(a859)),f784(f784(f252(a859),x65952),x65951)))
% 11.41/11.18 [6628]~P89(x66281)+E(f784(f113(x66281),x66282),f2(x66281))+~P30(x66281,f784(f113(x66281),f784(f784(f89(a1),a92),f784(f88(a1),x66282))))
% 11.41/11.18 [6629]~P89(x66291)+E(f784(f113(x66291),x66292),f2(x66291))+~P30(x66291,f784(f113(x66291),f784(f784(f89(a1),x66292),f784(f88(a1),a92))))
% 11.41/11.18 [6690]~P85(f784(f71(x66901),x66902))+~P85(f784(f71(x66901),f249(f869(x66901,a852))))+P85(f784(f71(x66901),f784(f88(f869(x66901,a852)),x66902)))
% 11.41/11.18 [6715]~P85(f784(f784(f243(a1),f2(a1)),x67152))+~P85(f784(f784(f242(a1),x67152),x67151))+P85(f784(f784(f243(a1),f2(a1)),f784(f784(f51(a1),x67151),x67152)))
% 11.41/11.18 [6716]~P85(f784(f784(f243(a1),x67162),f2(a1)))+~P85(f784(f784(f242(a1),x67161),f2(a1)))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f51(a1),x67161),x67162)))
% 11.41/11.18 [6757]~P85(f784(f784(f243(a859),f2(a859)),x67572))+~P85(f784(f784(f243(a859),f2(a859)),x67571))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f90(a859),x67571),x67572)))
% 11.41/11.18 [6758]~P85(f784(f784(f242(a1),f2(a1)),x67582))+~P85(f784(f784(f242(a1),f2(a1)),x67581))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),x67581),x67582)))
% 11.41/11.18 [6759]~P85(f784(f784(f242(a1),f2(a1)),x67592))+~P85(f784(f784(f242(a1),f2(a1)),x67591))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f90(a1),x67591),x67592)))
% 11.41/11.18 [6760]~P85(f784(f784(f243(a1),f2(a1)),x67602))+~P85(f784(f784(f242(a1),f2(a1)),x67601))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f51(a1),x67601),x67602)))
% 11.41/11.18 [6761]~P85(f784(f784(f242(a1),f2(a1)),x67612))+~P85(f784(f784(f242(a1),f2(a1)),x67611))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f51(a1),x67611),x67612)))
% 11.41/11.18 [6830]E(x68301,f2(a1))+E(f60(a1,x68302,x68301),f2(a1))+E(f784(f784(f3(a1),f784(f88(a1),f784(f784(f51(a1),x68302),x68301))),f87(a1)),f784(f784(f51(a1),f784(f88(a1),x68302)),x68301))
% 11.41/11.18 [6890]P85(f784(f784(f243(a859),f2(a859)),x68901))+P85(f784(f784(f243(a859),f2(a859)),x68902))+~P85(f784(f784(f243(a859),f2(a859)),f784(f784(f89(a859),x68902),x68901)))
% 11.41/11.18 [6891]~P69(x68911)+P85(f784(f784(f243(x68911),f2(x68911)),x68912))+~P85(f784(f784(f243(x68911),f2(x68911)),f784(f784(f89(x68911),x68912),x68912)))
% 11.41/11.18 [6892]~P69(x68921)+P85(f784(f784(f242(x68921),f2(x68921)),x68922))+~P85(f784(f784(f242(x68921),f2(x68921)),f784(f784(f89(x68921),x68922),x68922)))
% 11.41/11.18 [6943]~P85(f784(f71(x69431),x69432))+P85(f784(f71(x69431),f249(f869(x69431,a852))))+~P85(f784(f71(x69431),f784(f88(f869(x69431,a852)),x69432)))
% 11.41/11.18 [7003]P85(f784(f784(f242(a1),x70031),f2(a1)))+~P85(f784(f784(f243(a1),x70032),f2(a1)))+~P85(f784(f784(f242(a1),f2(a1)),f784(f784(f51(a1),x70031),x70032)))
% 11.41/11.18 [7009]~P85(f784(f784(f243(a1),f2(a1)),x70091))+P85(f784(f784(f242(a1),x70091),x70092))+~P85(f784(f784(f243(a1),f2(a1)),f784(f784(f51(a1),x70092),x70091)))
% 11.41/11.18 [7010]~P85(f784(f784(f242(a1),f2(a1)),x70102))+P85(f784(f784(f242(a1),x70101),x70102))+~P85(f784(f784(f243(a1),f2(a1)),f784(f784(f51(a1),x70102),x70101)))
% 11.41/11.18 [7042]P85(f784(f784(f243(a1),f2(a1)),x70421))+~P85(f784(f784(f242(a1),f2(a1)),x70422))+~P85(f784(f784(f243(a1),f2(a1)),f784(f784(f51(a1),x70422),x70421)))
% 11.41/11.18 [7043]P85(f784(f784(f242(a1),f2(a1)),x70431))+~P85(f784(f784(f243(a1),f2(a1)),x70432))+~P85(f784(f784(f242(a1),f2(a1)),f784(f784(f51(a1),x70431),x70432)))
% 11.41/11.18 [7142]E(f221(x71421,x71422),x71421)+~E(x71422,f2(a859))+~P85(f784(f334(f868(a859,a859),a224),f784(f784(f251(a859,a859),x71421),x71422)))
% 11.41/11.18 [7371]E(f169(x73711,x73712),f120(a1))+P85(f784(f784(f242(a1),x73711),x73712))+~P85(f784(f334(f868(a1,a1),a174),f784(f784(f251(a1,a1),x73711),x73712)))
% 11.41/11.18 [7396]E(f784(f784(f251(a1,a1),f784(f113(a1),a106)),f784(f784(f89(a1),x73961),x73962)),f65(x73961,x73962))+~P85(f784(f784(f243(a1),f2(a1)),x73962))+~P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),x73961),x73962)))
% 11.41/11.18 [7423]E(x74231,f2(a859))+E(f221(x74231,f60(a859,x74232,x74231)),f221(x74232,x74231))+~P85(f784(f334(f868(a859,a859),a224),f784(f784(f251(a859,a859),x74232),x74231)))
% 11.41/11.18 [7510]~P85(f784(f71(x75102),f249(f869(x75102,a852))))+~P85(f784(f71(x75101),f249(f869(x75101,a852))))+P85(f784(f71(f870(x75101,x75102)),f249(f869(f870(x75101,x75102),a852))))
% 11.41/11.18 [7511]~P85(f784(f71(x75112),f249(f869(x75112,a852))))+~P85(f784(f71(x75111),f249(f869(x75111,a852))))+P85(f784(f71(f868(x75111,x75112)),f249(f869(f868(x75111,x75112),a852))))
% 11.41/11.18 [7583]~P85(f784(f784(f243(a859),f784(a160,f2(a859))),x75831))+~P85(f784(f784(f243(a859),f784(a160,f2(a859))),x75832))+P85(f784(f784(f243(a859),x75831),f784(f784(f90(a859),x75832),x75831)))
% 11.41/11.18 [7584]~P85(f784(f784(f243(a859),f784(a160,f2(a859))),x75841))+~P85(f784(f784(f243(a859),f784(a160,f2(a859))),x75842))+P85(f784(f784(f243(a859),x75841),f784(f784(f90(a859),x75841),x75842)))
% 11.41/11.18 [7619]E(f784(f50(x76191),f249(f869(x76191,a852))),f784(a160,f2(a859)))+P85(f784(f71(x76192),f249(f869(x76192,a852))))+~P85(f784(f71(f869(x76192,x76191)),f249(f869(f869(x76192,x76191),a852))))
% 11.41/11.18 [7671]E(f62(x76711,x76712),f784(f784(f251(a1,a1),f2(a1)),x76711))+~P85(f784(f784(f243(a1),x76711),x76712))+~P85(f784(f334(f868(a1,a1),a70),f784(f784(f251(a1,a1),x76711),x76712)))
% 11.41/11.18 [7675]E(f220(f784(f88(a1),x76751),f784(f88(a1),x76752)),f220(x76751,x76752))+~P85(f784(f784(f243(a1),x76752),f2(a1)))+~P85(f784(f334(f868(a1,a1),a226),f784(f784(f251(a1,a1),x76751),x76752)))
% 11.41/11.18 [7691]E(f62(x76911,x76912),f784(f784(f251(a1,a1),f2(a1)),x76911))+~P85(f784(f784(f242(a1),x76912),f2(a1)))+~P85(f784(f334(f868(a1,a1),a70),f784(f784(f251(a1,a1),x76911),x76912)))
% 11.41/11.18 [7743]~P85(f784(f784(f243(a859),f784(a160,f2(a859))),x77432))+~P85(f784(f784(f243(a859),f784(a160,f2(a859))),x77431))+P85(f784(f784(f243(a859),f784(a160,f2(a859))),f784(f784(f90(a859),x77431),x77432)))
% 11.41/11.18 [7744]~P85(f784(f784(f242(a859),f784(a160,f2(a859))),x77441))+~P85(f784(f784(f242(a859),f784(a160,f2(a859))),x77442))+P85(f784(f784(f242(a859),f784(a160,f2(a859))),f784(f784(f90(a859),x77441),x77442)))
% 11.41/11.18 [7906]E(f784(f784(f251(a1,a1),f784(f113(a1),a106)),f784(f784(f89(a1),x79061),x79062)),f65(x79061,x79062))+~P85(f784(f784(f242(a1),x79062),f2(a1)))+~P85(f784(f334(f868(a1,a1),a67),f784(f784(f251(a1,a1),x79061),x79062)))
% 11.41/11.18 [7946]E(f784(f784(f144(a1),x79461),f169(f784(f784(f89(a1),x79461),f87(a1)),x79462)),f169(x79461,x79462))+~P85(f784(f784(f242(a1),x79461),x79462))+~P85(f784(f334(f868(a1,a1),a174),f784(f784(f251(a1,a1),x79461),x79462)))
% 11.41/11.18 [8215]E(f784(f784(f251(a1,a1),f784(f113(a1),a106)),f784(f784(f89(a1),x82151),x82152)),f65(x82151,x82152))+~P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),x82151),x82152)))+~P85(f784(f334(f868(a1,a1),a67),f784(f784(f251(a1,a1),x82151),x82152)))
% 11.41/11.18 [8497]E(f784(f784(f251(a1,a1),f784(f113(a1),a106)),f784(f784(f89(a1),f784(f113(a1),x84971)),f784(f113(a1),x84972))),f65(f784(f113(a1),x84971),f784(f113(a1),x84972)))+~P85(f784(f784(f243(a1),f2(a1)),f784(f113(a1),x84972)))+~P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),f784(f113(a1),x84971)),f784(f113(a1),x84972))))
% 11.41/11.18 [8518]~P37(x85182)+~P37(x85181)+E(f784(f313(a859,a1,f109(a1)),f784(f784(f110(f869(a859,a852)),f784(f313(a1,a859,a114),x85181)),f784(f313(a1,a859,a114),x85182))),f784(f784(f110(f869(a1,a852)),x85181),x85182))
% 11.41/11.18 [8519]~P37(x85192)+~P37(x85191)+E(f784(f313(a859,a1,f109(a1)),f784(f784(f111(f869(a859,a852)),f784(f313(a1,a859,a114),x85191)),f784(f313(a1,a859,a114),x85192))),f784(f784(f111(f869(a1,a852)),x85191),x85192))
% 11.41/11.18 [9112]~P89(x91121)+~E(f784(f113(x91121),x91122),f87(x91121))+P30(x91121,f784(f113(x91121),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f88(a1),x91122))))
% 11.41/11.18 [9326]~P89(x93261)+E(f784(f113(x93261),x93262),f87(x93261))+~P30(x93261,f784(f113(x93261),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f88(a1),x93262))))
% 11.41/11.18 [9748]~P100(x97482)+P51(a859,x97482,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97481)+P85(f784(f784(f289(a859),f382(x97481,x97482)),f383(x97481,x97482)))
% 11.41/11.18 [9751]~P100(x97511)+P51(a859,x97511,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97512)+~P85(f784(f784(f289(a859),f383(x97512,x97511)),f382(x97512,x97511)))
% 11.41/11.18 [9752]~P100(x97521)+P51(a859,x97521,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x97522)+~P85(f784(f784(f243(x97521),f784(x97522,f382(x97522,x97521))),f784(x97522,f383(x97522,x97521))))
% 11.41/11.18 [9844]~P100(x98441)+P49(a859,x98441,f289(a859),x98442)+~P51(a859,x98441,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x98442)
% 11.41/11.18 [10040]E(x100401,f2(a1))+E(x100402,f2(a1))+E(f784(f262(a1,a1,a1,a1,f41(a1),f784(f90(a1),f91(a1,x100402))),f784(f784(f784(f105(f868(a1,a1)),f784(f784(a343,f91(a1,x100401)),f91(a1,x100402))),f68(x100401,x100402)),f784(f784(f261(a1,a1,f868(a1,a1)),f784(f784(f20(a1,f869(a1,f868(a1,a1)),f869(a1,f868(a1,a1))),f784(f784(f10(f869(a1,f869(f868(a1,a1),f868(a1,a1))),f869(f869(a1,f868(a1,a1)),f869(a1,f868(a1,a1))),a1),f20(a1,f868(a1,a1),f868(a1,a1))),f784(f784(f10(f868(a1,a1),f869(a1,f869(f868(a1,a1),f868(a1,a1))),a1),f784(f9(a1,f868(a1,a1),f869(f868(a1,a1),f868(a1,a1))),f784(f784(f10(a852,f869(f868(a1,a1),f869(f868(a1,a1),f868(a1,a1))),a1),f105(f868(a1,a1))),f784(f784(f9(a1,a1,a852),a343),f2(a1))))),f784(f784(f9(a1,a1,f868(a1,a1)),f784(f784(f10(a1,f869(a1,f868(a1,a1)),a1),f251(a1,a1)),f88(a1))),f2(a1))))),f784(f784(f9(a1,f869(a1,a1),f869(a1,f868(a1,a1))),f784(f784(f10(f869(a1,f868(a1,a1)),f869(f869(a1,a1),f869(a1,f868(a1,a1))),a1),f10(a1,f868(a1,a1),a1)),f784(f784(f10(a1,f869(a1,f868(a1,a1)),a1),f251(a1,a1)),f784(f784(f9(a1,a1,a1),f784(f784(f10(a1,f869(a1,a1),a1),f3(a1)),f88(a1))),f87(a1))))),f784(f3(a1),f784(f84(a1),x100402))))),f68(x100401,x100402)))),f61(x100401,x100402))
% 11.41/11.18 [10041]E(x100411,f2(a1))+E(x100412,f2(a1))+E(f784(f262(a1,a1,a1,a1,f41(a1),f784(f90(a1),f91(a1,x100412))),f784(f784(f784(f105(f868(a1,a1)),f784(f784(a345,f784(f784(a344,f784(f784(f243(a1),f2(a1)),x100412)),f784(f784(f242(a1),f2(a1)),x100411))),f784(f784(a344,f784(f784(f243(a1),x100412),f2(a1))),f784(f784(f243(a1),x100411),f2(a1))))),f68(x100411,x100412)),f784(f784(f261(a1,a1,f868(a1,a1)),f784(f784(f20(a1,f869(a1,f868(a1,a1)),f869(a1,f868(a1,a1))),f784(f784(f10(f869(a1,f869(f868(a1,a1),f868(a1,a1))),f869(f869(a1,f868(a1,a1)),f869(a1,f868(a1,a1))),a1),f20(a1,f868(a1,a1),f868(a1,a1))),f784(f784(f10(f868(a1,a1),f869(a1,f869(f868(a1,a1),f868(a1,a1))),a1),f784(f9(a1,f868(a1,a1),f869(f868(a1,a1),f868(a1,a1))),f784(f784(f10(a852,f869(f868(a1,a1),f869(f868(a1,a1),f868(a1,a1))),a1),f105(f868(a1,a1))),f784(f784(f9(a1,a1,a852),a343),f2(a1))))),f784(f784(f9(a1,a1,f868(a1,a1)),f784(f784(f10(a1,f869(a1,f868(a1,a1)),a1),f251(a1,a1)),f88(a1))),f2(a1))))),f784(f784(f9(a1,f869(a1,a1),f869(a1,f868(a1,a1))),f784(f784(f10(f869(a1,f868(a1,a1)),f869(f869(a1,a1),f869(a1,f868(a1,a1))),a1),f10(a1,f868(a1,a1),a1)),f784(f784(f10(a1,f869(a1,f868(a1,a1)),a1),f251(a1,a1)),f784(f784(f9(a1,a1,a1),f784(f784(f10(a1,f869(a1,a1),a1),f3(a1)),f88(a1))),f87(a1))))),f784(f3(a1),f784(f84(a1),x100412))))),f68(x100411,x100412)))),f61(x100411,x100412))
% 11.41/11.18 [5599]~P113(x55991)+~P89(x55991)+E(f784(f84(x55991),f784(f784(f252(x55991),f784(f113(x55991),a106)),x55992)),f87(x55991))
% 11.41/11.18 [6097]~P136(x60971)+~P85(f784(f784(f243(a1),x60972),f2(a1)))+E(f784(f88(x60971),f784(f109(x60971),f784(a114,f784(f88(a1),x60972)))),f784(f112(x60971),x60972))
% 11.41/11.18 [6304]P85(f784(f784(f242(a108),x63041),f87(a108)))+E(f784(f784(f89(a108),f87(a108)),f277(x63041,f784(f784(f51(a108),x63042),x63041))),f277(x63041,x63042))+P85(f784(f784(f243(a108),x63042),x63041))
% 11.41/11.18 [6377]E(x63771,f2(a1))+~E(f784(f84(a1),x63772),f87(a1))+P85(f784(f784(f289(a1),f784(f784(f90(a1),x63771),x63772)),x63771))
% 11.41/11.18 [6799]~E(x67992,f87(a859))+~P85(f784(f784(f243(a859),f2(a859)),x67991))+P85(f784(f784(f289(a859),f784(f784(f90(a859),x67991),x67992)),x67991))
% 11.41/11.18 [6800]~E(x68001,f87(a859))+~P85(f784(f784(f243(a859),f2(a859)),x68002))+P85(f784(f784(f289(a859),f784(f784(f90(a859),x68001),x68002)),x68002))
% 11.41/11.18 [6932]~P88(x69321)+~P85(f784(f784(f347(x69321),x69322),f119(x69321)))+~E(f784(f784(f89(x69321),f784(f784(f89(x69321),f87(x69321)),x69322)),x69322),f2(x69321))
% 11.41/11.18 [7044]~P85(f784(f784(f243(a1),x70441),f2(a1)))+~P85(f784(f784(f242(a1),x70442),f2(a1)))+E(f784(f250(a1,a1),f784(a66,f62(f784(f88(a1),x70441),f784(f88(a1),x70442)))),f784(f784(f51(a1),x70441),x70442))
% 11.41/11.18 [7060]~P85(f784(f784(f243(a1),x70601),f2(a1)))+~P85(f784(f784(f242(a1),x70602),f2(a1)))+E(f784(f260(a1,a1),f784(a66,f62(f784(f88(a1),x70601),f784(f88(a1),x70602)))),f60(a1,x70601,x70602))
% 11.41/11.18 [7068]~P85(f784(f784(f243(a1),x70682),f2(a1)))+E(f784(f250(a1,a1),f784(a66,f65(f784(f88(a1),x70681),f784(f88(a1),x70682)))),f784(f784(f51(a1),x70681),x70682))+~P85(f784(f784(f243(a1),f2(a1)),x70681))
% 11.41/11.18 [7072]E(x70721,f2(a1))+E(f784(f84(a1),x70722),f87(a1))+~P85(f784(f784(f289(a1),f784(f784(f90(a1),x70721),x70722)),x70721))
% 11.41/11.18 [7087]~P85(f784(f784(f243(a1),x70872),f2(a1)))+E(f784(f260(a1,a1),f784(a66,f65(f784(f88(a1),x70871),f784(f88(a1),x70872)))),f60(a1,x70871,x70872))+~P85(f784(f784(f243(a1),f2(a1)),x70871))
% 11.41/11.18 [7137]E(f784(f784(f51(a1),f784(f784(f252(a1),x71371),x71372)),x71371),f784(f784(f252(a1),x71371),f784(f784(f3(a859),x71372),f784(a160,f2(a859)))))+~P85(f784(f784(f243(a859),f2(a859)),x71372))+~P85(f784(f784(f243(a1),f2(a1)),x71371))
% 11.41/11.18 [7242]~P85(f784(f784(f243(a859),f2(a859)),x72421))+~P85(f784(f784(f243(a859),f87(a859)),x72422))+P85(f784(f784(f243(a859),f784(f784(f51(a859),x72421),x72422)),x72421))
% 11.41/11.18 [7243]~P85(f784(f784(f243(a859),f2(a859)),x72431))+~P85(f784(f784(f243(a859),f2(a859)),x72432))+P85(f784(f784(f243(a859),f784(f784(f3(a859),x72431),x72432)),x72431))
% 11.41/11.18 [7244]~P85(f784(f784(f243(a1),f2(a1)),x72441))+~P85(f784(f784(f243(a1),f87(a1)),x72442))+P85(f784(f784(f243(a1),f784(f784(f51(a1),x72441),x72442)),x72441))
% 11.41/11.18 [7403]E(x74031,f2(a859))+~E(x74032,f2(a1))+~P85(f784(f784(f243(a1),f2(a1)),f784(f784(f252(a1),f784(f84(a1),x74032)),x74031)))
% 11.41/11.18 [7440]E(x74401,f87(a859))+~P85(f784(f784(f243(a859),f2(a859)),x74402))+~P85(f784(f784(f289(a859),f784(f784(f90(a859),x74402),x74401)),x74402))
% 11.41/11.18 [7441]E(x74411,f87(a859))+~P85(f784(f784(f243(a859),f2(a859)),x74412))+~P85(f784(f784(f289(a859),f784(f784(f90(a859),x74411),x74412)),x74412))
% 11.41/11.18 [7826]~E(x78262,f120(f860(x78261)))+E(f784(f188(f860(f860(x78261))),f170(x78261,x78262)),f2(a859))+~P15(a859,f784(f162(a859),f784(f784(f146(f860(x78261),a859),f188(f860(x78261))),x78262)))
% 11.41/11.18 [8074]P85(f784(x80741,x80742))+~P85(f784(x80741,f784(a116,f582(x80741,x80742))))+~P85(f784(f784(f347(f869(f868(a859,a859),a852)),x80742),a107))
% 11.41/11.18 [8088]E(x80881,f120(f860(x80882)))+E(f784(f188(f860(x80882)),f784(f784(f155(f860(x80882)),x80881),f2(a859))),f784(f188(f860(f860(x80882))),f170(x80882,x80881)))+~P15(a859,f784(f162(a859),f784(f784(f146(f860(x80882),a859),f188(f860(x80882))),x80881)))
% 11.41/11.18 [8758]~P85(f784(f71(x87581),f784(f266(x87581),x87582)))+~P85(f784(f71(x87581),f249(f869(x87581,a852))))+P85(f784(f71(x87581),f784(f266(x87581),f784(f784(f10(a852,a852,x87581),a341),x87582))))
% 11.41/11.18 [8811]E(f784(f784(f251(a859,a859),f784(a160,f784(f784(f51(a859),f784(f784(f3(a859),x88111),x88112)),x88112))),f60(a859,f784(f784(f3(a859),x88111),x88112),x88112)),f94(f868(a859,a859),f63(x88111,x88112)))+~P85(f784(f784(f243(a859),f2(a859)),x88112))+~P85(f784(f784(f242(a859),x88112),x88111))
% 11.41/11.18 [9080]~P85(f784(f71(x90801),f784(f266(x90801),x90802)))+P85(f784(f71(x90801),f249(f869(x90801,a852))))+~P85(f784(f71(x90801),f784(f266(x90801),f784(f784(f10(a852,a852,x90801),a341),x90802))))
% 11.41/11.18 [9745]P27(x97451,x97452)+~P35(x97451,f784(f250(f869(f868(x97451,x97451),a852),f869(f868(x97451,x97451),a852)),x97452))+~P85(f784(f784(f242(f869(f868(x97451,x97451),a852)),f784(f784(f291(x97451,x97451,x97451),f784(f250(f869(f868(x97451,x97451),a852),f869(f868(x97451,x97451),a852)),x97452)),f784(f260(f869(f868(x97451,x97451),a852),f869(f868(x97451,x97451),a852)),x97452))),f784(f250(f869(f868(x97451,x97451),a852),f869(f868(x97451,x97451),a852)),x97452)))
% 11.41/11.18 [9792]E(f784(f58(f784(f113(a1),x97921)),f62(f784(f113(a1),x97922),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f113(a1),x97921)))),f62(f784(f113(a1),x97922),f784(f113(a1),x97921)))+~P85(f784(f784(f243(a1),f2(a1)),f784(f113(a1),x97921)))+P85(f784(f784(f243(a1),f784(f113(a1),x97922)),f784(f113(a1),x97921)))
% 11.41/11.18 [9798]E(f784(f58(f784(f113(a1),x97981)),f65(f784(f113(a1),x97982),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f113(a1),x97981)))),f65(f784(f113(a1),x97982),f784(f113(a1),x97981)))+~P85(f784(f784(f243(a1),f2(a1)),f784(f113(a1),x97981)))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),f784(f113(a1),x97982)),f784(f113(a1),x97981))))
% 11.41/11.18 [9846]~E(f302(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x98462,x98461),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x98462),x98461))+P85(f784(f784(f289(a859),x98461),x98462))
% 11.41/11.18 [9847]~E(f299(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x98472,x98471),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x98472),x98471))+P85(f784(f784(f289(a859),x98471),x98472))
% 11.41/11.18 [9848]~E(f302(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x98482,x98481),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x98482),x98481))+P85(f784(f784(f289(a859),x98481),x98482))
% 11.41/11.18 [9849]~E(f299(a859,f289(a859),f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x98492,x98491),f187(f869(a859,a852)))+~P85(f784(f784(f289(a859),x98492),x98491))+P85(f784(f784(f289(a859),x98491),x98492))
% 11.41/11.18 [7160]~P85(f784(f784(f243(a859),f2(a859)),x71602))+P85(f784(f784(f243(a859),x71601),x71602))+E(f784(a160,f784(f784(f51(a859),f784(f784(f3(a859),x71601),x71602)),x71602)),f784(f784(f51(a859),x71601),x71602))
% 11.41/11.18 [7161]~P85(f784(f784(f243(a859),f2(a859)),x71612))+P85(f784(f784(f243(a859),x71611),x71612))+E(f784(a160,f784(f784(f51(a859),f784(f784(f3(a859),x71611),x71612)),x71612)),f784(f784(f51(a859),x71611),x71612))
% 11.41/11.18 [7318]~P85(f784(f784(f243(a859),f2(a859)),x73182))+~P85(f784(f784(f242(a859),x73182),x73181))+E(f784(a160,f784(f784(f51(a859),f784(f784(f3(a859),x73181),x73182)),x73182)),f784(f784(f51(a859),x73181),x73182))
% 11.41/11.18 [8286]~P89(x82861)+~P88(x82861)+~P30(x82861,f784(f113(x82861),f784(f784(f3(a1),f784(f784(f89(a1),x82862),x82862)),a106)))
% 11.41/11.18 [8987]E(x89871,f2(a859))+E(f784(f784(f261(a859,a859,f868(a859,a859)),f784(f784(f10(a859,f869(a859,f868(a859,a859)),a859),f251(a859,a859)),a160)),f94(f868(a859,a859),f63(f784(f784(f3(a859),x89872),x89871),x89871))),f94(f868(a859,a859),f63(x89872,x89871)))+P85(f784(f784(f243(a859),x89872),x89871))
% 11.41/11.18 [9384]P85(f784(x93842,f710(x93842,x93841)))+P85(f784(x93841,f710(x93842,x93841)))+E(f784(f266(a1),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),f2(a1)))),x93841)),f784(f266(a1),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),f2(a1)))),x93842)))
% 11.41/11.18 [9388]~P85(f784(x93882,f710(x93882,x93881)))+~P85(f784(x93881,f710(x93882,x93881)))+E(f784(f266(a1),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),f2(a1)))),x93881)),f784(f266(a1),f784(f784(f20(a1,a852,a852),f784(f784(f10(a852,f869(a852,a852),a1),a344),f784(f242(a1),f2(a1)))),x93882)))
% 11.41/11.18 [9928]~P85(f784(f784(f289(a859),x99282),x99281))+P85(f784(f784(f289(a859),x99281),x99282))+P85(f784(f784(f347(a859),x99281),f297(a859,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x99282)))
% 11.41/11.18 [9929]~P85(f784(f784(f289(a859),x99292),x99291))+P85(f784(f784(f289(a859),x99291),x99292))+P85(f784(f784(f347(a859),x99292),f300(a859,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x99291)))
% 11.41/11.18 [7539]~P89(x75391)+~P60(x75391)+E(f784(f784(f293(x75391),x75392),f784(f113(x75391),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),x75392)
% 11.41/11.18 [7540]~P89(x75401)+~P60(x75401)+E(f784(f784(f293(x75401),x75402),f784(f113(x75401),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))),x75402)
% 11.41/11.18 [9111]~P89(x91111)+~E(f784(f113(x91111),x91112),f87(x91111))+P30(x91111,f784(f113(x91111),f784(f784(f89(a1),x91112),f784(f88(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.18 [9264]~P135(x92641)+~E(x92642,f2(x92641))+E(f784(f784(f252(x92641),x92642),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f2(x92641))
% 11.41/11.18 [9265]~P135(x92651)+~E(x92652,f87(x92651))+E(f784(f784(f252(x92651),x92652),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f87(x92651))
% 11.41/11.18 [9279]~P135(x92791)+~E(x92792,f784(f88(x92791),f87(x92791)))+E(f784(f784(f252(x92791),x92792),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f87(x92791))
% 11.41/11.18 [9299]~P75(x92991)+~P90(x92991)+E(f784(f784(f252(x92991),f784(f113(x92991),x92992)),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f784(f90(x92991),f784(f113(x92991),x92992)),f784(f113(x92991),x92992)))
% 11.41/11.18 [9327]~P89(x93271)+E(f784(f113(x93271),x93272),f87(x93271))+~P30(x93271,f784(f113(x93271),f784(f784(f89(a1),x93272),f784(f88(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.18 [9435]~P135(x94352)+E(x94351,f2(x94352))+~E(f784(f784(f252(x94352),x94351),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f2(x94352))
% 11.41/11.18 [9686]~P113(x96862)+E(x96861,f2(x96862))+P85(f784(f784(f243(x96862),f2(x96862)),f784(f784(f252(x96862),x96861),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.18 [9744]~P113(x97442)+~E(x97441,f2(x97442))+~P85(f784(f784(f243(x97442),f2(x97442)),f784(f784(f252(x97442),x97441),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.18 [9783]P85(f784(f784(f242(a1),x97831),f2(a1)))+P85(f784(f784(f243(a1),x97832),x97831))+E(f784(f58(x97831),f62(x97832,f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97831))),f62(x97832,x97831))
% 11.41/11.18 [9784]~P85(f784(f784(f243(a1),f2(a1)),x97841))+P85(f784(f784(f243(a1),x97842),x97841))+E(f784(f58(x97841),f62(x97842,f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97841))),f62(x97842,x97841))
% 11.41/11.18 [9785]P85(f784(f784(f242(a1),x97851),f2(a1)))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),x97852),x97851)))+E(f784(f58(x97851),f65(x97852,f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97851))),f65(x97852,x97851))
% 11.41/11.18 [9786]~P85(f784(f784(f243(a1),f2(a1)),x97861))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),x97862),x97861)))+E(f784(f58(x97861),f65(x97862,f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97861))),f65(x97862,x97861))
% 11.41/11.18 [9787]~P112(x97871)+~P85(f784(f784(f242(a1),f2(a1)),x97872))+E(f784(f109(x97871),f784(a114,f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97872))),f784(f784(f89(x97871),f784(f109(x97871),f784(a114,x97872))),f784(f109(x97871),f784(a114,x97872))))
% 11.41/11.18 [4956]~P142(x49561,x49562,x49563)+~E(x49563,f2(a1))+P85(f784(x49561,x49562))
% 11.41/11.18 [5083]~P101(x50831)+~P15(x50831,x50833)+P15(x50831,f154(x50831,x50832,x50833))
% 11.41/11.18 [4666]~P70(x46662)+~E(x46663,f784(f88(x46662),x46661))+E(x46661,f784(f88(x46662),x46663))
% 11.41/11.18 [4667]~P70(x46672)+~E(x46673,f784(f88(x46672),x46671))+E(x46671,f784(f88(x46672),x46673))
% 11.41/11.18 [4668]~P70(x46681)+~E(f784(f88(x46681),x46683),x46682)+E(f784(f88(x46681),x46682),x46683)
% 11.41/11.18 [4669]~P70(x46691)+~E(f784(f88(x46691),x46693),x46692)+E(f784(f88(x46691),x46692),x46693)
% 11.41/11.18 [4740]~P87(x47403)+E(x47401,x47402)+~E(f784(f109(x47403),x47401),f784(f109(x47403),x47402))
% 11.41/11.18 [4741]~P88(x47413)+E(x47411,x47412)+~E(f784(f112(x47413),x47411),f784(f112(x47413),x47412))
% 11.41/11.18 [4742]~P70(x47423)+E(x47421,x47422)+~E(f784(f88(x47423),x47421),f784(f88(x47423),x47422))
% 11.41/11.18 [4743]~P91(x47433)+E(x47431,x47432)+~E(f784(f88(x47433),x47431),f784(f88(x47433),x47432))
% 11.41/11.18 [4744]~P101(x47443)+E(x47441,x47442)+~E(f784(f267(x47443),x47441),f784(f267(x47443),x47442))
% 11.41/11.18 [4745]~P101(x47453)+E(x47451,x47452)+~E(f784(f306(x47453),x47451),f784(f306(x47453),x47452))
% 11.41/11.18 [4746]~P101(x47463)+E(x47461,x47462)+~E(f784(f303(x47463),x47461),f784(f303(x47463),x47462))
% 11.41/11.18 [4747]~P101(x47473)+E(x47471,x47472)+~E(f784(f268(x47473),x47471),f784(f268(x47473),x47472))
% 11.41/11.18 [4980]~P143(x49801,x49803,x49802)+~E(x49802,f2(a1))+P85(f784(x49801,f2(a1)))
% 11.41/11.18 [5019]~E(x50191,f2(a859))+E(f386(x50191,x50192,x50193),f187(f869(x50193,a852)))+~E(f784(f50(x50193),x50192),f784(a160,x50191))
% 11.41/11.18 [5164]~E(x51642,f2(a859))+E(f784(f250(a859,a859),x51641),f2(a859))+~P85(f784(f63(x51643,x51642),x51641))
% 11.41/11.18 [5207]P85(f784(x52071,x52072))+~E(x52073,f784(f109(a1),x52072))+~P85(f784(x52071,f784(a114,x52073)))
% 11.41/11.18 [5661]~E(x56613,f2(a859))+~P85(f784(x56611,x56612))+P85(f784(x56611,f60(a859,x56612,x56613)))
% 11.41/11.18 [5806]~P85(f784(a26,x58063))+~P85(f784(a26,x58062))+P85(f784(a26,f35(x58061,x58062,x58063)))
% 11.41/11.18 [5807]~P85(f784(a26,x58073))+~P85(f784(a26,x58072))+P85(f784(a26,f35(x58071,x58072,x58073)))
% 11.41/11.18 [6079]~E(x60793,f2(a859))+P85(f784(x60791,x60792))+~P85(f784(x60791,f60(a859,x60792,x60793)))
% 11.41/11.18 [6783]E(x67831,f2(a859))+~P85(f784(x67832,f812(x67831,x67833,x67832)))+P85(f784(x67832,f60(a859,x67833,x67831)))
% 11.41/11.18 [6895]~P6(x68951)+~P85(f784(f784(f242(x68951),x68952),f684(x68953,x68952,x68951)))+P85(f784(f784(f242(x68951),x68952),f53(x68951,x68953)))
% 11.41/11.18 [6897]~P85(f784(x68971,x68972))+~P85(f784(x68971,f812(x68973,x68972,x68971)))+P85(f784(x68971,f60(a859,x68972,x68973)))
% 11.41/11.18 [6996]E(x69961,f120(x69962))+E(f784(f784(f144(x69962),f762(x69963,x69961,x69962)),f768(x69963,x69961,x69962)),x69961)+~P85(f784(f784(f347(f860(x69962)),x69961),f152(x69962,x69963)))
% 11.41/11.18 [7033]~P136(x70331)+~P85(f784(f784(f347(x70331),x70332),f119(x70331)))+P85(f784(f784(f347(x70331),f784(f784(f252(x70331),x70332),x70333)),f119(x70331)))
% 11.41/11.18 [7370]P35(x73701,x73702)+~P85(f784(f784(f347(x73701),x73703),f695(x73702,x73701)))+P85(f784(f784(f347(x73701),f709(x73702,x73701,x73703)),f695(x73702,x73701)))
% 11.41/11.18 [7645]E(x76451,f120(x76452))+~P85(f784(f784(f347(f860(x76452)),x76451),f152(x76452,x76453)))+P85(f784(f784(f347(f860(x76452)),f768(x76453,x76451,x76452)),f152(x76452,x76453)))
% 11.41/11.18 [7694]E(x76941,f2(a859))+E(f784(f784(f89(a859),f784(f784(f90(a859),x76941),f814(x76941,x76942,x76943))),f812(x76941,x76942,x76943)),x76942)+P85(f784(x76943,f60(a859,x76942,x76941)))
% 11.41/11.18 [7737]~P85(f784(x77373,x77372))+E(f784(f784(f89(a859),f784(f784(f90(a859),x77371),f814(x77371,x77372,x77373))),f812(x77371,x77372,x77373)),x77372)+P85(f784(x77373,f60(a859,x77372,x77371)))
% 11.41/11.18 [7881]P85(f784(f784(f243(a1),x78811),f803(x78812,x78813,x78811)))+P85(f784(f784(x78813,f784(f784(f51(a1),x78812),x78811)),f60(a1,x78812,x78811)))+~P85(f784(f784(f243(a1),x78811),f2(a1)))
% 11.41/11.18 [8144]P85(f784(f784(x81442,f784(f784(f51(a1),x81441),x81443)),f60(a1,x81441,x81443)))+~P85(f784(f784(f243(a1),x81443),f2(a1)))+P85(f784(f784(f242(a1),f803(x81441,x81442,x81443)),f2(a1)))
% 11.41/11.18 [8323]E(f784(f784(f89(a1),f784(f784(f90(a1),x83231),f806(x83232,x83233,x83231))),f803(x83232,x83233,x83231)),x83232)+P85(f784(f784(x83233,f784(f784(f51(a1),x83232),x83231)),f60(a1,x83232,x83231)))+~P85(f784(f784(f243(a1),x83231),f2(a1)))
% 11.41/11.18 [8556]~P85(f784(f784(x85561,f806(x85562,x85561,x85563)),f803(x85562,x85561,x85563)))+P85(f784(f784(x85561,f784(f784(f51(a1),x85562),x85563)),f60(a1,x85562,x85563)))+~P85(f784(f784(f243(a1),x85563),f2(a1)))
% 11.41/11.18 [8768]~P101(x87681)+~P15(x87681,x87683)+P15(x87681,f143(x87681,x87681,f7(x87681),x87682,x87683))
% 11.41/11.18 [9215]~P122(x92152)+E(x92151,f2(x92152))+~P85(f784(f784(f242(x92152),f784(f784(f89(x92152),f784(f784(f90(x92152),x92153),x92153)),f784(f784(f90(x92152),x92151),x92151))),f2(x92152)))
% 11.41/11.18 [9216]~P122(x92162)+E(x92161,f2(x92162))+~P85(f784(f784(f242(x92162),f784(f784(f89(x92162),f784(f784(f90(x92162),x92161),x92161)),f784(f784(f90(x92162),x92163),x92163))),f2(x92162)))
% 11.41/11.18 [9984]~P113(x99841)+~P85(f784(f784(f243(x99841),x99842),f2(x99841)))+P85(f784(f784(f243(x99841),f784(f784(f252(x99841),x99842),f784(a160,f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x99843)))),f2(x99841)))
% 11.41/11.18 [9994]~P113(x99942)+E(x99941,f2(x99942))+~P85(f784(f784(f242(x99942),f784(f784(f89(x99942),f784(f784(f252(x99942),x99943),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99942),x99941),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))),f2(x99942)))
% 11.41/11.18 [9995]~P113(x99952)+E(x99951,f2(x99952))+~P85(f784(f784(f242(x99952),f784(f784(f89(x99952),f784(f784(f252(x99952),x99951),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99952),x99953),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))),f2(x99952)))
% 11.41/11.18 [4698]~E(x46982,x46983)+~P70(x46981)+E(f784(f784(f3(x46981),x46982),x46983),f2(x46981))
% 11.41/11.18 [4699]~E(x46992,x46993)+~P3(x46991)+E(f784(f784(f3(x46991),x46992),x46993),f2(x46991))
% 11.41/11.18 [4712]~P111(x47121)+~E(x47123,f2(x47121))+E(f784(f784(f89(x47121),x47122),x47123),x47122)
% 11.41/11.18 [4727]~P137(x47271)+~E(x47273,f2(x47271))+E(f784(f784(f90(x47271),x47272),x47273),f2(x47271))
% 11.41/11.18 [4728]~P137(x47281)+~E(x47282,f2(x47281))+E(f784(f784(f90(x47281),x47282),x47283),f2(x47281))
% 11.41/11.18 [4748]~E(x47483,f120(x47481))+~E(x47482,f120(x47481))+E(f784(f784(f130(x47481),x47482),x47483),f120(x47481))
% 11.41/11.18 [4749]~E(x47493,f120(x47491))+~E(x47492,f120(x47491))+E(f784(f784(f130(x47491),x47492),x47493),f120(x47491))
% 11.41/11.18 [4832]~P111(x48322)+E(x48321,f2(x48322))+~E(f784(f784(f89(x48322),x48323),x48321),x48323)
% 11.41/11.18 [4833]~P70(x48331)+~E(x48332,f784(f88(x48331),x48333))+E(f784(f784(f89(x48331),x48332),x48333),f2(x48331))
% 11.41/11.18 [4840]E(x48401,f120(x48402))+E(x48403,f2(a859))+~E(f784(f784(f165(x48402),x48403),x48401),f120(x48402))
% 11.41/11.18 [4848]~P70(x48483)+E(x48481,x48482)+~E(f784(f784(f3(x48483),x48481),x48482),f2(x48483))
% 11.41/11.18 [4849]~P3(x48493)+E(x48491,x48492)+~E(f784(f784(f3(x48493),x48491),x48492),f2(x48493))
% 11.41/11.18 [4858]~P135(x48582)+E(x48581,f2(x48582))+~E(f784(f784(f252(x48582),x48581),x48583),f2(x48582))
% 11.41/11.18 [4859]~P94(x48592)+E(x48591,f249(x48592))+~E(f784(f784(f111(x48592),x48593),x48591),f249(x48592))
% 11.41/11.18 [4860]~P94(x48602)+E(x48601,f249(x48602))+~E(f784(f784(f111(x48602),x48601),x48603),f249(x48602))
% 11.41/11.18 [4861]~P95(x48612)+E(x48611,f187(x48612))+~E(f784(f784(f110(x48612),x48613),x48611),f187(x48612))
% 11.41/11.18 [4862]~P95(x48622)+E(x48621,f187(x48622))+~E(f784(f784(f110(x48622),x48621),x48623),f187(x48622))
% 11.41/11.18 [4927]~P70(x49272)+E(x49271,f784(f88(x49272),x49273))+~E(f784(f784(f89(x49272),x49271),x49273),f2(x49272))
% 11.41/11.18 [4928]~P70(x49281)+E(f784(f88(x49281),x49282),x49283)+~E(f784(f784(f89(x49281),x49282),x49283),f2(x49281))
% 11.41/11.18 [4929]~E(x49292,x49293)+~P100(x49291)+P85(f784(f784(f242(x49291),x49292),x49293))
% 11.41/11.18 [4930]~E(x49302,x49303)+~P100(x49301)+P85(f784(f784(f242(x49301),x49302),x49303))
% 11.41/11.18 [4931]~E(x49312,x49313)+~P100(x49311)+P85(f784(f784(f242(x49311),x49312),x49313))
% 11.41/11.18 [4932]~E(x49322,x49323)+~P104(x49321)+P85(f784(f784(f242(x49321),x49322),x49323))
% 11.41/11.18 [5033]~P114(x50331)+~E(x50332,f784(f88(x50331),x50333))+E(f784(f784(f90(x50331),x50332),x50332),f784(f784(f90(x50331),x50333),x50333))
% 11.41/11.18 [5041]~P101(x50411)+~P15(x50411,x50413)+P15(x50411,f784(f784(f165(x50411),x50412),x50413))
% 11.41/11.18 [5042]~P101(x50421)+~P15(x50421,x50423)+P15(x50421,f784(f784(f133(x50421),x50422),x50423))
% 11.41/11.18 [5080]E(x50801,x50802)+E(x50803,f2(a859))+~E(f784(f784(f90(a859),x50803),x50801),f784(f784(f90(a859),x50803),x50802))
% 11.41/11.18 [5081]E(x50811,x50812)+E(x50813,f2(a859))+~E(f784(f784(f90(a859),x50813),x50811),f784(f784(f90(a859),x50813),x50812))
% 11.41/11.18 [5082]E(x50821,x50822)+E(x50823,f2(a859))+~E(f784(f784(f90(a859),x50821),x50823),f784(f784(f90(a859),x50822),x50823))
% 11.41/11.18 [5156]~E(x51562,x51563)+~P100(x51561)+E(f305(x51561,x51562,x51563),f784(f784(f312(x51561),x51562),f187(f869(x51561,a852))))
% 11.41/11.18 [5195]~P113(x51951)+~E(f784(f84(x51951),x51952),f784(f84(x51951),x51953))+P85(f784(f784(f289(x51951),x51952),x51953))
% 11.41/11.18 [5199]~E(x51991,x51992)+~P100(x51993)+~P85(f784(f784(f243(x51993),x51991),x51992))
% 11.41/11.18 [5200]~E(x52001,x52002)+~P100(x52003)+~P85(f784(f784(f243(x52003),x52001),x52002))
% 11.41/11.18 [5201]~E(x52011,x52012)+~P100(x52013)+~P85(f784(f784(f243(x52013),x52011),x52012))
% 11.41/11.18 [5202]~E(x52021,x52022)+~P101(x52023)+~P85(f784(f784(f243(x52023),x52021),x52022))
% 11.41/11.18 [5203]~E(x52031,x52032)+~P101(x52033)+~P85(f784(f784(f243(x52033),x52031),x52032))
% 11.41/11.18 [5204]~E(x52041,x52042)+~P100(x52043)+~P85(f784(f784(f243(x52043),x52041),x52042))
% 11.41/11.18 [5205]~E(x52051,x52052)+~P101(x52053)+~P85(f784(f784(f243(x52053),x52051),x52052))
% 11.41/11.18 [5211]~P100(x52111)+E(f784(f304(x52111,x52112),x52113),f187(f869(x52111,a852)))+P85(f784(f784(f243(x52111),x52112),x52113))
% 11.41/11.18 [5212]~P100(x52121)+E(f784(f304(x52121,x52122),x52123),f187(f869(x52121,a852)))+P85(f784(f784(f243(x52121),x52122),x52123))
% 11.41/11.18 [5257]~P100(x52571)+E(f305(x52571,x52572,x52573),f187(f869(x52571,a852)))+P85(f784(f784(f242(x52571),x52572),x52573))
% 11.41/11.18 [5258]~P100(x52581)+E(f307(x52581,x52582,x52583),f187(f869(x52581,a852)))+P85(f784(f784(f243(x52581),x52582),x52583))
% 11.41/11.18 [5259]~P100(x52591)+E(f187(f869(x52591,a852)),f305(x52591,x52592,x52593))+P85(f784(f784(f242(x52591),x52592),x52593))
% 11.41/11.18 [5260]~P100(x52601)+E(f187(f869(x52601,a852)),f307(x52601,x52602,x52603))+P85(f784(f784(f243(x52601),x52602),x52603))
% 11.41/11.18 [5268]~P101(x52681)+~E(f784(f784(f246(x52681),x52682),x52683),x52682)+P85(f784(f784(f242(x52681),x52682),x52683))
% 11.41/11.18 [5269]~P101(x52691)+~E(f784(f784(f186(x52691),x52692),x52693),x52693)+P85(f784(f784(f242(x52691),x52692),x52693))
% 11.41/11.18 [5270]~P98(x52701)+~E(f784(f784(f110(x52701),x52702),x52703),x52703)+P85(f784(f784(f242(x52701),x52702),x52703))
% 11.41/11.18 [5271]~P99(x52711)+~E(f784(f784(f111(x52711),x52712),x52713),x52712)+P85(f784(f784(f242(x52711),x52712),x52713))
% 11.41/11.18 [5286]~P101(x52861)+P15(x52861,x52862)+~P15(x52861,f784(f784(f144(x52861),x52863),x52862))
% 11.41/11.18 [5287]~P101(x52871)+P15(x52871,x52872)+~P15(x52871,f784(f784(f144(x52871),x52873),x52872))
% 11.41/11.18 [5288]~P101(x52881)+P15(x52881,x52882)+~P15(x52881,f784(f784(f130(x52881),x52883),x52882))
% 11.41/11.18 [5289]~P101(x52891)+P15(x52891,x52892)+~P15(x52891,f784(f784(f130(x52891),x52892),x52893))
% 11.41/11.18 [5294]~P4(x52941)+~E(f60(x52941,x52943,x52942),f2(x52941))+P85(f784(f784(f289(x52941),x52942),x52943))
% 11.41/11.18 [5354]~P101(x53541)+P85(f784(f784(f242(x53541),x53543),x53542))+P85(f784(f784(f243(x53541),x53542),x53543))
% 11.41/11.18 [5355]~P101(x53551)+P85(f784(f784(f242(x53551),x53553),x53552))+P85(f784(f784(f243(x53551),x53552),x53553))
% 11.41/11.18 [5356]~P101(x53561)+P85(f784(f784(f242(x53561),x53563),x53562))+P85(f784(f784(f243(x53561),x53562),x53563))
% 11.41/11.18 [5357]~P101(x53571)+P85(f784(f784(f242(x53571),x53573),x53572))+P85(f784(f784(f243(x53571),x53572),x53573))
% 11.41/11.18 [5358]~P101(x53581)+P85(f784(f784(f242(x53581),x53583),x53582))+P85(f784(f784(f243(x53581),x53582),x53583))
% 11.41/11.18 [5359]~P101(x53591)+P85(f784(f784(f242(x53591),x53593),x53592))+P85(f784(f784(f242(x53591),x53592),x53593))
% 11.41/11.18 [5360]~P101(x53601)+P85(f784(f784(f242(x53601),x53603),x53602))+P85(f784(f784(f242(x53601),x53602),x53603))
% 11.41/11.18 [5399]~P101(x53991)+E(f784(f784(f246(x53991),x53992),x53993),x53993)+~P85(f784(f784(f242(x53991),x53993),x53992))
% 11.41/11.18 [5400]~P101(x54001)+E(f784(f784(f246(x54001),x54002),x54003),x54002)+~P85(f784(f784(f242(x54001),x54002),x54003))
% 11.41/11.18 [5401]~P101(x54011)+E(f784(f784(f246(x54011),x54012),x54013),x54012)+~P85(f784(f784(f242(x54011),x54012),x54013))
% 11.41/11.18 [5402]~P101(x54021)+E(f784(f784(f186(x54021),x54022),x54023),x54022)+~P85(f784(f784(f242(x54021),x54023),x54022))
% 11.41/11.18 [5403]~P101(x54031)+E(f784(f784(f186(x54031),x54032),x54033),x54033)+~P85(f784(f784(f242(x54031),x54032),x54033))
% 11.41/11.18 [5404]~P101(x54041)+E(f784(f784(f186(x54041),x54042),x54043),x54043)+~P85(f784(f784(f242(x54041),x54042),x54043))
% 11.41/11.18 [5405]~P98(x54051)+E(f784(f784(f110(x54051),x54052),x54053),x54052)+~P85(f784(f784(f242(x54051),x54053),x54052))
% 11.41/11.18 [5406]~P98(x54061)+E(f784(f784(f110(x54061),x54062),x54063),x54063)+~P85(f784(f784(f242(x54061),x54062),x54063))
% 11.41/11.18 [5407]~P98(x54071)+E(f784(f784(f110(x54071),x54072),x54073),x54073)+~P85(f784(f784(f242(x54071),x54072),x54073))
% 11.41/11.18 [5408]~P99(x54081)+E(f784(f784(f111(x54081),x54082),x54083),x54083)+~P85(f784(f784(f242(x54081),x54083),x54082))
% 11.41/11.18 [5409]~P99(x54091)+E(f784(f784(f111(x54091),x54092),x54093),x54092)+~P85(f784(f784(f242(x54091),x54092),x54093))
% 11.41/11.18 [5410]~P99(x54101)+E(f784(f784(f111(x54101),x54102),x54103),x54102)+~P85(f784(f784(f242(x54101),x54102),x54103))
% 11.41/11.18 [5417]~P116(x54172)+E(x54171,f2(x54172))+E(f784(f784(f293(x54172),f784(f88(x54172),x54173)),f784(f88(x54172),x54171)),f784(f784(f293(x54172),x54173),x54171))
% 11.41/11.18 [5423]~P4(x54231)+E(f60(x54231,x54232,x54233),f2(x54231))+~P85(f784(f784(f289(x54231),x54233),x54232))
% 11.41/11.18 [5424]~P4(x54241)+E(f60(x54241,x54242,x54243),f2(x54241))+~P85(f784(f784(f289(x54241),x54243),x54242))
% 11.41/11.18 [5464]~P100(x54641)+E(f784(f304(x54641,x54642),x54643),f187(f869(x54641,a852)))+~P85(f784(f784(f242(x54641),x54643),x54642))
% 11.41/11.18 [5492]~P100(x54921)+E(f305(x54921,x54922,x54923),f187(f869(x54921,a852)))+~P85(f784(f784(f243(x54921),x54923),x54922))
% 11.41/11.18 [5493]~P100(x54931)+E(f307(x54931,x54932,x54933),f187(f869(x54931,a852)))+~P85(f784(f784(f242(x54931),x54933),x54932))
% 11.41/11.18 [5494]~P100(x54941)+E(f308(x54941,x54942,x54943),f187(f869(x54941,a852)))+~P85(f784(f784(f242(x54941),x54943),x54942))
% 11.41/11.18 [5544]~E(f784(f784(f3(a859),x55441),x55443),x55442)+E(x55441,f784(f784(f89(a859),x55442),x55443))+~P85(f784(f784(f242(a859),x55443),x55441))
% 11.41/11.18 [5545]~E(x55451,f784(f784(f89(a859),x55453),x55452))+E(f784(f784(f3(a859),x55451),x55452),x55453)+~P85(f784(f784(f242(a859),x55452),x55451))
% 11.41/11.18 [5588]~P85(f784(x55881,x55883))+P85(f784(x55881,f808(x55881,x55882)))+~P85(f784(f784(f242(a859),x55883),x55882))
% 11.41/11.18 [5589]~P85(f784(x55891,x55893))+P85(f784(x55891,f352(x55891,x55892)))+~P85(f784(f784(f243(a859),x55893),x55892))
% 11.41/11.18 [5596]~P100(x55961)+~E(f784(f304(x55961,x55962),x55963),f187(f869(x55961,a852)))+~P85(f784(f784(f243(x55961),x55962),x55963))
% 11.41/11.18 [5597]~P100(x55971)+~E(f784(f304(x55971,x55972),x55973),f187(f869(x55971,a852)))+~P85(f784(f784(f243(x55971),x55972),x55973))
% 11.41/11.18 [5600]~P100(x56001)+~P85(f784(f784(f243(x56001),x56002),x56003))+P85(f784(f784(f242(x56001),x56002),x56003))
% 11.41/11.18 [5601]~P100(x56011)+~P85(f784(f784(f243(x56011),x56012),x56013))+P85(f784(f784(f242(x56011),x56012),x56013))
% 11.41/11.18 [5602]~P104(x56021)+~P85(f784(f784(f243(x56021),x56022),x56023))+P85(f784(f784(f242(x56021),x56022),x56023))
% 11.41/11.18 [5603]~P104(x56031)+~P85(f784(f784(f243(x56031),x56032),x56033))+P85(f784(f784(f242(x56031),x56032),x56033))
% 11.41/11.18 [5716]~P100(x57161)+~E(f305(x57161,x57162,x57163),f187(f869(x57161,a852)))+~P85(f784(f784(f242(x57161),x57162),x57163))
% 11.41/11.18 [5717]~P100(x57171)+~E(f307(x57171,x57172,x57173),f187(f869(x57171,a852)))+~P85(f784(f784(f243(x57171),x57172),x57173))
% 11.41/11.18 [5718]~P100(x57181)+~E(f187(f869(x57181,a852)),f305(x57181,x57182,x57183))+~P85(f784(f784(f242(x57181),x57182),x57183))
% 11.41/11.18 [5719]~P100(x57191)+~E(f187(f869(x57191,a852)),f307(x57191,x57192,x57193))+~P85(f784(f784(f243(x57191),x57192),x57193))
% 11.41/11.18 [5732]P85(f784(x57321,x57322))+~P85(f784(x57321,f847(x57321,x57323)))+~P85(f784(f784(f242(a859),x57322),x57323))
% 11.41/11.18 [5733]P85(f784(x57331,x57332))+~P85(f784(x57331,f354(x57331,x57333)))+~P85(f784(f784(f243(a859),x57332),x57333))
% 11.41/11.18 [5741]~E(x57411,f784(a160,x57413))+P85(f784(f784(f243(a859),x57411),f784(a160,x57412)))+~P85(f784(f784(f243(a859),x57413),x57412))
% 11.41/11.18 [5757]E(x57571,x57572)+~E(f784(f784(f90(a859),x57573),x57571),f784(f784(f90(a859),x57573),x57572))+~P85(f784(f784(f243(a859),f2(a859)),x57573))
% 11.41/11.18 [5817]E(f784(x58171,f416(x58171,x58172,x58173)),f87(a859))+~E(f784(f784(f8(x58173,a859),x58171),x58172),f87(a859))+~P85(f784(f71(x58173),x58172))
% 11.41/11.18 [5827]~P6(x58271)+P85(f784(f784(f242(x58271),x58272),f52(x58271,x58273)))+~P85(f784(f784(f347(x58271),x58272),x58273))
% 11.41/11.18 [5852]~P100(x58521)+~P85(f784(f784(f243(x58521),x58523),x58522))+~P85(f784(f784(f243(x58521),x58522),x58523))
% 11.41/11.18 [5853]~P101(x58531)+~P85(f784(f784(f243(x58531),x58533),x58532))+~P85(f784(f784(f243(x58531),x58532),x58533))
% 11.41/11.18 [5854]~P101(x58541)+~P85(f784(f784(f242(x58541),x58543),x58542))+~P85(f784(f784(f243(x58541),x58542),x58543))
% 11.41/11.18 [5855]~P101(x58551)+~P85(f784(f784(f242(x58551),x58553),x58552))+~P85(f784(f784(f243(x58551),x58552),x58553))
% 11.41/11.18 [5856]~P101(x58561)+~P85(f784(f784(f242(x58561),x58563),x58562))+~P85(f784(f784(f243(x58561),x58562),x58563))
% 11.41/11.18 [5857]~P104(x58571)+~P85(f784(f784(f243(x58571),x58573),x58572))+~P85(f784(f784(f243(x58571),x58572),x58573))
% 11.41/11.18 [5858]~P104(x58581)+~P85(f784(f784(f243(x58581),x58583),x58582))+~P85(f784(f784(f243(x58581),x58582),x58583))
% 11.41/11.18 [5859]~P104(x58591)+~P85(f784(f784(f243(x58591),x58593),x58592))+~P85(f784(f784(f243(x58591),x58592),x58593))
% 11.41/11.18 [5860]~P104(x58601)+~P85(f784(f784(f243(x58601),x58603),x58602))+~P85(f784(f784(f243(x58601),x58602),x58603))
% 11.41/11.18 [5861]~P104(x58611)+~P85(f784(f784(f242(x58611),x58613),x58612))+~P85(f784(f784(f243(x58611),x58612),x58613))
% 11.41/11.18 [5880]~E(x58802,x58803)+~E(x58801,x58802)+E(f292(a859,f289(a859),x58801,x58802),f784(f784(f312(a859),x58803),f187(f869(a859,a852))))
% 11.41/11.18 [5888]~E(f784(x58882,f417(x58882,x58883,x58881)),f2(a859))+E(f784(f784(f8(x58881,a859),x58882),x58883),f2(a859))+~P85(f784(f71(x58881),x58883))
% 11.41/11.18 [5889]~E(f784(x58892,f463(x58892,x58893,x58891)),f87(a859))+E(f784(f784(f11(x58891,a859),x58892),x58893),f87(a859))+~P85(f784(f71(x58891),x58893))
% 11.41/11.18 [5903]~P105(x59031)+~P85(f784(f784(f289(x59031),x59032),x59033))+P85(f784(f784(f289(x59031),x59032),f784(f88(x59031),x59033)))
% 11.41/11.18 [5904]~P113(x59041)+~P85(f784(f784(f289(x59041),x59042),x59043))+P85(f784(f784(f289(x59041),x59042),f784(f84(x59041),x59043)))
% 11.41/11.18 [5905]~P103(x59051)+~P85(f784(f784(f243(x59051),x59053),x59052))+P85(f784(f784(f347(x59051),x59052),f784(f306(x59051),x59053)))
% 11.41/11.18 [5906]~P103(x59061)+~P85(f784(f784(f242(x59061),x59063),x59062))+P85(f784(f784(f347(x59061),x59062),f784(f268(x59061),x59063)))
% 11.41/11.18 [5907]~P103(x59071)+~P85(f784(f784(f243(x59071),x59072),x59073))+P85(f784(f784(f347(x59071),x59072),f784(f267(x59071),x59073)))
% 11.41/11.18 [5908]~P103(x59081)+~P85(f784(f784(f242(x59081),x59082),x59083))+P85(f784(f784(f347(x59081),x59082),f784(f303(x59081),x59083)))
% 11.41/11.18 [5919]E(f784(x59191,f418(x59191,x59192,x59193)),f784(a160,f2(a859)))+~E(f784(f784(f8(x59193,a859),x59191),x59192),f784(a160,f2(a859)))+~P85(f784(f71(x59193),x59192))
% 11.41/11.18 [6001]~P6(x60011)+~P85(f784(f784(f347(x60011),x60013),x60012))+P85(f784(f784(f242(x60011),f53(x60011,x60012)),x60013))
% 11.41/11.18 [6019]~P85(f784(f784(f242(a859),x60191),x60193))+P85(f784(f784(f242(a859),x60191),x60192))+~P85(f784(f784(f242(a859),x60193),x60192))
% 11.41/11.18 [6020]~P85(f784(f784(f242(a1),x60201),x60203))+P85(f784(f784(f242(a1),x60201),x60202))+~P85(f784(f784(f242(a1),x60203),x60202))
% 11.41/11.18 [6021]~P85(f784(f784(f289(a859),x60211),x60213))+P85(f784(f784(f289(a859),x60211),x60212))+~P85(f784(f784(f289(a859),x60213),x60212))
% 11.41/11.18 [6039]~P103(x60391)+~P85(f784(f784(f347(x60391),x60393),f784(f306(x60391),x60392)))+P85(f784(f784(f243(x60391),x60392),x60393))
% 11.41/11.18 [6040]~P103(x60401)+~P85(f784(f784(f347(x60401),x60402),f784(f267(x60401),x60403)))+P85(f784(f784(f243(x60401),x60402),x60403))
% 11.41/11.18 [6041]~P103(x60411)+~P85(f784(f784(f347(x60411),x60413),f784(f268(x60411),x60412)))+P85(f784(f784(f242(x60411),x60412),x60413))
% 11.41/11.18 [6042]~P103(x60421)+~P85(f784(f784(f347(x60421),x60422),f784(f303(x60421),x60423)))+P85(f784(f784(f242(x60421),x60422),x60423))
% 11.41/11.18 [6043]~P113(x60431)+~P85(f784(f784(f289(x60431),x60432),f784(f84(x60431),x60433)))+P85(f784(f784(f289(x60431),x60432),x60433))
% 11.41/11.18 [6044]~P105(x60441)+~P85(f784(f784(f289(x60441),x60442),f784(f88(x60441),x60443)))+P85(f784(f784(f289(x60441),x60442),x60443))
% 11.41/11.18 [6265]~P61(x62651)+P85(f784(f784(f243(x62651),f2(x62651)),f810(x62653,x62652,x62651)))+P85(f784(f784(f242(x62651),x62652),x62653))
% 11.41/11.18 [6266]~P62(x62661)+P85(f784(f784(f243(x62661),f2(x62661)),f817(x62663,x62662,x62661)))+P85(f784(f784(f242(x62661),x62662),x62663))
% 11.41/11.18 [6336]~P77(x63361)+~P85(f784(f784(f243(x63361),x63363),f784(f88(x63361),x63362)))+P85(f784(f784(f243(x63361),x63362),f784(f88(x63361),x63363)))
% 11.41/11.18 [6337]~P77(x63371)+~P85(f784(f784(f243(x63371),x63373),f784(f88(x63371),x63372)))+P85(f784(f784(f243(x63371),x63372),f784(f88(x63371),x63373)))
% 11.41/11.18 [6338]~P77(x63381)+~P85(f784(f784(f242(x63381),x63383),f784(f88(x63381),x63382)))+P85(f784(f784(f242(x63381),x63382),f784(f88(x63381),x63383)))
% 11.41/11.18 [6339]~P77(x63391)+~P85(f784(f784(f242(x63391),x63393),f784(f88(x63391),x63392)))+P85(f784(f784(f242(x63391),x63392),f784(f88(x63391),x63393)))
% 11.41/11.18 [6350]~P85(f784(f784(f243(a859),x63501),x63503))+~P85(f784(f784(f243(a859),x63503),x63502))+P85(f784(f784(f243(a859),f784(a160,x63501)),x63502))
% 11.41/11.18 [6382]~P120(x63821)+P85(f784(f784(f243(x63821),f784(f109(x63821),x63822)),f784(f109(x63821),x63823)))+~P85(f784(f784(f243(a859),x63822),x63823))
% 11.41/11.18 [6383]~P113(x63831)+P85(f784(f784(f243(x63831),f784(f112(x63831),x63832)),f784(f112(x63831),x63833)))+~P85(f784(f784(f243(a1),x63832),x63833))
% 11.41/11.18 [6384]~P120(x63841)+P85(f784(f784(f243(x63841),f784(f109(x63841),x63842)),f784(f109(x63841),x63843)))+~P85(f784(f784(f243(a859),x63842),x63843))
% 11.41/11.18 [6385]~P120(x63851)+P85(f784(f784(f242(x63851),f784(f109(x63851),x63852)),f784(f109(x63851),x63853)))+~P85(f784(f784(f242(a859),x63852),x63853))
% 11.41/11.18 [6386]~P113(x63861)+P85(f784(f784(f242(x63861),f784(f112(x63861),x63862)),f784(f112(x63861),x63863)))+~P85(f784(f784(f242(a1),x63862),x63863))
% 11.41/11.18 [6392]~P101(x63921)+E(f784(f784(f110(f869(x63921,a852)),f784(f267(x63921),x63922)),f784(f304(x63921,x63922),x63923)),f784(f267(x63921),x63923))+~P85(f784(f784(f242(x63921),x63922),x63923))
% 11.41/11.18 [6423]~P77(x64231)+~P85(f784(f784(f243(x64231),x64233),x64232))+P85(f784(f784(f243(x64231),f784(f88(x64231),x64232)),f784(f88(x64231),x64233)))
% 11.41/11.18 [6424]~P77(x64241)+~P85(f784(f784(f242(x64241),x64243),x64242))+P85(f784(f784(f242(x64241),f784(f88(x64241),x64242)),f784(f88(x64241),x64243)))
% 11.41/11.18 [6425]~P77(x64251)+~P85(f784(f784(f242(x64251),x64253),x64252))+P85(f784(f784(f242(x64251),f784(f88(x64251),x64252)),f784(f88(x64251),x64253)))
% 11.41/11.18 [6426]~P91(x64261)+~P85(f784(f784(f242(x64261),x64263),x64262))+P85(f784(f784(f242(x64261),f784(f88(x64261),x64262)),f784(f88(x64261),x64263)))
% 11.41/11.18 [6427]~P91(x64271)+~P85(f784(f784(f242(x64271),x64273),x64272))+P85(f784(f784(f242(x64271),f784(f88(x64271),x64272)),f784(f88(x64271),x64273)))
% 11.41/11.18 [6462]~P101(x64621)+E(f784(f784(f110(f869(x64621,a852)),f784(f267(x64621),x64622)),f305(x64621,x64622,x64623)),f784(f303(x64621),x64623))+~P85(f784(f784(f242(x64621),x64622),x64623))
% 11.41/11.18 [6463]~P101(x64631)+E(f784(f784(f110(f869(x64631,a852)),f784(f303(x64631),x64632)),f307(x64631,x64632,x64633)),f784(f303(x64631),x64633))+~P85(f784(f784(f242(x64631),x64632),x64633))
% 11.41/11.18 [6464]~P101(x64641)+E(f784(f784(f110(f869(x64641,a852)),f784(f303(x64641),x64642)),f308(x64641,x64642,x64643)),f784(f267(x64641),x64643))+~P85(f784(f784(f243(x64641),x64642),x64643))
% 11.41/11.18 [6501]~P101(x65011)+E(f784(f784(f110(f869(x65011,a852)),f784(f304(x65011,x65012),x65013)),f784(f268(x65011),x65013)),f784(f268(x65011),x65012))+~P85(f784(f784(f242(x65011),x65012),x65013))
% 11.41/11.18 [6662]~P101(x66621)+E(f784(f784(f110(f869(x66621,a852)),f305(x66621,x66622,x66623)),f784(f306(x66621),x66623)),f784(f268(x66621),x66622))+~P85(f784(f784(f242(x66621),x66622),x66623))
% 11.41/11.18 [6663]~P101(x66631)+E(f784(f784(f110(f869(x66631,a852)),f307(x66631,x66632,x66633)),f784(f306(x66631),x66633)),f784(f306(x66631),x66632))+~P85(f784(f784(f242(x66631),x66632),x66633))
% 11.41/11.18 [6664]~P101(x66641)+E(f784(f784(f110(f869(x66641,a852)),f308(x66641,x66642,x66643)),f784(f268(x66641),x66643)),f784(f306(x66641),x66642))+~P85(f784(f784(f243(x66641),x66642),x66643))
% 11.41/11.18 [6681]P85(f784(x66811,x66812))+~P85(f784(f784(f242(a859),x66812),x66813))+P85(f784(f784(f347(a859),f847(x66811,x66813)),f305(a859,f2(a859),x66813)))
% 11.41/11.18 [6691]P85(f784(f784(f289(a1),x66911),f60(a1,x66912,x66913)))+~P85(f784(f784(f289(a1),x66911),x66912))+~P85(f784(f784(f289(a1),x66911),x66913))
% 11.41/11.18 [6717]E(x67171,x67172)+~E(f784(f784(f155(x67173),x67171),f742(x67173,x67172,x67171)),f784(f784(f155(x67173),x67172),f742(x67173,x67172,x67171)))+~E(f784(f188(f860(x67173)),x67171),f784(f188(f860(x67173)),x67172))
% 11.41/11.18 [6723]~E(x67233,f784(f784(f51(a859),x67231),x67232))+~P85(f784(f784(f243(a859),f2(a859)),x67232))+P85(f784(f784(f243(a859),x67231),f784(f784(f90(a859),x67232),f784(a160,x67233))))
% 11.41/11.18 [6738]~P85(f784(x67381,x67383))+~P85(f784(f784(f242(a859),x67383),x67382))+P85(f784(f784(f347(a859),f808(x67381,x67382)),f305(a859,f2(a859),x67382)))
% 11.41/11.18 [6780]~P85(f784(x67801,x67803))+P85(f784(x67801,f848(x67801,x67802)))+~P85(f784(f784(f347(a859),x67803),f305(a859,f2(a859),x67802)))
% 11.41/11.18 [6802]~P120(x68023)+~P85(f784(f784(f243(x68023),f784(f109(x68023),x68021)),f784(f109(x68023),x68022)))+P85(f784(f784(f243(a859),x68021),x68022))
% 11.41/11.18 [6803]~P120(x68033)+~P85(f784(f784(f243(x68033),f784(f109(x68033),x68031)),f784(f109(x68033),x68032)))+P85(f784(f784(f243(a859),x68031),x68032))
% 11.41/11.18 [6804]~P113(x68043)+~P85(f784(f784(f243(x68043),f784(f112(x68043),x68041)),f784(f112(x68043),x68042)))+P85(f784(f784(f243(a1),x68041),x68042))
% 11.41/11.18 [6805]~P120(x68053)+~P85(f784(f784(f242(x68053),f784(f109(x68053),x68051)),f784(f109(x68053),x68052)))+P85(f784(f784(f242(a859),x68051),x68052))
% 11.41/11.18 [6806]~P113(x68063)+~P85(f784(f784(f242(x68063),f784(f112(x68063),x68061)),f784(f112(x68063),x68062)))+P85(f784(f784(f242(a1),x68061),x68062))
% 11.41/11.18 [6822]~P120(x68221)+~P85(f784(f784(f243(x68221),f87(x68221)),x68222))+P85(f784(f784(f243(x68221),f87(x68221)),f784(f784(f252(x68221),x68222),f784(a160,x68223))))
% 11.41/11.18 [6826]~P77(x68261)+~P85(f784(f784(f243(x68261),f784(f88(x68261),x68263)),f784(f88(x68261),x68262)))+P85(f784(f784(f243(x68261),x68262),x68263))
% 11.41/11.18 [6827]~P77(x68271)+~P85(f784(f784(f242(x68271),f784(f88(x68271),x68273)),f784(f88(x68271),x68272)))+P85(f784(f784(f242(x68271),x68272),x68273))
% 11.41/11.18 [6828]~P91(x68281)+~P85(f784(f784(f242(x68281),f784(f88(x68281),x68283)),f784(f88(x68281),x68282)))+P85(f784(f784(f242(x68281),x68282),x68283))
% 11.41/11.18 [6854]P85(f784(x68541,x68542))+~P85(f784(x68541,f849(x68541,x68543)))+~P85(f784(f784(f347(a859),x68542),f305(a859,f2(a859),x68543)))
% 11.41/11.18 [6875]~P61(x68751)+P85(f784(f784(f243(x68751),f810(x68753,x68752,x68751)),f87(x68751)))+P85(f784(f784(f242(x68751),x68752),x68753))
% 11.41/11.18 [6893]~E(f60(a859,x68933,x68932),f60(a859,x68931,x68932))+E(f784(f784(f89(a859),x68931),f784(f784(f90(a859),x68932),f819(x68931,x68932,x68933))),x68933)+~P85(f784(f784(f242(a859),x68931),x68933))
% 11.41/11.18 [6911]E(f784(x69111,f618(x69111,x69112,x69113)),f190(x69112))+~P85(f784(f71(x69113),f175(x69113,x69112,x69111)))+P85(f784(f71(x69113),f249(f869(x69113,a852))))
% 11.41/11.18 [6951]E(f784(f784(f8(x69511,a859),x69512),x69513),f2(a859))+~P85(f784(f71(x69511),x69513))+P85(f784(f784(f347(x69511),f417(x69512,x69513,x69511)),x69513))
% 11.41/11.18 [6952]E(f784(f784(f11(x69521,a859),x69522),x69523),f87(a859))+~P85(f784(f71(x69521),x69523))+P85(f784(f784(f347(x69521),f463(x69522,x69523,x69521)),x69523))
% 11.41/11.18 [6974]~P101(x69741)+~P85(f784(f784(f243(x69741),x69742),x69743))+P85(f784(f784(f243(f869(x69741,a852)),f784(f267(x69741),x69742)),f784(f267(x69741),x69743)))
% 11.41/11.18 [6975]~P101(x69751)+~P85(f784(f784(f242(x69751),x69752),x69753))+P85(f784(f784(f242(f869(x69751,a852)),f784(f267(x69751),x69752)),f784(f267(x69751),x69753)))
% 11.41/11.18 [6976]~P101(x69761)+~P85(f784(f784(f242(x69761),x69763),x69762))+P85(f784(f784(f242(f869(x69761,a852)),f784(f306(x69761),x69762)),f784(f306(x69761),x69763)))
% 11.41/11.18 [6977]~P100(x69771)+~P85(f784(f784(f242(x69771),x69772),x69773))+P85(f784(f784(f242(f869(x69771,a852)),f784(f303(x69771),x69772)),f784(f303(x69771),x69773)))
% 11.41/11.18 [6978]~P100(x69781)+~P85(f784(f784(f242(x69781),x69783),x69782))+P85(f784(f784(f242(f869(x69781,a852)),f784(f268(x69781),x69782)),f784(f268(x69781),x69783)))
% 11.41/11.18 [6983]~P6(x69831)+P85(f784(f784(f242(x69831),x69832),f53(x69831,x69833)))+P85(f784(f784(f347(x69831),f684(x69833,x69832,x69831)),x69833))
% 11.41/11.18 [6988]~P77(x69881)+P85(f784(f784(f243(x69881),f784(f784(f3(x69881),x69882),x69883)),f2(x69881)))+~P85(f784(f784(f243(x69881),x69882),x69883))
% 11.41/11.18 [6989]~P77(x69891)+P85(f784(f784(f242(x69891),f784(f784(f3(x69891),x69892),x69893)),f2(x69891)))+~P85(f784(f784(f242(x69891),x69892),x69893))
% 11.41/11.18 [7027]~P85(f784(f784(f289(a1),x70271),f60(a1,x70272,x70273)))+~P85(f784(f784(f289(a1),x70271),x70273))+P85(f784(f784(f289(a1),x70271),x70272))
% 11.41/11.18 [7034]P85(f784(x70341,x70342))+P85(f784(f784(f242(a859),f849(x70341,x70343)),x70343))+~P85(f784(f784(f347(a859),x70342),f305(a859,f2(a859),x70343)))
% 11.41/11.18 [7076]~E(f784(f784(f8(x70761,a859),x70762),x70763),f87(a859))+~P85(f784(f71(x70761),x70763))+P85(f784(f784(f347(x70761),f416(x70762,x70763,x70761)),x70763))
% 11.41/11.18 [7077]~P85(f784(x70771,x70773))+P85(f784(f784(f242(a859),f848(x70771,x70772)),x70772))+~P85(f784(f784(f347(a859),x70773),f305(a859,f2(a859),x70772)))
% 11.41/11.18 [7114]~P6(x71141)+P85(f784(f784(f347(x71141),f685(x71143,x71142,x71141)),x71142))+P85(f784(f784(f242(x71141),f52(x71141,x71142)),x71143))
% 11.41/11.18 [7144]~E(f784(f784(f8(x71441,a859),x71442),x71443),f784(a160,f2(a859)))+~P85(f784(f71(x71441),x71443))+P85(f784(f784(f347(x71441),f418(x71442,x71443,x71441)),x71443))
% 11.41/11.18 [7155]E(x71551,f2(a859))+P85(f784(x71552,f60(a859,x71553,x71551)))+P85(f784(f784(f243(a859),f812(x71551,x71553,x71552)),x71551))
% 11.41/11.18 [7279]~P85(f784(x72791,x72792))+P85(f784(x72791,f60(a859,x72792,x72793)))+P85(f784(f784(f243(a859),f812(x72793,x72792,x72791)),x72793))
% 11.41/11.18 [7406]E(x74061,f120(x74062))+~P85(f784(f784(f347(f860(x74062)),x74061),f152(x74062,x74063)))+P85(f784(f784(f347(x74062),f762(x74063,x74061,x74062)),x74063))
% 11.41/11.18 [7426]~P101(x74261)+E(f784(f784(f110(f869(x74261,a852)),f784(f784(f312(x74261),x74262),f187(f869(x74261,a852)))),f308(x74261,x74262,x74263)),f784(f304(x74261,x74262),x74263))+~P85(f784(f784(f243(x74261),x74262),x74263))
% 11.41/11.18 [7450]~P101(x74501)+E(f784(f784(f110(f869(x74501,a852)),f784(f784(f312(x74501),x74502),f187(f869(x74501,a852)))),f307(x74501,x74502,x74503)),f305(x74501,x74502,x74503))+~P85(f784(f784(f242(x74501),x74502),x74503))
% 11.41/11.18 [7562]~P101(x75621)+P85(f784(f784(f243(x75621),x75622),x75623))+~P85(f784(f784(f243(f869(x75621,a852)),f784(f267(x75621),x75622)),f784(f267(x75621),x75623)))
% 11.41/11.18 [7563]~P100(x75631)+P85(f784(f784(f242(x75631),x75632),x75633))+~P85(f784(f784(f242(f869(x75631,a852)),f784(f268(x75631),x75633)),f784(f268(x75631),x75632)))
% 11.41/11.18 [7564]~P101(x75641)+P85(f784(f784(f242(x75641),x75642),x75643))+~P85(f784(f784(f242(f869(x75641,a852)),f784(f306(x75641),x75643)),f784(f306(x75641),x75642)))
% 11.41/11.18 [7565]~P100(x75651)+P85(f784(f784(f242(x75651),x75652),x75653))+~P85(f784(f784(f242(f869(x75651,a852)),f784(f303(x75651),x75652)),f784(f303(x75651),x75653)))
% 11.41/11.18 [7566]~P101(x75661)+P85(f784(f784(f242(x75661),x75662),x75663))+~P85(f784(f784(f242(f869(x75661,a852)),f784(f267(x75661),x75662)),f784(f267(x75661),x75663)))
% 11.41/11.18 [7590]~P77(x75901)+~P85(f784(f784(f243(x75901),f784(f784(f3(x75901),x75902),x75903)),f2(x75901)))+P85(f784(f784(f243(x75901),x75902),x75903))
% 11.41/11.18 [7591]~P77(x75911)+~P85(f784(f784(f242(x75911),f784(f784(f3(x75911),x75912),x75913)),f2(x75911)))+P85(f784(f784(f242(x75911),x75912),x75913))
% 11.41/11.18 [7750]E(x77501,f2(a859))+~E(f784(f136(a859,a859,f89(a859),x77502),x77503),f2(a859))+~P85(f784(f784(f347(a859),x77501),f784(f164(a859),x77503)))
% 11.41/11.18 [7754]~P6(x77541)+~P85(f784(f784(f242(x77541),f685(x77543,x77542,x77541)),x77543))+P85(f784(f784(f242(x77541),f52(x77541,x77542)),x77543))
% 11.41/11.18 [7905]P85(f784(f784(f242(a1),f2(a1)),f804(x79051,x79052,x79053)))+P85(f784(f784(x79052,f784(f784(f51(a1),x79051),x79053)),f60(a1,x79051,x79053)))+~P85(f784(f784(f243(a1),f2(a1)),x79053))
% 11.41/11.18 [7997]E(x79971,x79972)+~E(f784(f188(f860(x79973)),x79971),f784(f188(f860(x79973)),x79972))+~P85(f784(f784(f261(x79973,x79973,a852),a343),f726(x79973,x79971,x79972)))
% 11.41/11.18 [8062]~P35(x80622,x80623)+E(x80621,f187(f869(x80622,a852)))+~P85(f784(f784(f242(f869(x80622,a852)),x80621),f784(f287(x80622,x80622,x80623),x80621)))
% 11.41/11.18 [8090]~P62(x80901)+~P85(f784(f784(f242(x80901),x80902),f784(f784(f89(x80901),x80903),f817(x80903,x80902,x80901))))+P85(f784(f784(f242(x80901),x80902),x80903))
% 11.41/11.18 [8126]P46(x81261,x81262,x81263)+P85(f784(f784(f347(x81261),f605(x81263,x81262,x81261)),x81262))+P85(f784(f784(f347(f868(x81261,x81261)),f606(x81263,x81262,x81261)),x81263))
% 11.41/11.18 [8147]P85(f784(f784(x81472,f784(f784(f51(a1),x81471),x81473)),f60(a1,x81471,x81473)))+~P85(f784(f784(f243(a1),f2(a1)),x81473))+P85(f784(f784(f243(a1),f804(x81471,x81472,x81473)),x81473))
% 11.41/11.18 [8171]E(f784(f313(a859,a859,f784(f784(f9(a859,a859,a859),f3(a859)),x81711)),f784(f304(a859,x81712),x81713)),f187(f869(a859,a852)))+P85(f784(f784(f243(a859),x81711),x81713))+P85(f784(f784(f243(a859),x81712),x81713))
% 11.41/11.18 [8274]E(f784(f313(a859,a859,f784(f784(f9(a859,a859,a859),f3(a859)),x82741)),f784(f304(a859,x82742),x82743)),f784(f784(f312(a859),f2(a859)),f187(f869(a859,a852))))+P85(f784(f784(f243(a859),x82741),x82743))+~P85(f784(f784(f243(a859),x82742),x82743))
% 11.41/11.18 [8289]~P101(x82891)+E(f143(x82891,x82891,f7(x82891),x82892,x82893),x82893)+~P85(f784(f784(f347(x82891),x82892),f784(f164(x82891),x82893)))
% 11.41/11.18 [8304]P26(x83041,x83041,x83042,x83043)+~P85(f784(f71(x83041),x83043))+~P85(f784(f784(f242(f869(x83041,a852)),x83043),f784(f313(x83041,x83041,x83042),x83043)))
% 11.41/11.18 [8331]E(f784(f784(f89(a1),f784(f784(f90(a1),x83311),f805(x83312,x83313,x83311))),f804(x83312,x83313,x83311)),x83312)+P85(f784(f784(x83313,f784(f784(f51(a1),x83312),x83311)),f60(a1,x83312,x83311)))+~P85(f784(f784(f243(a1),f2(a1)),x83311))
% 11.41/11.18 [8561]~P85(f784(f784(x85611,f805(x85612,x85611,x85613)),f804(x85612,x85611,x85613)))+P85(f784(f784(x85611,f784(f784(f51(a1),x85612),x85613)),f60(a1,x85612,x85613)))+~P85(f784(f784(f243(a1),f2(a1)),x85613))
% 11.41/11.18 [9354]~P85(f784(f71(x93541),x93542))+~P85(f784(f784(f347(x93541),x93543),x93542))+P85(f784(f784(f243(a859),f784(f50(x93541),f784(f784(f3(f869(x93541,a852)),x93542),f784(f784(f312(x93541),x93543),f187(f869(x93541,a852)))))),f784(f50(x93541),x93542)))
% 11.41/11.18 [9938]P46(x99381,x99382,x99383)+~P85(f784(f784(f261(x99381,x99381,a852),f784(f784(f9(x99381,f869(x99381,a852),f869(x99381,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x99381,a852),f869(x99381,a852)),x99381),f10(a852,a852,x99381)),f784(f784(f10(a852,f869(a852,a852),x99381),a344),f784(f784(f9(x99381,f869(x99381,a852),a852),f347(x99381)),x99382)))),f784(f784(f9(x99381,f869(x99381,a852),a852),f347(x99381)),x99382))),f606(x99383,x99382,x99381)))+P85(f784(f784(f347(x99381),f605(x99383,x99382,x99381)),x99382))
% 11.41/11.18 [5378]~P116(x53782)+E(x53781,f2(x53782))+E(f784(f784(f293(x53782),x53783),f784(f88(x53782),x53781)),f784(f88(x53782),f784(f784(f293(x53782),x53783),x53781)))
% 11.41/11.18 [5508]~E(x55083,f187(f869(x55081,a852)))+~E(x55082,f187(f869(x55081,a852)))+E(f784(f784(f110(f869(x55081,a852)),x55082),x55083),f187(f869(x55081,a852)))
% 11.41/11.18 [5562]~E(x55623,f2(a859))+~P85(f784(x55621,f2(a859)))+P85(f784(x55621,f784(f784(f51(a859),x55622),x55623)))
% 11.41/11.18 [5563]~E(x55633,f2(a859))+~P85(f784(x55631,f2(a859)))+P85(f784(x55631,f784(f784(f51(a859),x55632),x55633)))
% 11.41/11.18 [5711]~P62(x57112)+E(x57111,f2(x57112))+E(f784(f784(f293(x57112),f784(f84(x57112),x57113)),f784(f84(x57112),x57111)),f784(f84(x57112),f784(f784(f293(x57112),x57113),x57111)))
% 11.41/11.18 [5805]~P86(x58051)+~E(x58052,f87(x58051))+P85(f784(f784(f289(x58051),x58052),f784(f784(f252(x58051),x58052),x58053)))
% 11.41/11.18 [5822]~P4(x58221)+E(f784(f784(f90(x58221),x58222),f784(f784(f51(x58221),x58223),x58222)),x58223)+~P85(f784(f784(f289(x58221),x58222),x58223))
% 11.41/11.18 [5876]~P85(f784(f71(x58761),x58763))+E(f784(f50(x58761),f784(f784(f312(x58761),x58762),x58763)),f784(a160,f784(f50(x58761),x58763)))+P85(f784(f784(f347(x58761),x58762),x58763))
% 11.41/11.18 [5877]~P85(f784(f71(x58771),x58773))+E(f784(f50(x58771),f784(f784(f312(x58771),x58772),x58773)),f784(a160,f784(f50(x58771),x58773)))+P85(f784(f784(f347(x58771),x58772),x58773))
% 11.41/11.18 [5952]~E(x59522,f2(a859))+P85(f784(x59521,f2(a859)))+~P85(f784(x59521,f784(f784(f51(a859),x59523),x59522)))
% 11.41/11.18 [5970]~P85(f784(f71(x59701),x59703))+E(f784(f50(x59701),f784(f784(f312(x59701),x59702),x59703)),f784(f50(x59701),x59703))+~P85(f784(f784(f347(x59701),x59702),x59703))
% 11.41/11.18 [6003]~P85(f784(f71(x60031),x60033))+E(f784(f50(x60031),f784(f784(f312(x60031),x60032),x60033)),f784(f784(f89(a859),f87(a859)),f784(f50(x60031),x60033)))+P85(f784(f784(f347(x60031),x60032),x60033))
% 11.41/11.18 [6010]~P5(x60101)+E(f784(f784(f51(x60101),x60102),f784(f88(x60101),x60103)),f784(f88(x60101),f784(f784(f51(x60101),x60102),x60103)))+~P85(f784(f784(f289(x60101),x60103),x60102))
% 11.41/11.18 [6124]E(f784(f784(f89(a859),x61241),f809(x61241,x61242,x61243)),x61242)+~P85(f784(x61243,f2(a859)))+P85(f784(x61243,f784(f784(f3(a859),x61242),x61241)))
% 11.41/11.18 [6125]E(f784(f784(f89(a859),x61251),f816(x61251,x61252,x61253)),x61252)+~P85(f784(x61253,f2(a859)))+P85(f784(x61253,f784(f784(f3(a859),x61252),x61251)))
% 11.41/11.18 [6149]~P5(x61491)+E(f784(f784(f51(x61491),f784(f88(x61491),x61492)),x61493),f784(f88(x61491),f784(f784(f51(x61491),x61492),x61493)))+~P85(f784(f784(f289(x61491),x61493),x61492))
% 11.41/11.18 [6172]~P6(x61721)+~P85(f784(f71(x61721),x61723))+E(f784(f784(f74(x61721,x61721,f110(x61721)),x61722),x61723),f784(f784(f110(x61721),x61722),f52(x61721,x61723)))
% 11.41/11.18 [6173]~P6(x61731)+~P85(f784(f71(x61731),x61733))+E(f784(f784(f74(x61731,x61731,f111(x61731)),x61732),x61733),f784(f784(f111(x61731),x61732),f53(x61731,x61733)))
% 11.41/11.18 [6179]~P89(x61791)+~E(f784(f113(x61791),x61792),f784(f113(x61791),x61793))+P30(x61791,f784(f113(x61791),f784(f784(f89(a1),x61792),f784(f88(a1),x61793))))
% 11.41/11.18 [6186]~P136(x61861)+E(f784(f784(f3(x61861),f784(f109(x61861),x61862)),f784(f109(x61861),x61863)),f784(f109(x61861),f784(f784(f3(a859),x61862),x61863)))+~P85(f784(f784(f242(a859),x61863),x61862))
% 11.41/11.18 [6192]~P105(x61921)+~P85(f784(f784(f289(x61921),x61922),x61923))+P85(f784(f784(f289(x61921),f784(f88(x61921),x61922)),x61923))
% 11.41/11.18 [6193]~P113(x61931)+~P85(f784(f784(f289(x61931),x61932),x61933))+P85(f784(f784(f289(x61931),f784(f84(x61931),x61932)),x61933))
% 11.41/11.18 [6276]E(f784(f784(f89(a859),x62761),f809(x62761,x62762,x62763)),x62762)+P85(f784(f784(f243(a859),x62762),x62761))+P85(f784(x62763,f784(f784(f3(a859),x62762),x62761)))
% 11.41/11.18 [6277]E(f784(f784(f89(a859),x62771),f816(x62771,x62772,x62773)),x62772)+P85(f784(f784(f243(a859),x62772),x62771))+P85(f784(x62773,f784(f784(f3(a859),x62772),x62771)))
% 11.41/11.18 [6295]~P113(x62951)+E(f784(f784(f90(x62951),f784(f84(x62951),x62952)),x62953),f784(f84(x62951),f784(f784(f90(x62951),x62952),x62953)))+~P85(f784(f784(f242(x62951),f2(x62951)),x62953))
% 11.41/11.18 [6296]~P61(x62961)+E(f784(f784(f293(x62961),f784(f84(x62961),x62962)),x62963),f784(f84(x62961),f784(f784(f293(x62961),x62962),x62963)))+~P85(f784(f784(f243(x62961),f2(x62961)),x62963))
% 11.41/11.18 [6305]~P93(x63051)+~P85(f784(f71(x63051),x63053))+E(f784(f784(f74(x63051,x63051,f110(x63051)),x63052),x63053),f15(x63051,f784(f784(f312(x63051),x63052),x63053)))
% 11.41/11.18 [6306]~P101(x63061)+~P85(f784(f71(x63061),x63063))+E(f784(f784(f74(x63061,x63061,f186(x63061)),x63062),x63063),f16(x63061,f784(f784(f312(x63061),x63062),x63063)))
% 11.41/11.18 [6307]~P101(x63071)+~P85(f784(f71(x63071),x63073))+E(f784(f784(f74(x63071,x63071,f246(x63071)),x63072),x63073),f17(x63071,f784(f784(f312(x63071),x63072),x63073)))
% 11.41/11.18 [6308]~P93(x63081)+~P85(f784(f71(x63081),x63083))+E(f784(f784(f74(x63081,x63081,f111(x63081)),x63082),x63083),f12(x63081,f784(f784(f312(x63081),x63082),x63083)))
% 11.41/11.18 [6352]E(x63521,f120(x63522))+~E(f170(x63522,x63523),f120(f860(x63522)))+~P85(f784(f784(f347(f860(x63522)),x63521),f784(f164(f860(x63522)),x63523)))
% 11.41/11.19 [6371]~P86(x63711)+~P85(f784(f784(f243(a859),f2(a859)),x63713))+P85(f784(f784(f289(x63711),x63712),f784(f784(f252(x63711),x63712),x63713)))
% 11.41/11.19 [6402]~P85(f784(f132(x64021),x64023))+P85(f784(f784(f347(x64021),x64022),f784(f164(x64021),x64023)))+P85(f784(f132(x64021),f784(f784(f144(x64021),x64022),x64023)))
% 11.41/11.19 [6414]~P92(x64141)+~P85(f784(f71(x64141),x64143))+E(f784(f73(x64141,f90(x64141)),f784(f784(f312(x64141),x64142),x64143)),f784(f784(f74(x64141,x64141,f90(x64141)),x64142),x64143))
% 11.41/11.19 [6435]~P101(x64351)+~P85(f784(f71(x64351),x64353))+E(f13(x64351,f186(x64351),f784(f784(f312(x64351),x64352),x64353)),f784(f784(f74(x64351,x64351,f186(x64351)),x64352),x64353))
% 11.41/11.19 [6436]~P101(x64361)+~P85(f784(f71(x64361),x64363))+E(f14(x64361,f246(x64361),f784(f784(f312(x64361),x64362),x64363)),f784(f784(f74(x64361,x64361,f246(x64361)),x64362),x64363))
% 11.41/11.19 [6437]P85(f784(x64371,f2(a859)))+~P85(f784(f784(f243(a859),x64372),x64373))+~P85(f784(x64371,f784(f784(f3(a859),x64372),x64373)))
% 11.41/11.19 [6438]P85(f784(x64381,f2(a859)))+~P85(f784(f784(f243(a859),x64382),x64383))+~P85(f784(x64381,f784(f784(f3(a859),x64382),x64383)))
% 11.41/11.19 [6457]~P113(x64571)+P85(f784(f784(f243(x64571),x64572),x64573))+~P85(f784(f784(f243(x64571),f784(f84(x64571),x64572)),x64573))
% 11.41/11.19 [6458]~P79(x64581)+P85(f784(f784(f242(x64581),x64582),x64583))+~P85(f784(f784(f242(x64581),f784(f84(x64581),x64582)),x64583))
% 11.41/11.19 [6459]~P79(x64591)+P85(f784(f784(f242(x64591),x64592),x64593))+~P85(f784(f784(f242(x64591),f784(f84(x64591),x64592)),x64593))
% 11.41/11.19 [6460]~P113(x64601)+P85(f784(f784(f289(x64601),x64602),x64603))+~P85(f784(f784(f289(x64601),f784(f84(x64601),x64602)),x64603))
% 11.41/11.19 [6461]~P105(x64611)+P85(f784(f784(f289(x64611),x64612),x64613))+~P85(f784(f784(f289(x64611),f784(f88(x64611),x64612)),x64613))
% 11.41/11.19 [6480]E(x64801,f120(x64802))+E(f784(f135(x64802),f784(f784(f133(x64802),x64803),x64801)),f784(f784(f155(x64802),x64801),x64803))+~P85(f784(f784(f243(a859),x64803),f784(f188(f860(x64802)),x64801)))
% 11.41/11.19 [6533]~P85(f784(x65331,x65333))+P85(f784(x65331,f355(x65331,x65332)))+~P85(f784(f784(f347(a859),x65333),f784(f304(a859,f2(a859)),x65332)))
% 11.41/11.19 [6556]P85(f784(x65561,x65562))+~P85(f784(f784(f243(a859),x65562),x65563))+P85(f784(f784(f347(a859),f354(x65561,x65563)),f784(f304(a859,f2(a859)),x65563)))
% 11.41/11.19 [6571]~P120(x65711)+~P85(f784(f784(f243(x65711),f2(x65711)),x65712))+P85(f784(f784(f243(x65711),f2(x65711)),f784(f784(f252(x65711),x65712),x65713)))
% 11.41/11.19 [6573]~P120(x65731)+~P85(f784(f784(f242(x65731),f2(x65731)),x65732))+P85(f784(f784(f242(x65731),f2(x65731)),f784(f784(f252(x65731),x65732),x65733)))
% 11.41/11.19 [6574]~P120(x65741)+~P85(f784(f784(f242(x65741),f87(x65741)),x65742))+P85(f784(f784(f242(x65741),f87(x65741)),f784(f784(f252(x65741),x65742),x65743)))
% 11.41/11.19 [6598]~P85(f784(x65981,x65983))+~P85(f784(f784(f243(a859),x65983),x65982))+P85(f784(f784(f347(a859),f352(x65981,x65982)),f784(f304(a859,f2(a859)),x65982)))
% 11.41/11.19 [6602]P85(f784(f71(x66021),x66022))+~P85(f784(f71(x66021),x66023))+~P85(f784(f784(f242(f869(x66021,a852)),x66022),x66023))
% 11.41/11.19 [6603]P85(f784(f71(x66031),x66032))+~P85(f784(f71(x66031),x66033))+~P85(f784(f784(f242(f869(x66031,a852)),x66032),x66033))
% 11.41/11.19 [6612]~P85(f784(f784(f289(a859),x66121),x66122))+~P85(f784(f784(f289(a859),x66121),x66123))+P85(f784(f784(f289(a859),x66121),f784(f784(f3(a859),x66122),x66123)))
% 11.41/11.19 [6613]P85(f784(x66131,x66132))+~P85(f784(x66131,f356(x66131,x66133)))+~P85(f784(f784(f347(a859),x66132),f784(f304(a859,f2(a859)),x66133)))
% 11.41/11.19 [6626]E(x66261,f2(a859))+P85(f784(x66262,f802(x66261,x66263,x66262)))+~P85(f784(x66262,f784(f784(f51(a859),x66263),x66261)))
% 11.41/11.19 [6635]~P122(x66352)+E(x66351,f2(x66352))+~E(f784(f784(f89(x66352),f784(f784(f90(x66352),x66353),x66353)),f784(f784(f90(x66352),x66351),x66351)),f2(x66352))
% 11.41/11.19 [6636]~P122(x66362)+E(x66361,f2(x66362))+~E(f784(f784(f89(x66362),f784(f784(f90(x66362),x66361),x66361)),f784(f784(f90(x66362),x66363),x66363)),f2(x66362))
% 11.41/11.19 [6682]E(x66821,f2(a859))+~P85(f784(x66822,f811(x66821,x66823,x66822)))+P85(f784(x66822,f784(f784(f51(a859),x66823),x66821)))
% 11.41/11.19 [6687]~P101(x66871)+~P15(x66871,x66873)+P15(x66871,f784(f784(f142(x66871,x66871,f7(x66871)),x66872),x66873))
% 11.41/11.19 [6731]P85(f784(x67311,f802(x67312,x67313,x67311)))+P85(f784(x67311,f2(a859)))+~P85(f784(x67311,f784(f784(f51(a859),x67313),x67312)))
% 11.41/11.19 [6737]~P89(x67371)+E(f784(f113(x67371),x67372),f784(f113(x67371),x67373))+~P30(x67371,f784(f113(x67371),f784(f784(f89(a1),x67372),f784(f88(a1),x67373))))
% 11.41/11.19 [6809]E(x68091,f2(a1))+E(x68092,f2(a1))+~P85(f784(f64(x68092,x68092),f784(f784(f251(a1,a1),x68093),x68091)))
% 11.41/11.19 [6810]E(x68101,f87(a1))+E(x68102,f2(a1))+~P85(f784(f64(x68102,x68102),f784(f784(f251(a1,a1),x68101),x68103)))
% 11.41/11.19 [6824]P85(f784(x68241,x68242))+P85(f784(f784(f243(a859),f356(x68241,x68243)),x68243))+~P85(f784(f784(f347(a859),x68242),f784(f304(a859,f2(a859)),x68243)))
% 11.41/11.19 [6849]~P85(f784(x68491,f811(x68493,x68492,x68491)))+~P85(f784(x68491,f2(a859)))+P85(f784(x68491,f784(f784(f51(a859),x68492),x68493)))
% 11.41/11.19 [6850]~P85(f784(x68501,f809(x68503,x68502,x68501)))+~P85(f784(x68501,f2(a859)))+P85(f784(x68501,f784(f784(f3(a859),x68502),x68503)))
% 11.41/11.19 [6851]~P85(f784(x68511,f816(x68513,x68512,x68511)))+~P85(f784(x68511,f2(a859)))+P85(f784(x68511,f784(f784(f3(a859),x68512),x68513)))
% 11.41/11.19 [6871]~P85(f784(x68711,x68713))+P85(f784(f784(f243(a859),f355(x68711,x68712)),x68712))+~P85(f784(f784(f347(a859),x68713),f784(f304(a859,f2(a859)),x68712)))
% 11.41/11.19 [6872]E(f784(f784(f3(a859),f784(f784(f3(a859),x68721),x68722)),f784(f784(f3(a859),x68723),x68722)),f784(f784(f3(a859),x68721),x68723))+~P85(f784(f784(f242(a859),x68722),x68721))+~P85(f784(f784(f242(a859),x68722),x68723))
% 11.41/11.19 [6904]~P77(x69041)+~P85(f784(f784(f243(x69041),f784(f88(x69041),x69043)),x69042))+P85(f784(f784(f243(x69041),f784(f88(x69041),x69042)),x69043))
% 11.41/11.19 [6905]~P77(x69051)+~P85(f784(f784(f243(x69051),f784(f88(x69051),x69053)),x69052))+P85(f784(f784(f243(x69051),f784(f88(x69051),x69052)),x69053))
% 11.41/11.19 [6906]~P113(x69061)+~P85(f784(f784(f243(x69061),f784(f84(x69061),x69062)),x69063))+P85(f784(f784(f243(x69061),f784(f88(x69061),x69062)),x69063))
% 11.41/11.19 [6907]~P77(x69071)+~P85(f784(f784(f242(x69071),f784(f88(x69071),x69073)),x69072))+P85(f784(f784(f242(x69071),f784(f88(x69071),x69072)),x69073))
% 11.41/11.19 [6908]~P77(x69081)+~P85(f784(f784(f242(x69081),f784(f88(x69081),x69083)),x69082))+P85(f784(f784(f242(x69081),f784(f88(x69081),x69082)),x69083))
% 11.41/11.19 [6909]~P79(x69091)+~P85(f784(f784(f242(x69091),f784(f84(x69091),x69092)),x69093))+P85(f784(f784(f242(x69091),f784(f88(x69091),x69092)),x69093))
% 11.41/11.19 [6910]~P79(x69101)+~P85(f784(f784(f242(x69101),f784(f84(x69101),x69102)),x69103))+P85(f784(f784(f242(x69101),f784(f88(x69101),x69102)),x69103))
% 11.41/11.19 [6913]~P85(f784(f784(f289(a1),x69131),x69133))+P85(f784(f784(f289(a1),x69131),x69132))+~P85(f784(f784(f289(a1),x69131),f784(f784(f3(a1),x69132),x69133)))
% 11.41/11.19 [6945]~P85(f784(x69453,f809(x69452,x69451,x69453)))+P85(f784(f784(f243(a859),x69451),x69452))+P85(f784(x69453,f784(f784(f3(a859),x69451),x69452)))
% 11.41/11.19 [6946]~P85(f784(x69463,f816(x69462,x69461,x69463)))+P85(f784(f784(f243(a859),x69461),x69462))+P85(f784(x69463,f784(f784(f3(a859),x69461),x69462)))
% 11.41/11.19 [6992]~E(f691(x69923,x69922,x69921),f692(x69923,x69922,x69921))+E(f784(f784(f111(f869(x69921,a852)),x69922),f52(f869(x69921,a852),x69923)),f187(f869(x69921,a852)))+P85(f784(f784(f347(f869(x69921,a852)),x69922),x69923))
% 11.41/11.19 [7001]~P85(f784(f71(x70011),x70013))+P85(f784(f71(x70011),f53(f869(x70011,a852),x70012)))+~P85(f784(f784(f347(f869(x70011,a852)),x70013),x70012))
% 11.41/11.19 [7062]~P101(x70621)+E(f784(f784(f110(f869(x70621,a852)),f784(f304(x70621,x70622),x70623)),f784(f784(f312(x70621),x70623),f187(f869(x70621,a852)))),f305(x70621,x70622,x70623))+~P85(f784(f784(f242(x70621),x70622),x70623))
% 11.41/11.19 [7065]E(x70651,f2(a859))+P85(f784(f784(f243(a859),f813(x70651,x70653,x70652)),x70651))+P85(f784(x70652,f784(f784(f51(a859),x70653),x70651)))
% 11.41/11.19 [7099]E(x70991,x70992)+~P85(f784(f784(f242(f869(x70993,a852)),x70991),x70992))+P85(f784(f784(f243(f869(x70993,a852)),x70991),x70992))
% 11.41/11.19 [7100]E(x71001,x71002)+~P85(f784(f784(f242(f869(x71003,a852)),x71001),x71002))+P85(f784(f784(f243(f869(x71003,a852)),x71001),x71002))
% 11.41/11.19 [7111]E(x71111,x71112)+~E(f784(f188(f860(x71113)),x71111),f784(f188(f860(x71113)),x71112))+P85(f784(f784(f243(a859),f742(x71113,x71111,x71112)),f784(f188(f860(x71113)),x71112)))
% 11.41/11.19 [7156]P9(x71561,x71562,x71563)+~E(f784(f271(x71561,x71561),x71563),x71562)+~E(f784(f784(f291(x71561,x71561,x71561),f784(f288(x71561,x71561),x71563)),x71563),x71563)
% 11.41/11.19 [7238]E(x72381,f2(a1))+~P85(f784(f784(f289(a1),x72382),x72383))+P85(f784(f784(f289(a1),f784(f784(f90(a1),x72381),x72382)),f784(f784(f90(a1),x72381),x72383)))
% 11.41/11.19 [7241]~P85(f784(x72411,f2(a859)))+P85(f784(f784(f243(a859),f813(x72413,x72412,x72411)),x72413))+P85(f784(x72411,f784(f784(f51(a859),x72412),x72413)))
% 11.41/11.19 [7254]~P101(x72541)+E(f784(f784(f110(f869(x72541,a852)),f308(x72541,x72542,x72543)),f784(f784(f312(x72541),x72543),f187(f869(x72541,a852)))),f307(x72541,x72542,x72543))+~P85(f784(f784(f243(x72541),x72542),x72543))
% 11.41/11.19 [7359]~P85(f784(f71(x73591),x73593))+P85(f784(f784(f243(a859),f784(f50(x73591),x73592)),f784(f50(x73591),x73593)))+~P85(f784(f784(f243(f869(x73591,a852)),x73592),x73593))
% 11.41/11.19 [7360]~P85(f784(f71(x73601),x73603))+P85(f784(f784(f242(a859),f784(f50(x73601),x73602)),f784(f50(x73601),x73603)))+~P85(f784(f784(f242(f869(x73601,a852)),x73602),x73603))
% 11.41/11.19 [7401]~P85(f784(x74013,x74012))+P85(f784(f784(f194(x74011),x74012),f391(x74012,x74011,x74013)))+~P85(f784(f784(f194(f37(x74013,x74011)),x74012),x74012))
% 11.41/11.19 [7497]E(x74971,x74972)+~P85(f784(f784(f242(f869(x74973,a852)),x74972),x74971))+~P85(f784(f784(f242(f869(x74973,a852)),x74971),x74972))
% 11.41/11.19 [7498]E(x74981,x74982)+~P85(f784(f784(f242(f869(x74983,a852)),x74982),x74981))+~P85(f784(f784(f242(f869(x74983,a852)),x74981),x74982))
% 11.41/11.19 [7501]~P101(x75011)+P15(x75011,x75012)+~P15(x75011,f784(f784(f142(x75011,x75011,f7(x75011)),x75013),x75012))
% 11.41/11.19 [7570]~P85(f784(f784(f243(a859),x75703),x75702))+~P85(f784(f784(f243(a859),x75703),x75701))+P85(f784(f784(f243(a859),f784(f784(f3(a859),x75701),x75702)),f784(f784(f3(a859),x75701),x75703)))
% 11.41/11.19 [7571]~P85(f784(f784(f243(a859),x75711),x75713))+~P85(f784(f784(f242(a859),x75712),x75711))+P85(f784(f784(f243(a859),f784(f784(f3(a859),x75711),x75712)),f784(f784(f3(a859),x75713),x75712)))
% 11.41/11.19 [7588]~P85(f784(f784(f243(a1),x75882),f2(a1)))+~P85(f784(f784(f242(a1),x75883),x75881))+P85(f784(f784(f242(a1),f784(f784(f51(a1),x75881),x75882)),f784(f784(f51(a1),x75883),x75882)))
% 11.41/11.19 [7605]~P85(f784(f784(f243(a859),f2(a859)),x76051))+~P85(f784(f784(f243(a859),x76052),x76053))+P85(f784(f784(f243(a859),f784(f784(f90(a859),x76051),x76052)),f784(f784(f90(a859),x76051),x76053)))
% 11.41/11.19 [7606]~P85(f784(f784(f243(a859),f2(a859)),x76061))+~P85(f784(f784(f243(a859),x76062),x76063))+P85(f784(f784(f243(a859),f784(f784(f90(a859),x76061),x76062)),f784(f784(f90(a859),x76061),x76063)))
% 11.41/11.19 [7607]~P85(f784(f784(f243(a859),f2(a859)),x76072))+~P85(f784(f784(f243(a859),x76071),x76073))+P85(f784(f784(f243(a859),f784(f784(f90(a859),x76071),x76072)),f784(f784(f90(a859),x76073),x76072)))
% 11.41/11.19 [7608]~P85(f784(f784(f243(a859),f2(a859)),x76082))+~P85(f784(f784(f243(a859),x76081),x76083))+P85(f784(f784(f243(a859),f784(f784(f90(a859),x76081),x76082)),f784(f784(f90(a859),x76083),x76082)))
% 11.41/11.19 [7609]~P85(f784(f784(f243(a859),f2(a859)),x76091))+~P85(f784(f784(f243(a859),x76092),x76093))+P85(f784(f784(f243(a859),f784(f784(f90(a859),x76091),x76092)),f784(f784(f90(a859),x76091),x76093)))
% 11.41/11.19 [7610]~P85(f784(f784(f243(a1),f2(a1)),x76101))+~P85(f784(f784(f243(a1),x76102),x76103))+P85(f784(f784(f243(a1),f784(f784(f90(a1),x76101),x76102)),f784(f784(f90(a1),x76101),x76103)))
% 11.41/11.19 [7611]~P85(f784(f784(f243(a859),f2(a859)),x76111))+~P85(f784(f784(f242(a859),x76112),x76113))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x76111),x76112)),f784(f784(f90(a859),x76111),x76113)))
% 11.41/11.19 [7612]~P85(f784(f784(f243(a859),f2(a859)),x76123))+~P85(f784(f784(f242(a859),x76123),x76122))+P85(f784(f784(f242(a859),f784(f784(f51(a859),x76121),x76122)),f784(f784(f51(a859),x76121),x76123)))
% 11.41/11.19 [7613]~P85(f784(f784(f243(a1),f2(a1)),x76132))+~P85(f784(f784(f242(a1),x76131),x76133))+P85(f784(f784(f242(a1),f784(f784(f51(a1),x76131),x76132)),f784(f784(f51(a1),x76133),x76132)))
% 11.41/11.19 [7614]~P85(f784(f784(f243(a859),f2(a859)),x76141))+~P85(f784(f784(f289(a859),x76142),x76143))+P85(f784(f784(f289(a859),f784(f784(f90(a859),x76141),x76142)),f784(f784(f90(a859),x76141),x76143)))
% 11.41/11.19 [7662]E(x76621,f2(a859))+E(f784(f784(f89(a859),f784(f784(f90(a859),x76621),f811(x76621,x76622,x76623))),f813(x76621,x76622,x76623)),x76622)+P85(f784(x76623,f784(f784(f51(a859),x76622),x76621)))
% 11.41/11.19 [7719]E(f784(f784(f89(a859),f784(f784(f90(a859),x77191),f811(x77191,x77192,x77193))),f813(x77191,x77192,x77193)),x77192)+~P85(f784(x77193,f2(a859)))+P85(f784(x77193,f784(f784(f51(a859),x77192),x77191)))
% 11.41/11.19 [7735]~P85(f784(f71(x77351),x77353))+P85(f784(f784(f347(x77351),f477(x77352,x77353,x77351)),x77353))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f11(x77351,a859),x77352),x77353)))
% 11.41/11.19 [7736]~P85(f784(f71(x77361),x77363))+P85(f784(f784(f347(x77361),f574(x77362,x77363,x77361)),x77363))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f11(x77361,a859),x77362),x77363)))
% 11.41/11.19 [7841]E(x78411,f2(a859))+P85(f784(f784(f289(a859),x78412),x78413))+~P85(f784(f784(f289(a859),f784(f784(f90(a859),x78411),x78412)),f784(f784(f90(a859),x78411),x78413)))
% 11.41/11.19 [7842]E(x78421,f2(a1))+P85(f784(f784(f289(a1),x78422),x78423))+~P85(f784(f784(f289(a1),f784(f784(f90(a1),x78421),x78422)),f784(f784(f90(a1),x78421),x78423)))
% 11.41/11.19 [7843]E(x78431,f2(a1))+P85(f784(f784(f289(a1),x78432),x78433))+~P85(f784(f784(f289(a1),f784(f784(f90(a1),x78431),x78432)),f784(f784(f90(a1),x78431),x78433)))
% 11.41/11.19 [8027]E(x80271,f187(f869(x80272,a852)))+E(x80271,f784(f784(f312(x80272),x80273),f187(f869(x80272,a852))))+~P85(f784(f784(f242(f869(x80272,a852)),x80271),f784(f784(f312(x80272),x80273),f187(f869(x80272,a852)))))
% 11.41/11.19 [8063]~P85(f784(f784(f243(a859),f2(a859)),x80633))+P85(f784(f784(f243(a859),x80631),x80632))+~P85(f784(f784(f243(a859),f784(f784(f90(a859),x80633),x80631)),f784(f784(f90(a859),x80633),x80632)))
% 11.41/11.19 [8064]~P85(f784(f784(f243(a859),f2(a859)),x80643))+P85(f784(f784(f243(a859),x80641),x80642))+~P85(f784(f784(f243(a859),f784(f784(f252(a859),x80643),x80641)),f784(f784(f252(a859),x80643),x80642)))
% 11.41/11.19 [8065]~P85(f784(f784(f243(a859),f2(a859)),x80653))+P85(f784(f784(f242(a859),x80651),x80652))+~P85(f784(f784(f242(a859),f784(f784(f90(a859),x80653),x80651)),f784(f784(f90(a859),x80653),x80652)))
% 11.41/11.19 [8066]~P85(f784(f784(f243(a859),f2(a859)),x80663))+P85(f784(f784(f242(a859),x80661),x80662))+~P85(f784(f784(f242(a859),f784(f784(f90(a859),x80663),x80661)),f784(f784(f90(a859),x80663),x80662)))
% 11.41/11.19 [8067]~P85(f784(f784(f243(a859),f87(a859)),x80673))+P85(f784(f784(f242(a859),x80671),x80672))+~P85(f784(f784(f289(a859),f784(f784(f252(a859),x80673),x80671)),f784(f784(f252(a859),x80673),x80672)))
% 11.41/11.19 [8068]~P85(f784(f784(f243(a859),f2(a859)),x80683))+P85(f784(f784(f242(a859),x80681),x80682))+~P85(f784(f784(f242(a859),f784(f784(f90(a859),x80681),x80683)),f784(f784(f90(a859),x80682),x80683)))
% 11.41/11.19 [8069]~P85(f784(f784(f243(a859),f2(a859)),x80693))+P85(f784(f784(f289(a859),x80691),x80692))+~P85(f784(f784(f289(a859),f784(f784(f90(a859),x80693),x80691)),f784(f784(f90(a859),x80693),x80692)))
% 11.41/11.19 [8070]~P85(f784(f784(f243(a859),f2(a859)),x80703))+P85(f784(f784(f289(a859),x80701),x80702))+~P85(f784(f784(f289(a859),f784(f784(f90(a859),x80703),x80701)),f784(f784(f90(a859),x80703),x80702)))
% 11.41/11.19 [8098]~P85(f784(x80981,x80983))+P85(f784(f784(f194(f37(x80981,x80982)),f391(x80983,x80982,x80981)),x80983))+~P85(f784(f784(f194(f37(x80981,x80982)),x80983),x80983))
% 11.41/11.19 [8106]~E(f784(f784(f111(f869(x81061,a852)),f692(x81063,x81062,x81061)),f691(x81063,x81062,x81061)),f187(f869(x81061,a852)))+E(f784(f784(f111(f869(x81061,a852)),x81062),f52(f869(x81061,a852),x81063)),f187(f869(x81061,a852)))+P85(f784(f784(f347(f869(x81061,a852)),x81062),x81063))
% 11.41/11.19 [8120]E(x81201,f120(x81202))+~E(f784(f136(f860(x81202),f860(x81202),f130(x81202),f120(x81202)),x81203),f120(x81202))+~P85(f784(f784(f347(f860(x81202)),x81201),f784(f164(f860(x81202)),x81203)))
% 11.41/11.19 [8121]E(x81211,f120(x81212))+~E(f784(f136(f860(x81212),f860(x81212),f130(x81212),f120(x81212)),x81213),f120(x81212))+~P85(f784(f784(f347(f860(x81212)),x81211),f784(f164(f860(x81212)),x81213)))
% 11.41/11.19 [8176]E(x81761,f187(f869(f869(x81762,a852),a852)))+P85(f784(f784(f347(f869(x81762,a852)),f699(x81763,x81761,x81762)),x81761))+P85(f784(f784(f242(f869(x81762,a852)),f53(f869(x81762,a852),x81761)),x81763))
% 11.41/11.19 [8182]~P68(x81821)+~P71(x81821)+E(f784(f784(f8(a1,x81821),f784(f784(f10(a859,x81821,a1),x81822),a114)),f784(f313(a859,a1,f109(a1)),x81823)),f784(f784(f8(a859,x81821),x81822),x81823))
% 11.41/11.19 [8183]~P68(x81831)+~P71(x81831)+E(f784(f784(f11(a1,x81831),f784(f784(f10(a859,x81831,a1),x81832),a114)),f784(f313(a859,a1,f109(a1)),x81833)),f784(f784(f11(a859,x81831),x81832),x81833))
% 11.41/11.19 [8220]~P85(f784(f71(x82201),x82203))+~P85(f784(f784(f243(a859),f2(a859)),f784(x82202,f477(x82202,x82203,x82201))))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f11(x82201,a859),x82202),x82203)))
% 11.41/11.19 [8221]~P85(f784(f71(x82211),x82213))+~P85(f784(f784(f243(a859),f2(a859)),f784(x82212,f574(x82212,x82213,x82211))))+P85(f784(f784(f243(a859),f2(a859)),f784(f784(f11(x82211,a859),x82212),x82213)))
% 11.41/11.19 [8257]~P60(x82572)+E(x82571,f87(x82572))+E(f784(f784(f293(x82572),f784(f784(f3(x82572),f784(f784(f252(x82572),x82571),x82573)),f87(x82572))),f784(f784(f3(x82572),x82571),f87(x82572))),f784(f784(f8(a859,x82572),f784(f252(x82572),x82571)),f784(f304(a859,f2(a859)),x82573)))
% 11.41/11.19 [8316]E(x83161,f2(a859))+~P85(f784(x83163,f784(f784(f51(a859),x83162),x83161)))+P85(f784(f784(f243(a859),x83162),f784(f784(f90(a859),x83161),f784(a160,f802(x83161,x83162,x83163)))))
% 11.41/11.19 [8337]P85(f784(x83371,f2(a859)))+~P85(f784(x83371,f784(f784(f51(a859),x83372),x83373)))+P85(f784(f784(f243(a859),x83372),f784(f784(f90(a859),x83373),f784(a160,f802(x83373,x83372,x83371)))))
% 11.41/11.19 [8376]E(x83761,f2(a859))+~P85(f784(x83763,f784(f784(f51(a859),x83762),x83761)))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x83761),f802(x83761,x83762,x83763))),x83762))
% 11.41/11.19 [8413]P85(f784(x84131,f2(a859)))+~P85(f784(x84131,f784(f784(f51(a859),x84133),x84132)))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x84132),f802(x84132,x84133,x84131))),x84133))
% 11.41/11.19 [8416]~P101(x84161)+E(f784(f784(f142(x84161,x84161,f7(x84161)),x84162),x84163),f143(x84161,x84161,f7(x84161),x84162,x84163))+P85(f784(f784(f347(x84161),x84162),f784(f164(x84161),x84163)))
% 11.41/11.19 [8455]~E(f784(x84553,f621(x84552,x84553,x84551)),f784(x84553,f623(x84552,x84553,x84551)))+~P57(x84551,f784(x84553,f622(x84552,x84553,x84551)))+P57(x84551,f784(f784(f54(x84552,f869(x84551,f869(x84551,a852))),f249(f869(x84552,a852))),x84553))
% 11.41/11.19 [8463]E(x84631,f187(f869(f869(x84632,a852),a852)))+~P85(f784(f784(f242(f869(x84632,a852)),f699(x84633,x84631,x84632)),x84633))+P85(f784(f784(f242(f869(x84632,a852)),f53(f869(x84632,a852),x84631)),x84633))
% 11.41/11.19 [8521]~P62(x85211)+~P85(f784(f784(f243(x85211),x85212),x85213))+P85(f784(f784(f243(x85211),x85212),f784(f784(f293(x85211),f784(f784(f89(x85211),x85212),x85213)),f784(f784(f89(x85211),f87(x85211)),f87(x85211)))))
% 11.41/11.19 [8564]~P85(f784(f784(x85641,f833(x85641,x85643,x85642)),f834(x85641,x85643,x85642)))+P85(f784(f784(x85641,x85642),x85643))+~P85(f784(f334(f868(a1,a1),a67),f784(f784(f251(a1,a1),x85642),x85643)))
% 11.41/11.19 [8565]~P85(f784(f784(x85651,f835(x85651,x85653,x85652)),f836(x85651,x85653,x85652)))+P85(f784(f784(x85651,x85652),x85653))+~P85(f784(f334(f868(a1,a1),a70),f784(f784(f251(a1,a1),x85652),x85653)))
% 11.41/11.19 [8566]~P85(f784(f784(x85661,f837(x85661,x85663,x85662)),f840(x85661,x85663,x85662)))+P85(f784(f784(x85661,x85662),x85663))+~P85(f784(f334(f868(a1,a1),a226),f784(f784(f251(a1,a1),x85662),x85663)))
% 11.41/11.19 [8567]~P85(f784(f784(x85671,f841(x85671,x85673,x85672)),f843(x85671,x85673,x85672)))+P85(f784(f784(x85671,x85672),x85673))+~P85(f784(f334(f868(a859,a859),a224),f784(f784(f251(a859,a859),x85672),x85673)))
% 11.41/11.19 [8568]~P85(f784(f784(x85681,f407(x85681,x85683,x85682)),f408(x85681,x85683,x85682)))+P85(f784(f784(x85681,x85682),x85683))+~P85(f784(f334(f868(a1,a1),a174),f784(f784(f251(a1,a1),x85682),x85683)))
% 11.41/11.19 [8803]P85(f784(f784(x88031,x88032),x88033))+P85(f784(f334(f868(a859,a859),a224),f784(f784(f251(a859,a859),f841(x88031,x88033,x88032)),f843(x88031,x88033,x88032))))+~P85(f784(f334(f868(a859,a859),a224),f784(f784(f251(a859,a859),x88032),x88033)))
% 11.41/11.19 [8804]P85(f784(f784(x88041,x88042),x88043))+P85(f784(f334(f868(a1,a1),a67),f784(f784(f251(a1,a1),f833(x88041,x88043,x88042)),f834(x88041,x88043,x88042))))+~P85(f784(f334(f868(a1,a1),a67),f784(f784(f251(a1,a1),x88042),x88043)))
% 11.41/11.19 [8805]P85(f784(f784(x88051,x88052),x88053))+P85(f784(f334(f868(a1,a1),a70),f784(f784(f251(a1,a1),f835(x88051,x88053,x88052)),f836(x88051,x88053,x88052))))+~P85(f784(f334(f868(a1,a1),a70),f784(f784(f251(a1,a1),x88052),x88053)))
% 11.41/11.19 [8806]P85(f784(f784(x88061,x88062),x88063))+P85(f784(f334(f868(a1,a1),a226),f784(f784(f251(a1,a1),f837(x88061,x88063,x88062)),f840(x88061,x88063,x88062))))+~P85(f784(f334(f868(a1,a1),a226),f784(f784(f251(a1,a1),x88062),x88063)))
% 11.41/11.19 [8807]P85(f784(f784(x88071,x88072),x88073))+P85(f784(f334(f868(a1,a1),a174),f784(f784(f251(a1,a1),f407(x88071,x88073,x88072)),f408(x88071,x88073,x88072))))+~P85(f784(f334(f868(a1,a1),a174),f784(f784(f251(a1,a1),x88072),x88073)))
% 11.41/11.19 [9122]~P85(f784(f71(x91221),x91223))+P85(f784(f784(f347(f868(f869(x91221,a852),f869(x91221,a852))),f784(f784(f251(f869(x91221,a852),f869(x91221,a852)),x91222),x91223)),f309(x91221)))+~P85(f784(f784(f243(f869(x91221,a852)),x91222),x91223))
% 11.41/11.19 [9175]~P57(x91751,f784(x91753,f622(x91752,x91753,x91751)))+P57(x91751,f784(f784(f54(x91752,f869(x91751,f869(x91751,a852))),f249(f869(x91752,a852))),x91753))+~E(f784(f784(f111(f869(x91751,a852)),f256(x91751,x91751,f784(x91753,f621(x91752,x91753,x91751)))),f257(x91751,x91751,f784(x91753,f623(x91752,x91753,x91751)))),f187(f869(x91751,a852)))
% 11.41/11.19 [9366]P46(x93661,x93662,x93663)+P85(f784(f784(f347(f868(x93661,x93661)),f606(x93663,x93662,x93661)),x93663))+~P85(f784(f784(f347(f868(x93661,x93661)),f784(f784(f251(x93661,x93661),f605(x93663,x93662,x93661)),f605(x93663,x93662,x93661))),x93663))
% 11.41/11.19 [9940]P46(x99401,x99402,x99403)+~P85(f784(f784(f261(x99401,x99401,a852),f784(f784(f9(x99401,f869(x99401,a852),f869(x99401,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x99401,a852),f869(x99401,a852)),x99401),f10(a852,a852,x99401)),f784(f784(f10(a852,f869(a852,a852),x99401),a344),f784(f784(f9(x99401,f869(x99401,a852),a852),f347(x99401)),x99402)))),f784(f784(f9(x99401,f869(x99401,a852),a852),f347(x99401)),x99402))),f606(x99403,x99402,x99401)))+~P85(f784(f784(f347(f868(x99401,x99401)),f784(f784(f251(x99401,x99401),f605(x99403,x99402,x99401)),f605(x99403,x99402,x99401))),x99403))
% 11.41/11.19 [5546]~P4(x55462)+E(x55461,f2(x55462))+E(f784(f784(f51(x55462),f784(f784(f90(x55462),x55463),x55461)),x55461),x55463)
% 11.41/11.19 [5547]~P4(x55472)+E(x55471,f2(x55472))+E(f784(f784(f51(x55472),f784(f784(f90(x55472),x55471),x55473)),x55471),x55473)
% 11.41/11.19 [6187]~P4(x61871)+E(f784(f784(f90(x61871),f784(f784(f51(x61871),x61872),x61873)),x61873),x61872)+~P85(f784(f784(f289(x61871),x61873),x61872))
% 11.41/11.19 [6351]~P68(x63511)+~E(f784(x63512,f2(a859)),f2(x63511))+E(f784(f784(f8(a859,x63511),x63512),f784(f304(a859,f784(a160,f2(a859))),x63513)),f784(f784(f8(a859,x63511),x63512),f784(f304(a859,f2(a859)),x63513)))
% 11.41/11.19 [6493]~P4(x64932)+E(x64931,f2(x64932))+E(f784(f784(f51(x64932),f784(f784(f89(x64932),x64933),x64931)),x64931),f784(f784(f89(x64932),f784(f784(f51(x64932),x64933),x64931)),f87(x64932)))
% 11.41/11.19 [6494]~P4(x64942)+E(x64941,f2(x64942))+E(f784(f784(f51(x64942),f784(f784(f89(x64942),x64941),x64943)),x64941),f784(f784(f89(x64942),f784(f784(f51(x64942),x64943),x64941)),f87(x64942)))
% 11.41/11.19 [6721]~P85(f784(x67213,f2(a1)))+P85(f784(f784(f242(a859),x67211),x67212))+P85(f784(x67213,f784(f109(a1),f784(f784(f3(a859),x67212),x67211))))
% 11.41/11.19 [6831]P85(f784(f784(f242(a859),x68312),x68311))+P85(f784(f784(f243(a859),x68311),x68312))+P85(f784(x68313,f784(f109(a1),f784(f784(f3(a859),x68311),x68312))))
% 11.41/11.19 [6903]E(f784(f784(f89(a859),f784(f113(a859),x69031)),f784(f784(f89(a859),f784(f113(a859),x69032)),x69033)),f784(f784(f89(a859),f784(f113(a859),x69031)),x69033))+P85(f784(a193,f784(f113(a1),x69031)))+~P85(f784(a193,f784(f113(a1),x69032)))
% 11.41/11.19 [6980]~E(x69802,f784(f784(f51(a859),x69803),x69801))+~P85(f784(f784(f243(a859),f2(a859)),x69801))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x69801),x69802)),x69803))
% 11.41/11.19 [7096]~P85(f784(f71(x70961),x70963))+~P85(f784(f71(x70961),x70962))+P85(f784(f71(x70961),f784(f784(f3(f869(x70961,a852)),x70962),x70963)))
% 11.41/11.19 [7097]~P85(f784(f71(x70971),x70973))+~P85(f784(f71(x70971),x70972))+P85(f784(f71(x70971),f784(f784(f110(f869(x70971,a852)),x70972),x70973)))
% 11.41/11.19 [7098]~P85(f784(f71(x70981),x70983))+~P85(f784(f71(x70981),x70982))+P85(f784(f71(x70981),f784(f784(f110(f869(x70981,a852)),x70982),x70983)))
% 11.41/11.19 [7412]~P101(x74121)+~P85(f784(f71(x74121),x74122))+E(f134(x74121,f784(f784(f3(f869(x74121,a852)),x74122),f784(f784(f312(x74121),x74123),f187(f869(x74121,a852))))),f154(x74121,x74123,f134(x74121,x74122)))
% 11.41/11.19 [7477]P85(f784(x74771,f2(a1)))+~P85(f784(f784(f243(a859),x74772),x74773))+~P85(f784(x74771,f784(f109(a1),f784(f784(f3(a859),x74772),x74773))))
% 11.41/11.19 [7495]~P85(f784(f71(x74951),x74952))+E(f784(f50(x74951),f784(f784(f3(f869(x74951,a852)),x74952),f784(f784(f312(x74951),x74953),f187(f869(x74951,a852))))),f784(f50(x74951),x74952))+P85(f784(f784(f347(x74951),x74953),x74952))
% 11.41/11.19 [7629]~P120(x76291)+~P85(f784(f784(f243(x76291),f87(x76291)),x76292))+P85(f784(f784(f243(x76291),f87(x76291)),f784(f784(f90(x76291),x76292),f784(f784(f252(x76291),x76292),x76293))))
% 11.41/11.19 [7673]~P85(f784(f71(x76731),x76733))+E(f784(f784(f3(a859),f784(f50(x76731),x76732)),f784(f50(x76731),x76733)),f784(f50(x76731),f784(f784(f3(f869(x76731,a852)),x76732),x76733)))+~P85(f784(f784(f242(f869(x76731,a852)),x76733),x76732))
% 11.41/11.19 [7727]~P85(f784(f784(f242(a859),x77272),x77273))+~P85(f784(f784(f242(a859),x77271),f784(f784(f3(a859),x77273),x77272)))+P85(f784(f784(f242(a859),f784(f784(f89(a859),x77271),x77272)),x77273))
% 11.41/11.19 [7784]P85(f784(f71(x77841),x77842))+~P85(f784(f71(x77841),x77843))+~P85(f784(f71(x77841),f784(f784(f3(f869(x77841,a852)),x77842),x77843)))
% 11.41/11.19 [7790]~P85(f784(f71(x77901),x77902))+E(f784(f50(x77901),f784(f784(f3(f869(x77901,a852)),x77902),f784(f784(f312(x77901),x77903),f187(f869(x77901,a852))))),f784(f784(f3(a859),f784(f50(x77901),x77902)),f87(a859)))+~P85(f784(f784(f347(x77901),x77903),x77902))
% 11.41/11.19 [7791]~P85(f784(f71(x77911),x77912))+E(f784(f50(x77911),f784(f784(f3(f869(x77911,a852)),x77912),f784(f784(f312(x77911),x77913),f187(f869(x77911,a852))))),f784(f784(f3(a859),f784(f50(x77911),x77912)),f87(a859)))+~P85(f784(f784(f347(x77911),x77913),x77912))
% 11.41/11.19 [7866]P57(x78661,x78662)+~P57(x78661,x78663)+~P85(f784(f784(f242(f869(x78661,f869(x78661,a852))),x78662),x78663))
% 11.41/11.19 [7904]~P85(f784(f784(f242(a859),x79043),x79042))+P85(f784(f784(f242(a859),x79041),f784(f784(f3(a859),x79042),x79043)))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),x79041),x79043)),x79042))
% 11.41/11.19 [7923]P35(x79231,x79232)+~P35(x79231,x79233)+~P85(f784(f784(f242(f869(f868(x79231,x79231),a852)),x79232),x79233))
% 11.41/11.19 [7924]P55(x79241,x79242)+~P55(x79241,x79243)+~P85(f784(f784(f242(f869(f868(x79241,x79241),a852)),x79242),x79243))
% 11.41/11.19 [8154]~P120(x81541)+~P85(f784(f784(f243(x81541),f87(x81541)),x81542))+P85(f784(f784(f243(x81541),f784(f784(f252(x81541),x81542),x81543)),f784(f784(f90(x81541),x81542),f784(f784(f252(x81541),x81542),x81543))))
% 11.41/11.19 [8240]~P85(f784(x82401,f2(a1)))+~P85(f784(x82401,f784(f784(f3(a1),f784(f109(a1),x82402)),f784(f109(a1),x82403))))+P85(f784(x82401,f784(f109(a1),f784(f784(f3(a859),x82402),x82403))))
% 11.41/11.19 [8253]~P85(f784(f784(f242(a859),x82533),x82532))+P85(f784(x82531,f784(f784(f3(a1),f784(f109(a1),x82532)),f784(f109(a1),x82533))))+~P85(f784(x82531,f784(f109(a1),f784(f784(f3(a859),x82532),x82533))))
% 11.41/11.19 [8271]P85(f784(f784(f243(a859),x82711),x82712))+~P85(f784(x82713,f784(f784(f3(a1),f784(f109(a1),x82711)),f784(f109(a1),x82712))))+P85(f784(x82713,f784(f109(a1),f784(f784(f3(a859),x82711),x82712))))
% 11.41/11.19 [8328]~P122(x83282)+E(x83281,f2(x83282))+P85(f784(f784(f243(x83282),f2(x83282)),f784(f784(f89(x83282),f784(f784(f90(x83282),x83283),x83283)),f784(f784(f90(x83282),x83281),x83281))))
% 11.41/11.19 [8329]~P122(x83292)+E(x83291,f2(x83292))+P85(f784(f784(f243(x83292),f2(x83292)),f784(f784(f89(x83292),f784(f784(f90(x83292),x83291),x83291)),f784(f784(f90(x83292),x83293),x83293))))
% 11.41/11.19 [8434]~P85(f784(f784(f243(a859),f2(a859)),x84341))+~P85(f784(f784(f243(a1),x84342),x84343))+P85(f784(f784(f243(a1),f784(f784(f90(a1),f784(f109(a1),x84341)),x84342)),f784(f784(f90(a1),f784(f109(a1),x84341)),x84343)))
% 11.41/11.19 [8493]E(f784(f784(f111(f869(x84931,a852)),x84932),f52(f869(x84931,a852),x84933)),f187(f869(x84931,a852)))+P85(f784(f784(f347(f869(x84931,a852)),x84932),x84933))+P85(f784(f784(f347(f869(x84931,a852)),f692(x84933,x84932,x84931)),f784(f784(f312(f869(x84931,a852)),x84932),x84933)))
% 11.41/11.19 [8494]E(f784(f784(f111(f869(x84941,a852)),x84942),f52(f869(x84941,a852),x84943)),f187(f869(x84941,a852)))+P85(f784(f784(f347(f869(x84941,a852)),x84942),x84943))+P85(f784(f784(f347(f869(x84941,a852)),f691(x84943,x84942,x84941)),f784(f784(f312(f869(x84941,a852)),x84942),x84943)))
% 11.41/11.19 [8520]E(x85201,x85202)+~E(f784(f188(f860(x85203)),x85201),f784(f188(f860(x85203)),x85202))+P85(f784(f784(f347(f868(x85203,x85203)),f726(x85203,x85201,x85202)),f784(f164(f868(x85203,x85203)),f784(f784(f173(x85203,x85203),x85202),x85201))))
% 11.41/11.19 [8731]E(f310(x87311,x87312),f310(x87311,x87313))+~P85(f784(f784(f242(f869(f868(x87311,x87311),a852)),x87313),f310(x87311,x87312)))+~P85(f784(f784(f242(f869(f868(x87311,x87311),a852)),x87312),x87313))
% 11.41/11.19 [8784]~P46(x87841,f249(f869(x87841,a852)),x87843)+P85(f784(f784(f242(f869(f868(f860(x87841),f860(x87841)),a852)),f149(x87841,x87842)),f150(x87841,x87843)))+~P85(f784(f784(f242(f869(f868(x87841,x87841),a852)),x87842),x87843))
% 11.41/11.19 [8964]P35(x89641,x89642)+~P85(f784(f784(f347(x89641),x89643),f695(x89642,x89641)))+P85(f784(f784(f347(f868(x89641,x89641)),f784(f784(f251(x89641,x89641),f709(x89642,x89641,x89643)),x89643)),x89642))
% 11.41/11.19 [9003]~P85(f784(f71(x90031),x90032))+P85(f784(f71(f869(x90031,a852)),f784(f784(f69(x90031),x90032),x90033)))+~P85(f784(f784(f242(f869(f868(x90031,x90031),a852)),x90033),f784(f784(f258(x90031,x90031),x90032),f784(f18(f869(x90031,a852),x90031),x90032))))
% 11.41/11.19 [9035]P46(x90351,x90352,x90353)+P85(f784(f784(f347(x90351),f566(x90353,x90352,x90351)),x90352))+~P85(f784(f784(f242(f869(f868(x90351,x90351),a852)),x90353),f784(f784(f258(x90351,x90351),x90352),f784(f18(f869(x90351,a852),x90351),x90352))))
% 11.41/11.19 [9036]P46(x90361,x90362,x90363)+P85(f784(f784(f347(x90361),f570(x90362,x90363,x90361)),x90362))+~P85(f784(f784(f242(f869(f868(x90361,x90361),a852)),x90363),f784(f784(f258(x90361,x90361),x90362),f784(f18(f869(x90361,a852),x90361),x90362))))
% 11.41/11.19 [9070]~P62(x90701)+~P85(f784(f784(f243(x90701),x90702),x90703))+P85(f784(f784(f243(x90701),f784(f784(f293(x90701),f784(f784(f89(x90701),x90702),x90703)),f784(f784(f89(x90701),f87(x90701)),f87(x90701)))),x90703))
% 11.41/11.19 [9098]~P61(x90981)+P85(f784(f784(f242(x90981),x90982),x90983))+~P85(f784(f784(f242(x90981),f784(f784(f90(x90981),f810(x90983,x90982,x90981)),x90982)),x90983))
% 11.41/11.19 [9203]E(f317(x92031,x92032,x92033),f190(f860(a851)))+~P85(f784(f784(f243(a1),x92032),x92033))+~P85(f784(f334(f868(f869(a1,f864(f860(a851))),f868(a1,a1)),a321),f784(f784(f251(f869(a1,f864(f860(a851))),f868(a1,a1)),x92031),f784(f784(f251(a1,a1),x92032),x92033))))
% 11.41/11.19 [9206]E(f784(f188(f860(f860(x92061))),f784(f131(f860(x92061),f784(f784(f10(a859,a852,f860(x92061)),f784(f243(a859),x92062)),f188(f860(x92061)))),f170(x92061,x92063))),f784(f188(f860(x92061)),f784(f784(f155(f860(x92061)),x92063),x92062)))+~P15(a859,f784(f162(a859),f784(f784(f146(f860(x92061),a859),f188(f860(x92061))),x92063)))+~P85(f784(f784(f243(a859),x92062),f784(f188(f860(f860(x92061))),x92063)))
% 11.41/11.19 [9317]~P35(x93171,x93172)+P27(x93171,f784(f784(f251(f869(f868(x93171,x93171),a852),f869(f868(x93171,x93171),a852)),x93172),x93173))+~P85(f784(f784(f242(f869(f868(x93171,x93171),a852)),f784(f784(f291(x93171,x93171,x93171),x93172),x93173)),x93172))
% 11.41/11.19 [9319]E(f784(f239(f864(f860(a851)),f860(a851),f317(x93191,x93192,f784(f784(f89(a1),x93193),f87(a1))),f237(f860(a851))),f784(x93191,x93193)),f317(x93191,x93192,x93193))+P85(f784(f784(f243(a1),x93192),x93193))+~P85(f784(f334(f868(f869(a1,f864(f860(a851))),f868(a1,a1)),a321),f784(f784(f251(f869(a1,f864(f860(a851))),f868(a1,a1)),x93191),f784(f784(f251(a1,a1),x93192),x93193))))
% 11.41/11.19 [9324]E(f784(f784(f146(f860(x93241),x93241),f784(f784(f9(f860(x93241),a859,x93241),f155(x93241)),x93242)),f784(f131(f860(x93241),f784(f784(f10(a859,a852,f860(x93241)),f784(f243(a859),x93242)),f188(f860(x93241)))),f170(x93241,x93243))),f784(f784(f155(f860(x93241)),x93243),x93242))+~P15(a859,f784(f162(a859),f784(f784(f146(f860(x93241),a859),f188(f860(x93241))),x93243)))+~P85(f784(f784(f243(a859),x93242),f784(f188(f860(f860(x93241))),x93243)))
% 11.41/11.19 [9449]P46(x94491,x94492,x94493)+~P85(f784(f784(f347(f868(x94491,x94491)),f784(f784(f251(x94491,x94491),f566(x94493,x94492,x94491)),f566(x94493,x94492,x94491))),x94493))+~P85(f784(f784(f242(f869(f868(x94491,x94491),a852)),x94493),f784(f784(f258(x94491,x94491),x94492),f784(f18(f869(x94491,a852),x94491),x94492))))
% 11.41/11.19 [9450]P46(x94501,x94502,x94503)+~P85(f784(f784(f347(f868(x94501,x94501)),f784(f784(f251(x94501,x94501),f570(x94502,x94503,x94501)),f570(x94502,x94503,x94501))),x94503))+~P85(f784(f784(f242(f869(f868(x94501,x94501),a852)),x94503),f784(f784(f258(x94501,x94501),x94502),f784(f18(f869(x94501,a852),x94501),x94502))))
% 11.41/11.19 [9621]~P136(x96211)+~P119(x96211)+E(f784(f784(f293(x96211),f784(f112(x96211),f784(f784(f82(f868(a1,a1),a1,x96212,f250(a1,a1)),f217(x96212)),x96213))),f784(f112(x96211),f784(f784(f82(f868(a1,a1),a1,x96212,f260(a1,a1)),f217(x96212)),x96213))),f227(x96212,x96211,x96213))
% 11.41/11.19 [9815]~E(x98153,f2(a859))+~E(f784(f188(f860(x98151)),f784(f784(f155(f860(x98151)),x98152),f779(x98153,x98151,x98152))),x98153)+E(f784(f784(f146(a859,f860(x98151)),f784(f784(f9(a859,f860(a859),f860(x98151)),f784(f784(f10(f869(a859,x98151),f869(f860(a859),f860(x98151)),a859),f146(a859,x98151)),f784(f9(a859,a859,x98151),f784(f784(f10(f860(x98151),f869(a859,x98151),a859),f155(x98151)),f784(f155(f860(x98151)),x98152))))),f134(a859,f784(f304(a859,f2(a859)),f784(f188(f860(f860(x98151))),x98152))))),f134(a859,f784(f304(a859,f2(a859)),x98153))),f170(x98151,x98152))
% 11.41/11.19 [9816]E(x98161,f120(f860(x98162)))+~E(f784(f188(f860(x98162)),f784(f784(f155(f860(x98162)),x98161),f779(x98163,x98162,x98161))),x98163)+E(f784(f784(f146(a859,f860(x98162)),f784(f784(f9(a859,f860(a859),f860(x98162)),f784(f784(f10(f869(a859,x98162),f869(f860(a859),f860(x98162)),a859),f146(a859,x98162)),f784(f9(a859,a859,x98162),f784(f784(f10(f860(x98162),f869(a859,x98162),a859),f155(x98162)),f784(f155(f860(x98162)),x98161))))),f134(a859,f784(f304(a859,f2(a859)),f784(f188(f860(f860(x98162))),x98161))))),f134(a859,f784(f304(a859,f2(a859)),x98163))),f170(x98162,x98161))
% 11.41/11.19 [9817]~E(x98173,f2(a859))+E(f784(f784(f146(a859,f860(x98171)),f784(f784(f9(a859,f860(a859),f860(x98171)),f784(f784(f10(f869(a859,x98171),f869(f860(a859),f860(x98171)),a859),f146(a859,x98171)),f784(f9(a859,a859,x98171),f784(f784(f10(f860(x98171),f869(a859,x98171),a859),f155(x98171)),f784(f155(f860(x98171)),x98172))))),f134(a859,f784(f304(a859,f2(a859)),f784(f188(f860(f860(x98171))),x98172))))),f134(a859,f784(f304(a859,f2(a859)),x98173))),f170(x98171,x98172))+P85(f784(f784(f243(a859),f779(x98173,x98171,x98172)),f784(f188(f860(f860(x98171))),x98172)))
% 11.41/11.19 [9818]E(x98181,f120(f860(x98182)))+E(f784(f784(f146(a859,f860(x98182)),f784(f784(f9(a859,f860(a859),f860(x98182)),f784(f784(f10(f869(a859,x98182),f869(f860(a859),f860(x98182)),a859),f146(a859,x98182)),f784(f9(a859,a859,x98182),f784(f784(f10(f860(x98182),f869(a859,x98182),a859),f155(x98182)),f784(f155(f860(x98182)),x98181))))),f134(a859,f784(f304(a859,f2(a859)),f784(f188(f860(f860(x98182))),x98181))))),f134(a859,f784(f304(a859,f2(a859)),x98183))),f170(x98182,x98181))+P85(f784(f784(f243(a859),f779(x98183,x98182,x98181)),f784(f188(f860(f860(x98182))),x98181)))
% 11.41/11.19 [7670]E(f784(f784(f89(a859),f784(f113(a859),x76701)),f784(f784(f89(a859),f784(f113(a859),x76702)),x76703)),f784(f784(f89(a859),f784(f113(a859),f784(f784(f89(a1),x76701),x76702))),x76703))+P85(f784(a193,f784(f113(a1),x76701)))+P85(f784(a193,f784(f113(a1),x76702)))
% 11.41/11.19 [8425]~P85(f784(f71(x84251),x84252))+~P85(f784(f784(f347(x84251),x84253),x84252))+E(f784(a160,f784(f50(x84251),f784(f784(f3(f869(x84251,a852)),x84252),f784(f784(f312(x84251),x84253),f187(f869(x84251,a852)))))),f784(f50(x84251),x84252))
% 11.41/11.19 [8445]~P85(f784(f71(x84451),x84452))+~P85(f784(f784(f347(x84451),x84453),x84452))+E(f784(f784(f89(a859),f87(a859)),f784(f50(x84451),f784(f784(f3(f869(x84451,a852)),x84452),f784(f784(f312(x84451),x84453),f187(f869(x84451,a852)))))),f784(f50(x84451),x84452))
% 11.41/11.19 [8528]~P101(x85281)+~P85(f784(f71(x85281),x85283))+E(f784(f784(f142(x85281,x85281,f7(x85281)),x85282),f134(x85281,f784(f784(f3(f869(x85281,a852)),x85283),f784(f784(f312(x85281),x85282),f187(f869(x85281,a852)))))),f134(x85281,f784(f784(f312(x85281),x85282),x85283)))
% 11.41/11.19 [8666]~P85(f784(f71(x86661),x86663))+~P85(f784(f71(x86661),x86662))+E(f784(f784(f89(a859),f784(f50(x86661),f784(f784(f110(f869(x86661,a852)),x86662),x86663))),f784(f50(x86661),f784(f784(f111(f869(x86661,a852)),x86662),x86663))),f784(f784(f89(a859),f784(f50(x86661),x86662)),f784(f50(x86661),x86663)))
% 11.41/11.19 [8667]~P85(f784(f71(x86671),x86673))+~P85(f784(f71(x86671),x86672))+E(f784(f784(f89(a859),f784(f50(x86671),f784(f784(f110(f869(x86671,a852)),x86672),x86673))),f784(f50(x86671),f784(f784(f111(f869(x86671,a852)),x86672),x86673))),f784(f784(f89(a859),f784(f50(x86671),x86672)),f784(f50(x86671),x86673)))
% 11.41/11.19 [9764]~P26(x97641,f869(f869(x97641,a852),a852),f784(f784(f9(x97641,f869(f868(x97641,x97641),a852),f869(f869(x97641,a852),a852)),f784(f784(f10(f869(x97641,a852),f869(f869(f868(x97641,x97641),a852),f869(f869(x97641,a852),a852)),x97641),f69(x97641)),f784(f784(f9(x97641,f869(x97641,a852),f869(x97641,a852)),f312(x97641)),f187(f869(x97641,a852))))),x97643),x97642)+~P85(f784(f71(x97641),x97642))+E(f784(f50(f869(x97641,a852)),f784(f784(f69(x97641),x97642),x97643)),f784(f50(x97641),x97642))
% 11.41/11.19 [7940]~P89(x79401)+P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x79403)))+E(f784(f784(f252(x79401),x79402),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),x79403),x79403)),a106))),f87(x79401))
% 11.41/11.19 [8028]~P89(x80281)+P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x80283)))+E(f784(f784(f252(x80281),f784(f113(x80281),x80282)),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),x80283),x80283)),a106))),f87(x80281))
% 11.41/11.19 [9300]~P89(x93001)+~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x93003)))+E(f784(f784(f252(x93001),x93002),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),x93003),x93003)),a106))),f784(f784(f95(x93001,x93001),f784(f784(f252(x93001),x93002),f784(f113(a859),x93003))),f784(f784(f20(x93001,x93001,x93001),f784(f784(f10(x93001,f869(x93001,x93001),x93001),f90(x93001)),f784(f90(x93001),x93002))),f7(x93001))))
% 11.41/11.19 [9365]~P89(x93651)+~P85(f784(f784(f242(a1),f2(a1)),f784(f113(a1),x93653)))+E(f784(f784(f252(x93651),f784(f113(x93651),x93652)),f784(f113(a859),f784(f784(f3(a1),f784(f784(f89(a1),x93653),x93653)),a106))),f784(f784(f95(x93651,x93651),f784(f784(f252(x93651),f784(f113(x93651),x93652)),f784(f113(a859),x93653))),f784(f784(f20(x93651,x93651,x93651),f784(f784(f10(x93651,f869(x93651,x93651),x93651),f90(x93651)),f784(f90(x93651),f784(f113(x93651),x93652)))),f7(x93651))))
% 11.41/11.19 [9729]P85(f784(f784(f242(f869(f868(x97291,x97291),a852)),f310(x97291,x97292)),x97293))+~P85(f784(f784(f242(f869(f868(x97291,x97291),a852)),f310(x97291,f187(f869(f868(x97291,x97291),a852)))),x97293))+~P85(f784(f784(f242(f869(f868(x97291,x97291),a852)),f784(f784(f291(x97291,x97291,x97291),f784(f784(f111(f869(f868(x97291,x97291),a852)),f310(x97291,x97292)),x97293)),x97292)),x97293))
% 11.41/11.19 [9593]~P85(f784(f71(x95931),f784(f266(x95931),x95933)))+~P85(f784(f71(x95931),f784(f266(x95931),x95932)))+P85(f784(f71(x95931),f784(f266(x95931),f784(f784(f20(x95931,a852,a852),f784(f784(f10(a852,f869(a852,a852),x95931),a345),x95932)),x95933))))
% 11.41/11.19 [9885]P85(f784(f784(f242(f869(f868(x98851,x98851),a852)),f784(f784(f291(x98851,x98851,x98851),x98852),f310(x98851,x98852))),x98853))+~P85(f784(f784(f242(f869(f868(x98851,x98851),a852)),x98852),x98853))+~P85(f784(f784(f242(f869(f868(x98851,x98851),a852)),f784(f784(f291(x98851,x98851,x98851),f784(f784(f111(f869(f868(x98851,x98851),a852)),f784(f784(f291(x98851,x98851,x98851),x98852),f310(x98851,x98852))),x98853)),x98852)),x98853))
% 11.41/11.19 [9832]~P113(x98322)+E(x98321,f2(x98322))+~E(f784(f784(f89(x98322),f784(f784(f252(x98322),x98323),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x98322),x98321),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f2(x98322))
% 11.41/11.19 [9833]~P113(x98332)+E(x98331,f2(x98332))+~E(f784(f784(f89(x98332),f784(f784(f252(x98332),x98331),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x98332),x98333),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f2(x98332))
% 11.41/11.19 [9925]~P113(x99252)+E(x99251,f2(x99252))+P85(f784(f784(f243(x99252),f2(x99252)),f784(f784(f89(x99252),f784(f784(f252(x99252),x99253),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99252),x99251),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))))
% 11.41/11.19 [9926]~P113(x99262)+E(x99261,f2(x99262))+P85(f784(f784(f243(x99262),f2(x99262)),f784(f784(f89(x99262),f784(f784(f252(x99262),x99261),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99262),x99263),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))))
% 11.41/11.19 [9976]~P113(x99761)+P85(f784(f784(f242(x99761),f2(x99761)),x99762))+~P85(f784(f784(f242(x99761),f2(x99761)),f784(f784(f252(x99761),x99762),f784(a160,f784(f784(f90(a859),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x99763)))))
% 11.41/11.19 [5391]~P25(x53911,x53914,x53913)+P25(x53911,x53912,x53913)+~P25(x53911,x53912,x53914)
% 11.41/11.19 [4868]~E(x48682,f99(x48683,x48681))+P85(f784(x48681,x48682))+~P85(f784(x48681,x48684))
% 11.41/11.19 [6627]~P35(x66272,x66274)+~P35(x66271,x66273)+P35(f868(x66271,x66272),f339(x66271,x66272,x66273,x66274))
% 11.41/11.19 [8011]~P38(f37(x80114,x80111),x80112,x80113,x80112)+P38(x80111,x80112,x80113,f357(x80113,x80112,x80111,x80114))+~P85(f784(x80114,x80112))
% 11.41/11.19 [8037]~P38(f37(x80371,x80372),x80374,x80373,x80374)+P38(f37(x80371,x80372),f357(x80373,x80374,x80372,x80371),x80373,x80374)+~P85(f784(x80371,x80374))
% 11.41/11.19 [5052]~P8(x50524,x50521)+~E(f784(x50521,x50522),f784(x50521,x50523))+P85(f784(f784(x50521,x50522),x50523))
% 11.41/11.19 [5210]~P8(x52104,x52101)+E(f784(x52101,x52102),f784(x52101,x52103))+~P85(f784(f784(x52101,x52102),x52103))
% 11.41/11.19 [5297]~P19(x52973,x52974,x52971)+E(f784(x52971,x52972),f784(f73(x52973,x52974),x52972))+~P85(f784(f71(x52973),x52972))
% 11.41/11.19 [5298]~P11(x52983,x52984,x52981)+E(f784(x52981,x52982),f784(f73(x52983,x52984),x52982))+~P85(f784(f71(x52983),x52982))
% 11.41/11.19 [5426]~P8(x54264,x54261)+~P85(f784(f784(x54261,x54263),x54262))+P85(f784(f784(x54261,x54262),x54263))
% 11.41/11.19 [5488]E(x54881,x54882)+~E(f784(f250(x54883,x54884),x54881),f784(f250(x54883,x54884),x54882))+~E(f784(f260(x54883,x54884),x54881),f784(f260(x54883,x54884),x54882))
% 11.41/11.19 [5489]E(x54891,x54892)+~E(f784(f250(x54893,x54894),x54891),f784(f250(x54893,x54894),x54892))+~E(f784(f260(x54893,x54894),x54891),f784(f260(x54893,x54894),x54892))
% 11.41/11.19 [5515]E(x55151,x55152)+~P85(f784(f63(x55153,x55154),x55152))+~P85(f784(f63(x55153,x55154),x55151))
% 11.41/11.19 [5710]~P68(x57102)+E(f235(x57101,x57102,x57103,x57104),f2(x57102))+P85(f784(f71(x57101),x57104))
% 11.41/11.19 [5845]~P85(f784(f334(x58451,x58452),x58454))+P85(f784(f334(x58451,x58452),x58453))+~P85(f784(f784(x58452,x58453),x58454))
% 11.41/11.19 [5846]~P85(f784(f334(x58461,x58462),x58464))+P85(f784(f334(x58461,x58462),x58463))+~P85(f784(f784(x58462,x58463),x58464))
% 11.41/11.19 [5847]~P85(f784(f334(x58471,x58472),x58474))+P85(f784(f334(x58471,x58472),x58473))+~P85(f784(f784(x58472,x58473),x58474))
% 11.41/11.19 [8080]~P85(f784(f71(x80802),x80804))+~P85(f784(f71(x80801),x80803))+P85(f784(f71(f870(x80801,x80802)),f327(x80801,x80802,x80803,x80804)))
% 11.41/11.19 [8081]~P85(f784(f71(x80812),x80814))+~P85(f784(f71(x80811),x80813))+P85(f784(f71(f870(x80811,x80812)),f327(x80811,x80812,x80813,x80814)))
% 11.41/11.19 [8084]P85(f784(f784(f347(f860(x80841)),f784(f784(f130(x80841),x80842),x80843)),f152(x80841,x80844)))+~P85(f784(f784(f347(f860(x80841)),x80843),f152(x80841,x80844)))+~P85(f784(f784(f347(f860(x80841)),x80842),f152(x80841,x80844)))
% 11.41/11.19 [8656]~P85(f784(f784(f347(f868(x86561,x86561)),f784(f784(f251(x86561,x86561),x86562),x86564)),f310(x86561,x86563)))+P85(f784(f784(f347(x86561),x86562),f335(x86561,x86563)))+~P85(f784(f784(f347(x86561),x86564),f335(x86561,x86563)))
% 11.41/11.19 [8657]~P85(f784(f784(f347(f868(x86571,x86571)),f784(f784(f251(x86571,x86571),x86572),x86574)),f310(x86571,x86573)))+P85(f784(f784(f347(x86571),x86572),f335(x86571,x86573)))+~P85(f784(f784(f347(x86571),x86574),f335(x86571,x86573)))
% 11.41/11.19 [5034]~P68(x50342)+E(f784(f784(f8(x50341,x50342),x50343),x50344),f2(x50342))+P85(f784(f71(x50341),x50344))
% 11.41/11.19 [5035]~P68(x50352)+E(f784(f784(f8(x50351,x50352),x50353),x50354),f2(x50352))+P85(f784(f71(x50351),x50354))
% 11.41/11.19 [5036]~P68(x50362)+E(f784(f784(f8(x50361,x50362),x50363),x50364),f2(x50362))+P85(f784(f71(x50361),x50364))
% 11.41/11.19 [5037]~P71(x50372)+E(f784(f784(f11(x50371,x50372),x50373),x50374),f87(x50372))+P85(f784(f71(x50371),x50374))
% 11.41/11.19 [5038]~P71(x50382)+E(f784(f784(f11(x50381,x50382),x50383),x50384),f87(x50382))+P85(f784(f71(x50381),x50384))
% 11.41/11.19 [5039]~P71(x50392)+E(f784(f784(f11(x50391,x50392),x50393),x50394),f87(x50392))+P85(f784(f71(x50391),x50394))
% 11.41/11.19 [5179]~P63(x51793)+E(x51791,x51792)+~E(f784(f784(f89(x51793),x51794),x51791),f784(f784(f89(x51793),x51794),x51792))
% 11.41/11.19 [5180]~P63(x51803)+E(x51801,x51802)+~E(f784(f784(f89(x51803),x51804),x51801),f784(f784(f89(x51803),x51804),x51802))
% 11.41/11.19 [5181]~P64(x51813)+E(x51811,x51812)+~E(f784(f784(f89(x51813),x51814),x51811),f784(f784(f89(x51813),x51814),x51812))
% 11.41/11.19 [5182]~P63(x51823)+E(x51821,x51822)+~E(f784(f784(f89(x51823),x51821),x51824),f784(f784(f89(x51823),x51822),x51824))
% 11.41/11.19 [5183]~P63(x51833)+E(x51831,x51832)+~E(f784(f784(f89(x51833),x51831),x51834),f784(f784(f89(x51833),x51832),x51834))
% 11.41/11.19 [5267]~P115(x52671)+~E(x52673,f784(f784(f90(x52671),x52672),x52674))+P85(f784(f784(f289(x52671),x52672),x52673))
% 11.41/11.19 [5292]~P6(x52923)+E(x52921,f187(f869(x52922,a852)))+E(f784(f784(f54(x52922,x52923),x52921),f784(f18(x52923,x52922),x52924)),x52924)
% 11.41/11.19 [5293]~P6(x52933)+E(x52931,f187(f869(x52932,a852)))+E(f784(f784(f55(x52932,x52933),x52931),f784(f18(x52933,x52932),x52934)),x52934)
% 11.41/11.19 [5503]~P100(x55033)+E(x55031,x55032)+~E(f305(x55033,x55034,x55031),f784(f784(f312(x55033),x55032),f187(f869(x55033,a852))))
% 11.41/11.19 [5504]~P100(x55043)+E(x55041,x55042)+~E(f305(x55043,x55041,x55042),f784(f784(f312(x55043),x55044),f187(f869(x55043,a852))))
% 11.41/11.19 [5808]P85(f784(x58081,x58082))+~P85(f784(f255(x58083,x58081),x58084))+~P85(f784(f784(f347(x58083),x58082),x58084))
% 11.41/11.19 [5838]E(x58381,x58382)+~P85(f784(f784(f194(x58383),x58384),x58382))+~P85(f784(f784(f194(x58383),x58384),x58381))
% 11.41/11.19 [5920]~P68(x59201)+E(f784(f784(f8(a859,x59201),x59202),f784(f304(a859,x59203),f784(a160,x59204))),f2(x59201))+~P85(f784(f784(f243(a859),x59204),x59203))
% 11.41/11.19 [5924]~P5(x59241)+~E(f60(x59241,x59242,x59243),f60(x59241,x59244,x59243))+E(f60(x59241,f784(f88(x59241),x59242),x59243),f60(x59241,f784(f88(x59241),x59244),x59243))
% 11.41/11.19 [5992]P85(f784(x59921,x59922))+~E(f784(f131(x59923,x59921),x59924),x59924)+~P85(f784(f784(f347(x59923),x59922),f784(f164(x59923),x59924)))
% 11.41/11.19 [6011]~E(f784(f784(f89(a859),x60113),x60112),f784(f784(f89(a859),x60111),x60114))+~P85(f784(f784(f243(a859),x60113),x60114))+P85(f784(f784(f243(a859),x60111),x60112))
% 11.41/11.19 [6018]~P4(x60181)+E(f60(x60181,f60(x60181,x60182,x60183),x60184),f60(x60181,x60182,x60184))+~P85(f784(f784(f289(x60181),x60184),x60183))
% 11.41/11.19 [6056]~E(f784(f131(x60561,x60562),x60563),f120(x60561))+~P85(f784(x60562,x60564))+~P85(f784(f784(f347(x60561),x60564),f784(f164(x60561),x60563)))
% 11.41/11.19 [6091]~E(x60914,f187(f869(x60912,a852)))+~E(x60913,f187(f869(x60911,a852)))+E(f327(x60911,x60912,x60913,x60914),f187(f869(f870(x60911,x60912),a852)))
% 11.41/11.19 [6522]~P68(x65221)+E(f784(f784(f8(a859,x65221),x65222),f305(a859,x65223,f784(a160,x65224))),f2(x65221))+~P85(f784(f784(f243(a859),f784(a160,x65224)),x65223))
% 11.41/11.19 [6669]~P101(x66691)+E(f784(f784(f3(f869(x66691,a852)),f784(f304(x66691,x66692),x66693)),f784(f304(x66691,x66692),x66694)),f784(f304(x66691,x66694),x66693))+~P85(f784(f784(f242(x66691),x66692),x66694))
% 11.41/11.19 [7028]~P85(f784(f784(f347(f860(x70281)),x70284),f152(x70281,x70283)))+P85(f784(f784(f347(x70281),x70282),x70283))+~P85(f784(f784(f347(x70281),x70282),f784(f164(x70281),x70284)))
% 11.41/11.19 [7035]~P35(x70351,x70352)+P85(f784(f784(f347(x70351),f697(x70352,x70351,x70353)),x70353))+~P85(f784(f784(f347(x70351),x70354),x70353))
% 11.41/11.19 [7067]~P26(x70672,x70671,x70673,x70674)+E(f784(f50(x70671),f784(f313(x70672,x70671,x70673),x70674)),f784(f50(x70672),x70674))+~P85(f784(f71(x70672),x70674))
% 11.41/11.19 [7091]~P68(x70911)+E(f784(f784(f784(f75(x70911,x70912,f89(x70911)),x70913),f2(x70911)),x70914),f784(f784(f8(x70912,x70911),x70913),x70914))+~P85(f784(f71(x70912),x70914))
% 11.41/11.19 [7092]~P68(x70921)+E(f784(f784(f784(f75(x70921,x70922,f89(x70921)),x70923),f2(x70921)),x70924),f784(f784(f8(x70922,x70921),x70923),x70924))+~P85(f784(f71(x70922),x70924))
% 11.41/11.19 [7093]~P71(x70931)+E(f784(f784(f784(f75(x70931,x70932,f90(x70931)),x70933),f87(x70931)),x70934),f784(f784(f11(x70932,x70931),x70933),x70934))+~P85(f784(f71(x70932),x70934))
% 11.41/11.19 [7094]~P71(x70941)+E(f784(f784(f784(f75(x70941,x70942,f90(x70941)),x70943),f87(x70941)),x70944),f784(f784(f11(x70942,x70941),x70943),x70944))+~P85(f784(f71(x70942),x70944))
% 11.41/11.19 [7119]P26(x71191,x71192,x71193,x71194)+~E(f784(f50(x71192),f784(f313(x71191,x71192,x71193),x71194)),f784(f50(x71191),x71194))+~P85(f784(f71(x71191),x71194))
% 11.41/11.19 [7120]P26(x71201,x71202,x71203,x71204)+~E(f784(f50(x71202),f784(f313(x71201,x71202,x71203),x71204)),f784(f50(x71201),x71204))+~P85(f784(f71(x71201),x71204))
% 11.41/11.19 [7324]~P68(x73241)+E(f784(f784(f89(x73241),f784(x73242,x73243)),f784(f784(f8(a859,x73241),x73242),f307(a859,x73243,x73244))),f784(f784(f8(a859,x73241),x73242),f305(a859,x73243,x73244)))+~P85(f784(f784(f242(a859),x73243),x73244))
% 11.41/11.19 [7334]~P68(x73341)+~P26(x73342,x73341,x73343,x73344)+E(f784(f784(f8(x73341,x73341),f41(x73341)),f784(f313(x73342,x73341,x73343),x73344)),f784(f784(f8(x73342,x73341),x73343),x73344))
% 11.41/11.19 [7335]~P71(x73351)+~P26(x73352,x73351,x73353,x73354)+E(f784(f784(f11(x73351,x73351),f41(x73351)),f784(f313(x73352,x73351,x73353),x73354)),f784(f784(f11(x73352,x73351),x73353),x73354))
% 11.41/11.19 [7393]E(f784(f50(f870(x73931,x73932)),f327(x73931,x73932,x73933,x73934)),f784(f784(f89(a859),f784(f50(x73931),x73933)),f784(f50(x73932),x73934)))+~P85(f784(f71(x73932),x73934))+~P85(f784(f71(x73931),x73933))
% 11.41/11.19 [7394]E(f784(f50(f870(x73941,x73942)),f327(x73941,x73942,x73943,x73944)),f784(f784(f89(a859),f784(f50(x73941),x73943)),f784(f50(x73942),x73944)))+~P85(f784(f71(x73942),x73944))+~P85(f784(f71(x73941),x73943))
% 11.41/11.19 [7478]E(x74781,x74782)+P85(f784(f784(f347(x74783),x74781),f784(f164(x74783),f154(x74783,x74782,x74784))))+~P85(f784(f784(f347(x74783),x74781),f784(f164(x74783),x74784)))
% 11.41/11.19 [7703]~P68(x77031)+E(f784(f784(f89(x77031),f784(f784(f8(a859,x77031),x77032),f784(f304(a859,x77033),x77034))),f784(x77032,x77034)),f784(f784(f8(a859,x77031),x77032),f784(f304(a859,x77033),f784(a160,x77034))))+P85(f784(f784(f243(a859),x77034),x77033))
% 11.41/11.19 [7760]~P26(x77601,x77602,x77603,f249(f869(x77601,a852)))+~P85(f784(f71(x77602),x77604))+P85(f784(f71(x77601),f784(f315(x77601,x77602,x77603),x77604)))
% 11.41/11.19 [7874]P85(f784(f784(f347(f860(x78741)),f784(f784(f144(x78741),x78742),x78743)),f152(x78741,x78744)))+~P85(f784(f784(f347(f860(x78741)),x78743),f152(x78741,x78744)))+~P85(f784(f784(f347(x78741),x78742),x78744))
% 11.41/11.19 [7922]E(x79221,x79222)+~P85(f784(f784(f347(x79223),x79221),f784(f164(x79223),f154(x79223,x79222,x79224))))+P85(f784(f784(f347(x79223),x79221),f784(f164(x79223),x79224)))
% 11.41/11.19 [7964]~E(f784(f313(x79643,x79641,x79644),f249(f869(x79643,a852))),f249(f869(x79641,a852)))+P85(f784(f71(x79641),x79642))+~P85(f784(f71(x79643),f784(f315(x79643,x79641,x79644),x79642)))
% 11.41/11.19 [8053]~P26(x80531,x80533,x80534,x80532)+P85(f784(f71(x80531),x80532))+~P85(f784(f71(x80533),f784(f313(x80531,x80533,x80534),x80532)))
% 11.41/11.19 [8075]~E(x80752,x80753)+P85(f784(f784(f347(f868(x80751,x80751)),f784(f784(f251(x80751,x80751),x80752),x80753)),f270(x80751,x80754)))+~P85(f784(f784(f347(x80751),x80752),x80754))
% 11.41/11.19 [8076]~E(x80762,x80763)+P85(f784(f784(f347(f868(x80761,x80761)),f784(f784(f251(x80761,x80761),x80762),x80763)),f270(x80761,x80764)))+~P85(f784(f784(f347(x80761),x80762),x80764))
% 11.41/11.19 [8107]~P68(x81071)+E(f784(f784(f89(x81071),f784(f784(f8(a859,x81071),x81072),f305(a859,x81073,x81074))),f784(x81072,f784(a160,x81074))),f784(f784(f8(a859,x81071),x81072),f305(a859,x81073,f784(a160,x81074))))+P85(f784(f784(f243(a859),f784(a160,x81074)),x81073))
% 11.41/11.19 [8166]~E(x81662,x81664)+P85(f784(f784(f347(f868(x81661,x81661)),f784(f784(f251(x81661,x81661),x81662),x81664)),f310(x81661,x81663)))+P85(f784(f784(f347(x81661),x81662),f784(f271(x81661,x81661),x81663)))
% 11.41/11.19 [8168]P85(f784(x81681,x81682))+~P85(f784(x81681,f784(f784(f155(x81683),x81684),f737(x81681,x81684,x81683))))+~P85(f784(f784(f347(x81683),x81682),f784(f164(x81683),x81684)))
% 11.41/11.19 [8303]~P85(f784(f784(f347(x83031),x83032),f335(x83031,x83034)))+P85(f784(f784(f347(f860(x83031)),f784(f784(f144(x83031),x83032),x83033)),f335(f860(x83031),f149(x83031,x83034))))+~P85(f784(f784(f347(f860(x83031)),x83033),f335(f860(x83031),f149(x83031,x83034))))
% 11.41/11.19 [8319]~P26(x83192,x83193,x83194,f700(x83194,x83193,x83192,x83191))+P26(x83192,x83193,x83194,f53(f869(x83192,a852),x83191))+E(x83191,f187(f869(f869(x83192,a852),a852)))
% 11.41/11.19 [8578]E(x85781,x85782)+~P85(f784(f784(f347(f868(x85783,x85783)),f784(f784(f251(x85783,x85783),x85781),x85782)),f310(x85783,x85784)))+P85(f784(f784(f347(x85783),x85781),f784(f271(x85783,x85783),x85784)))
% 11.41/11.19 [8829]P26(x88292,x88293,x88294,f53(f869(x88292,a852),x88291))+E(x88291,f187(f869(f869(x88292,a852),a852)))+P85(f784(f784(f347(f869(x88292,a852)),f700(x88294,x88293,x88292,x88291)),x88291))
% 11.41/11.19 [8955]P85(f784(f71(x89551),x89552))+~P85(f784(f71(x89554),f784(f313(x89551,x89554,x89553),x89552)))+P85(f784(f784(f347(x89551),f607(x89553,x89554,x89552,x89551)),x89552))
% 11.41/11.19 [9049]~P6(x90492)+E(f784(f784(f74(x90491,x90492,f784(f784(f10(x90492,f869(x90492,x90492),x90491),f110(x90492)),x90493)),f187(x90492)),x90494),f784(f784(f54(x90491,x90492),x90494),x90493))+~P85(f784(f71(x90491),x90494))
% 11.41/11.19 [9050]~P6(x90502)+E(f784(f784(f74(x90501,x90502,f784(f784(f10(x90502,f869(x90502,x90502),x90501),f111(x90502)),x90503)),f249(x90502)),x90504),f784(f784(f55(x90501,x90502),x90504),x90503))+~P85(f784(f71(x90501),x90504))
% 11.41/11.19 [9077]~P85(f784(f784(f289(a859),x90773),x90774))+P85(f784(f784(f289(a859),x90771),x90772))+P85(f784(f784(f243(f869(a859,a852)),f292(a859,f289(a859),x90771,x90772)),f292(a859,f289(a859),x90773,x90774)))
% 11.41/11.19 [9088]~P85(f784(f784(f289(a859),x90882),x90884))+~P85(f784(f784(f289(a859),x90883),x90881))+P85(f784(f784(f242(f869(a859,a852)),f292(a859,f289(a859),x90881,x90882)),f292(a859,f289(a859),x90883,x90884)))
% 11.41/11.19 [9144]E(x91441,x91442)+~P85(f784(f784(f347(f868(x91443,x91443)),f784(f784(f251(x91443,x91443),x91441),x91442)),f310(x91443,x91444)))+P85(f784(f784(f347(f868(x91443,x91443)),f784(f784(f251(x91443,x91443),x91441),x91442)),f784(f784(f291(x91443,x91443,x91443),x91444),f310(x91443,x91444))))
% 11.41/11.19 [9145]E(x91451,x91452)+~P85(f784(f784(f347(f868(x91453,x91453)),f784(f784(f251(x91453,x91453),x91451),x91452)),f310(x91453,x91454)))+P85(f784(f784(f347(f868(x91453,x91453)),f784(f784(f251(x91453,x91453),x91451),x91452)),f784(f784(f291(x91453,x91453,x91453),x91454),f310(x91453,x91454))))
% 11.41/11.19 [9176]~E(f784(f188(f860(x91761)),x91762),f784(f188(f860(x91761)),x91763))+~P85(f784(f784(f347(f868(f860(x91761),f860(x91761))),f784(f784(f251(f860(x91761),f860(x91761)),x91762),x91763)),f141(x91761,x91764)))+P85(f784(f784(f347(f868(f860(x91761),f860(x91761))),f784(f784(f251(f860(x91761),f860(x91761)),x91762),x91763)),f139(x91761,x91764)))
% 11.41/11.19 [9195]E(x91951,x91952)+P85(f784(f784(f347(f868(x91953,x91953)),f784(f784(f251(x91953,x91953),x91951),x91952)),f310(x91953,x91954)))+~P85(f784(f784(f347(f868(x91953,x91953)),f784(f784(f251(x91953,x91953),x91951),x91952)),f784(f784(f291(x91953,x91953,x91953),x91954),f310(x91953,x91954))))
% 11.41/11.19 [9287]P85(f784(f784(f289(a859),x92871),x92872))+~P85(f784(f784(f289(a859),x92873),x92871))+~P85(f784(f784(f243(f869(a859,a852)),f292(a859,f289(a859),x92873,x92871)),f292(a859,f289(a859),x92874,x92872)))
% 11.41/11.19 [9288]P85(f784(f784(f289(a859),x92881),x92882))+~P85(f784(f784(f289(a859),x92883),x92881))+~P85(f784(f784(f242(f869(a859,a852)),f292(a859,f289(a859),x92883,x92881)),f292(a859,f289(a859),x92884,x92882)))
% 11.41/11.19 [9289]P85(f784(f784(f289(a859),x92891),x92892))+~P85(f784(f784(f289(a859),x92892),x92893))+~P85(f784(f784(f243(f869(a859,a852)),f292(a859,f289(a859),x92892,x92893)),f292(a859,f289(a859),x92891,x92894)))
% 11.41/11.19 [9290]P85(f784(f784(f289(a859),x92901),x92902))+~P85(f784(f784(f289(a859),x92902),x92903))+~P85(f784(f784(f242(f869(a859,a852)),f292(a859,f289(a859),x92902,x92903)),f292(a859,f289(a859),x92901,x92904)))
% 11.41/11.19 [9596]~P3(x95961)+E(f784(f784(f8(a859,x95961),f784(f784(f20(a859,x95961,x95961),f784(f784(f10(x95961,f869(x95961,x95961),a859),f3(x95961)),x95962)),f784(f784(f10(a859,x95961,a859),x95962),f784(f784(f9(a859,a859,a859),f89(a859)),f87(a859))))),f305(a859,x95963,x95964)),f2(x95961))+P85(f784(f784(f242(a859),x95963),x95964))
% 11.41/11.19 [9830]~P35(x98302,x98304)+~P26(x98302,x98301,x98303,f249(f869(x98302,a852)))+P35(x98301,f784(f313(f868(x98302,x98302),f868(x98301,x98301),f262(x98302,x98301,x98302,x98301,x98303,x98303)),x98304))
% 11.41/11.19 [10004]~E(f784(f188(f860(x100041)),x100043),f784(f188(f860(x100041)),x100042))+P85(f784(f784(f347(f868(f860(x100041),f860(x100041))),f784(f784(f251(f860(x100041),f860(x100041)),x100042),x100043)),f150(x100041,x100044)))+~P85(f784(f784(f261(x100041,x100041,a852),f784(f784(f9(x100041,f869(f868(x100041,x100041),a852),f869(x100041,a852)),f784(f784(f10(f869(x100041,f869(f869(f868(x100041,x100041),a852),a852)),f869(f869(f868(x100041,x100041),a852),f869(x100041,a852)),x100041),f9(x100041,f869(f868(x100041,x100041),a852),a852)),f784(f784(f10(f869(x100041,f868(x100041,x100041)),f869(x100041,f869(f869(f868(x100041,x100041),a852),a852)),x100041),f784(f10(f868(x100041,x100041),f869(f869(f868(x100041,x100041),a852),a852),x100041),f347(f868(x100041,x100041)))),f251(x100041,x100041)))),x100044)),f728(x100044,x100043,x100042,x100041)))
% 11.41/11.19 [5884]~E(x58844,x58842)+P85(f784(x58841,x58842))+P85(f784(f784(f194(f37(x58841,x58843)),x58842),x58844))
% 11.41/11.19 [5976]~P4(x59761)+~E(x59762,f2(x59761))+E(f784(f784(f51(x59761),f784(f784(f90(x59761),x59762),x59763)),f784(f784(f90(x59761),x59762),x59764)),f2(x59761))
% 11.41/11.19 [6015]E(x60151,f120(x60152))+E(x60153,f784(f784(f3(a859),f784(f188(f860(x60152)),x60151)),f87(a859)))+E(f138(x60152,f784(f784(f151(x60152,x60151),x60153),x60154)),f138(x60152,x60151))
% 11.41/11.19 [6047]E(x60471,x60472)+P85(f784(x60473,x60472))+~P85(f784(f784(f784(f312(x60474),x60471),x60473),x60472))
% 11.41/11.19 [6060]~P68(x60601)+~P85(f784(f132(x60602),x60604))+E(f784(f157(x60601),f784(f784(f146(x60602,x60601),x60603),x60604)),f784(f784(f8(x60602,x60601),x60603),f784(f164(x60602),x60604)))
% 11.41/11.19 [6084]~P71(x60842)+~P85(f784(f71(x60841),x60844))+E(f784(f784(f11(x60841,x60842),f784(f18(x60842,x60841),x60843)),x60844),f784(f784(f252(x60842),x60843),f784(f50(x60841),x60844)))
% 11.41/11.19 [6138]~P4(x61382)+E(x61381,f2(x61382))+E(f784(f784(f51(x61382),f784(f784(f90(x61382),x61383),x61381)),f784(f784(f90(x61382),x61384),x61381)),f784(f784(f51(x61382),x61383),x61384))
% 11.41/11.19 [6139]~P4(x61392)+E(x61391,f2(x61392))+E(f784(f784(f51(x61392),f784(f784(f90(x61392),x61391),x61393)),f784(f784(f90(x61392),x61391),x61394)),f784(f784(f51(x61392),x61393),x61394))
% 11.41/11.19 [6140]~P59(x61402)+E(x61401,f2(x61402))+E(f784(f784(f293(x61402),f784(f784(f90(x61402),x61403),x61401)),f784(f784(f90(x61402),x61404),x61401)),f784(f784(f293(x61402),x61403),x61404))
% 11.41/11.19 [6141]~P59(x61412)+E(x61411,f2(x61412))+E(f784(f784(f293(x61412),f784(f784(f90(x61412),x61411),x61413)),f784(f784(f90(x61412),x61411),x61414)),f784(f784(f293(x61412),x61413),x61414))
% 11.41/11.19 [6142]~P4(x61422)+E(x61421,f2(x61422))+E(f784(f784(f51(x61422),f784(f784(f90(x61422),x61421),x61423)),f784(f784(f90(x61422),x61421),x61424)),f784(f784(f51(x61422),x61423),x61424))
% 11.41/11.19 [6207]P85(f784(x62071,x62072))+~E(x62073,f784(f784(f89(a859),x62074),x62072))+~P85(f784(x62071,f784(f784(f3(a859),x62073),x62074)))
% 11.41/11.19 [6208]P85(f784(x62081,x62082))+~E(x62083,f784(f784(f89(a859),x62084),x62082))+~P85(f784(x62081,f784(f784(f3(a859),x62083),x62084)))
% 11.41/11.19 [6289]P31(x62891,x62892,x62893)+P32(x62891,f615(x62893,x62892,x62891),x62894)+~P85(f784(f784(f347(f858(x62891)),x62894),x62892))
% 11.41/11.19 [6335]E(x63351,f120(x63352))+~E(x63353,f784(f784(f3(a859),f784(f188(f860(x63352)),x63351)),f87(a859)))+E(f138(x63352,f784(f784(f151(x63352,x63351),x63353),x63354)),x63354)
% 11.41/11.19 [6357]~P101(x63571)+~P85(f784(f784(f243(x63571),x63572),x63574))+P85(f784(f784(f243(x63571),x63572),f784(f784(f186(x63571),x63573),x63574)))
% 11.41/11.19 [6358]~P101(x63581)+~P85(f784(f784(f243(x63581),x63582),x63584))+P85(f784(f784(f243(x63581),x63582),f784(f784(f186(x63581),x63583),x63584)))
% 11.41/11.19 [6359]~P101(x63591)+~P85(f784(f784(f243(x63591),x63592),x63593))+P85(f784(f784(f243(x63591),x63592),f784(f784(f186(x63591),x63593),x63594)))
% 11.41/11.19 [6360]~P101(x63601)+~P85(f784(f784(f243(x63601),x63602),x63603))+P85(f784(f784(f243(x63601),x63602),f784(f784(f186(x63601),x63603),x63604)))
% 11.41/11.19 [6361]~P98(x63611)+~P85(f784(f784(f243(x63611),x63612),x63614))+P85(f784(f784(f243(x63611),x63612),f784(f784(f110(x63611),x63613),x63614)))
% 11.41/11.19 [6362]~P98(x63621)+~P85(f784(f784(f243(x63621),x63622),x63623))+P85(f784(f784(f243(x63621),x63622),f784(f784(f110(x63621),x63623),x63624)))
% 11.41/11.19 [6363]~P101(x63631)+~P85(f784(f784(f242(x63631),x63632),x63634))+P85(f784(f784(f242(x63631),x63632),f784(f784(f186(x63631),x63633),x63634)))
% 11.41/11.19 [6364]~P101(x63641)+~P85(f784(f784(f242(x63641),x63642),x63644))+P85(f784(f784(f242(x63641),x63642),f784(f784(f186(x63641),x63643),x63644)))
% 11.41/11.19 [6365]~P101(x63651)+~P85(f784(f784(f242(x63651),x63652),x63653))+P85(f784(f784(f242(x63651),x63652),f784(f784(f186(x63651),x63653),x63654)))
% 11.41/11.19 [6366]~P101(x63661)+~P85(f784(f784(f242(x63661),x63662),x63663))+P85(f784(f784(f242(x63661),x63662),f784(f784(f186(x63661),x63663),x63664)))
% 11.41/11.19 [6367]~P98(x63671)+~P85(f784(f784(f242(x63671),x63672),x63674))+P85(f784(f784(f242(x63671),x63672),f784(f784(f110(x63671),x63673),x63674)))
% 11.41/11.19 [6368]~P98(x63681)+~P85(f784(f784(f242(x63681),x63682),x63683))+P85(f784(f784(f242(x63681),x63682),f784(f784(f110(x63681),x63683),x63684)))
% 11.41/11.19 [6369]~P86(x63691)+~P85(f784(f784(f289(x63691),x63692),x63694))+P85(f784(f784(f289(x63691),x63692),f784(f784(f90(x63691),x63693),x63694)))
% 11.41/11.19 [6370]~P86(x63701)+~P85(f784(f784(f289(x63701),x63702),x63703))+P85(f784(f784(f289(x63701),x63702),f784(f784(f90(x63701),x63703),x63704)))
% 11.41/11.19 [6465]~E(f784(f784(f155(x64651),x64652),x64653),x64654)+E(f784(f784(f151(x64651,x64652),x64653),x64654),x64652)+~P85(f784(f784(f243(a859),x64653),f784(f188(f860(x64651)),x64652)))
% 11.41/11.19 [6484]E(x64841,x64842)+P85(f784(x64843,x64841))+~P85(f784(f784(f194(f37(x64843,x64844)),x64841),x64842))
% 11.41/11.19 [6485]E(x64851,x64852)+P85(f784(x64853,x64851))+~P85(f784(f784(f194(f37(x64853,x64854)),x64851),x64852))
% 11.41/11.19 [6504]P85(f784(x65041,x65042))+~P85(f784(x65043,x65042))+~P85(f784(f784(f242(f869(x65044,a852)),x65043),x65041))
% 11.41/11.19 [6505]P85(f784(x65051,x65052))+~P85(f784(x65053,x65052))+~P85(f784(f784(f242(f869(x65054,a852)),x65053),x65051))
% 11.41/11.19 [6541]~E(f784(f784(f151(x65411,x65412),x65413),x65414),x65412)+E(f784(f784(f155(x65411),x65412),x65413),x65414)+~P85(f784(f784(f243(a859),x65413),f784(f188(f860(x65411)),x65412)))
% 11.41/11.19 [6666]E(x66661,f187(f869(x66662,a852)))+E(x66663,f187(f869(x66664,a852)))+~E(f784(f784(f258(x66664,x66662),x66663),f784(f18(f869(x66662,a852),x66664),x66661)),f187(f869(f868(x66664,x66662),a852)))
% 11.41/11.19 [6683]E(x66831,x66832)+P85(f784(f784(f347(x66833),x66831),x66834))+~P85(f784(f784(f347(x66833),x66831),f784(f784(f312(x66833),x66832),x66834)))
% 11.41/11.19 [6684]E(x66841,x66842)+P85(f784(f784(f347(x66843),x66841),x66844))+~P85(f784(f784(f347(x66843),x66841),f784(f784(f312(x66843),x66842),x66844)))
% 11.41/11.19 [6701]~P101(x67011)+P85(f784(f784(f243(x67011),x67012),x67013))+~P85(f784(f784(f243(x67011),x67012),f784(f784(f246(x67011),x67014),x67013)))
% 11.41/11.19 [6702]~P101(x67021)+P85(f784(f784(f243(x67021),x67022),x67023))+~P85(f784(f784(f243(x67021),x67022),f784(f784(f246(x67021),x67023),x67024)))
% 11.41/11.19 [6703]~P101(x67031)+P85(f784(f784(f242(x67031),x67032),x67033))+~P85(f784(f784(f242(x67031),x67032),f784(f784(f246(x67031),x67034),x67033)))
% 11.41/11.19 [6704]~P101(x67041)+P85(f784(f784(f242(x67041),x67042),x67043))+~P85(f784(f784(f242(x67041),x67042),f784(f784(f246(x67041),x67044),x67043)))
% 11.41/11.19 [6705]~P101(x67051)+P85(f784(f784(f242(x67051),x67052),x67053))+~P85(f784(f784(f242(x67051),x67052),f784(f784(f246(x67051),x67053),x67054)))
% 11.41/11.19 [6706]~P101(x67061)+P85(f784(f784(f242(x67061),x67062),x67063))+~P85(f784(f784(f242(x67061),x67062),f784(f784(f246(x67061),x67063),x67064)))
% 11.41/11.19 [6707]~P99(x67071)+P85(f784(f784(f242(x67071),x67072),x67073))+~P85(f784(f784(f242(x67071),x67072),f784(f784(f111(x67071),x67074),x67073)))
% 11.41/11.19 [6708]~P99(x67081)+P85(f784(f784(f242(x67081),x67082),x67083))+~P85(f784(f784(f242(x67081),x67082),f784(f784(f111(x67081),x67084),x67083)))
% 11.41/11.19 [6709]~P99(x67091)+P85(f784(f784(f242(x67091),x67092),x67093))+~P85(f784(f784(f242(x67091),x67092),f784(f784(f111(x67091),x67093),x67094)))
% 11.41/11.19 [6710]~P99(x67101)+P85(f784(f784(f242(x67101),x67102),x67103))+~P85(f784(f784(f242(x67101),x67102),f784(f784(f111(x67101),x67103),x67104)))
% 11.41/11.19 [6732]~E(f784(f784(f155(x67321),x67323),x67324),x67322)+P85(f784(f784(f347(x67321),x67322),f784(f164(x67321),x67323)))+~P85(f784(f784(f243(a859),x67324),f784(f188(f860(x67321)),x67323)))
% 11.41/11.19 [6744]~P101(x67441)+~P15(x67441,f784(f784(f144(x67441),x67442),f784(f784(f144(x67441),x67443),x67444)))+P85(f784(f784(f242(x67441),x67442),x67443))
% 11.41/11.19 [6801]~P101(x68011)+P15(x68011,f784(f784(f144(x68011),x68012),x68013))+~P15(x68011,f784(f784(f144(x68011),x68014),f784(f784(f144(x68011),x68012),x68013)))
% 11.41/11.19 [6912]E(x69121,f2(a1))+E(f784(f784(f51(a1),x69122),x69121),x69123)+~P85(f784(f64(x69122,x69121),f784(f784(f251(a1,a1),x69123),x69124)))
% 11.41/11.19 [6935]E(f60(a1,x69352,x69351),x69353)+E(x69351,f2(a1))+~P85(f784(f64(x69352,x69351),f784(f784(f251(a1,a1),x69354),x69353)))
% 11.41/11.19 [7049]P85(f784(f784(f347(x70491),x70492),x70493))+~P85(f784(f784(f347(x70491),x70492),x70494))+~P85(f784(f784(f243(f869(x70491,a852)),x70494),x70493))
% 11.41/11.19 [7050]P85(f784(f784(f347(x70501),x70502),x70503))+~P85(f784(f784(f347(x70501),x70502),x70504))+~P85(f784(f784(f242(f869(x70501,a852)),x70504),x70503))
% 11.41/11.19 [7051]P85(f784(f784(f347(x70511),x70512),x70513))+~P85(f784(f784(f347(x70511),x70512),x70514))+~P85(f784(f784(f242(f869(x70511,a852)),x70514),x70513))
% 11.41/11.19 [7052]P85(f784(f784(f347(x70521),x70522),x70523))+~P85(f784(f784(f347(x70521),x70522),x70524))+~P85(f784(f784(f242(f869(x70521,a852)),x70524),x70523))
% 11.41/11.19 [7053]P85(f784(f784(f347(x70531),x70532),x70533))+~P85(f784(f784(f347(x70531),x70532),x70534))+~P85(f784(f784(f242(f869(x70531,a852)),x70534),x70533))
% 11.41/11.19 [7063]~P114(x70631)+~E(x70633,f2(x70631))+P85(f784(f784(f289(x70631),f784(f784(f90(x70631),x70632),x70633)),f784(f784(f90(x70631),x70634),x70633)))
% 11.41/11.19 [7064]~P114(x70641)+~E(x70642,f2(x70641))+P85(f784(f784(f289(x70641),f784(f784(f90(x70641),x70642),x70643)),f784(f784(f90(x70641),x70642),x70644)))
% 11.41/11.19 [7288]~P103(x72882)+~P85(f784(f784(f243(f869(x72881,x72882)),x72883),x72884))+P85(f784(f784(f242(f869(x72881,x72882)),x72883),x72884))
% 11.41/11.19 [7383]~P25(x73831,x73832,x73834)+P25(x73831,x73832,f784(f784(f312(f858(x73831)),x73833),x73834))+~P25(x73831,x73832,f784(f784(f312(f858(x73831)),x73833),f187(f869(f858(x73831),a852))))
% 11.41/11.19 [7422]~P85(f784(f784(f347(x74221),x74222),x74224))+P85(f784(f784(f347(x74221),x74222),f52(f869(x74221,a852),x74223)))+~P85(f784(f784(f347(f869(x74221,a852)),x74224),x74223))
% 11.41/11.19 [7424]~P86(x74241)+~P85(f784(f784(f242(a859),x74243),x74244))+P85(f784(f784(f289(x74241),f784(f784(f252(x74241),x74242),x74243)),f784(f784(f252(x74241),x74242),x74244)))
% 11.41/11.19 [7453]~P74(x74531)+~P85(f784(f784(f243(x74531),x74533),x74534))+P85(f784(f784(f243(x74531),f784(f784(f89(x74531),x74532),x74533)),f784(f784(f89(x74531),x74532),x74534)))
% 11.41/11.19 [7454]~P80(x74541)+~P85(f784(f784(f243(x74541),x74543),x74544))+P85(f784(f784(f243(x74541),f784(f784(f89(x74541),x74542),x74543)),f784(f784(f89(x74541),x74542),x74544)))
% 11.41/11.19 [7455]~P74(x74551)+~P85(f784(f784(f243(x74551),x74552),x74554))+P85(f784(f784(f243(x74551),f784(f784(f89(x74551),x74552),x74553)),f784(f784(f89(x74551),x74554),x74553)))
% 11.41/11.19 [7456]~P80(x74561)+~P85(f784(f784(f243(x74561),x74562),x74564))+P85(f784(f784(f243(x74561),f784(f784(f89(x74561),x74562),x74563)),f784(f784(f89(x74561),x74564),x74563)))
% 11.41/11.19 [7457]~P74(x74571)+~P85(f784(f784(f242(x74571),x74573),x74574))+P85(f784(f784(f242(x74571),f784(f784(f89(x74571),x74572),x74573)),f784(f784(f89(x74571),x74572),x74574)))
% 11.41/11.19 [7458]~P78(x74581)+~P85(f784(f784(f242(x74581),x74583),x74584))+P85(f784(f784(f242(x74581),f784(f784(f89(x74581),x74582),x74583)),f784(f784(f89(x74581),x74582),x74584)))
% 11.41/11.19 [7459]~P74(x74591)+~P85(f784(f784(f242(x74591),x74592),x74594))+P85(f784(f784(f242(x74591),f784(f784(f89(x74591),x74592),x74593)),f784(f784(f89(x74591),x74594),x74593)))
% 11.41/11.19 [7460]~P78(x74601)+~P85(f784(f784(f242(x74601),x74602),x74604))+P85(f784(f784(f242(x74601),f784(f784(f89(x74601),x74602),x74603)),f784(f784(f89(x74601),x74604),x74603)))
% 11.41/11.19 [7461]~P114(x74611)+~P85(f784(f784(f289(x74611),x74613),x74614))+P85(f784(f784(f289(x74611),f784(f784(f90(x74611),x74612),x74613)),f784(f784(f90(x74611),x74612),x74614)))
% 11.41/11.19 [7462]~P114(x74621)+~P85(f784(f784(f289(x74621),x74622),x74624))+P85(f784(f784(f289(x74621),f784(f784(f90(x74621),x74622),x74623)),f784(f784(f90(x74621),x74624),x74623)))
% 11.41/11.19 [7463]~P86(x74631)+~P85(f784(f784(f289(x74631),x74632),x74634))+P85(f784(f784(f289(x74631),f784(f784(f252(x74631),x74632),x74633)),f784(f784(f252(x74631),x74634),x74633)))
% 11.41/11.19 [7472]~P138(x74721)+~P90(x74721)+E(f784(f784(f89(x74721),f784(f784(f90(x74721),x74722),f784(f113(x74721),x74723))),f784(f784(f90(x74721),x74724),f784(f113(x74721),x74723))),f784(f784(f90(x74721),f784(f784(f89(x74721),x74722),x74724)),f784(f113(x74721),x74723)))
% 11.41/11.19 [7473]~P123(x74731)+~P90(x74731)+E(f784(f784(f3(x74731),f784(f784(f90(x74731),x74732),f784(f113(x74731),x74733))),f784(f784(f90(x74731),x74734),f784(f113(x74731),x74733))),f784(f784(f90(x74731),f784(f784(f3(x74731),x74732),x74734)),f784(f113(x74731),x74733)))
% 11.41/11.19 [7509]~P68(x75091)+E(f784(f784(f89(x75091),f784(x75092,x75093)),f784(f784(f8(a859,x75091),x75092),f305(a859,f784(a160,x75093),x75094))),f784(f784(f8(a859,x75091),x75092),f305(a859,x75093,x75094)))+~P85(f784(f784(f242(a859),x75093),x75094))
% 11.41/11.19 [7520]~P26(x75202,x75201,x75203,f784(f164(x75202),x75204))+~P85(f784(f132(x75202),x75204))+P85(f784(f132(x75201),f784(f784(f146(x75202,x75201),x75203),x75204)))
% 11.41/11.19 [7569]~P85(f784(f784(f243(a859),x75692),x75694))+~P85(f784(f784(f243(a859),x75691),x75693))+P85(f784(f784(f243(a859),f784(f784(f89(a859),x75691),x75692)),f784(f784(f89(a859),x75693),x75694)))
% 11.41/11.19 [7572]~P85(f784(f784(f243(a1),x75721),x75723))+~P85(f784(f784(f242(a1),x75722),x75724))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x75721),x75722)),f784(f784(f89(a1),x75723),x75724)))
% 11.41/11.19 [7573]~P85(f784(f784(f242(a859),x75732),x75734))+~P85(f784(f784(f242(a859),x75731),x75733))+P85(f784(f784(f242(a859),f784(f784(f89(a859),x75731),x75732)),f784(f784(f89(a859),x75733),x75734)))
% 11.41/11.19 [7574]~P85(f784(f784(f242(a859),x75742),x75744))+~P85(f784(f784(f242(a859),x75741),x75743))+P85(f784(f784(f242(a859),f784(f784(f90(a859),x75741),x75742)),f784(f784(f90(a859),x75743),x75744)))
% 11.41/11.19 [7623]P85(f784(f784(f347(x76231),x76232),x76233))+~P85(f784(f784(f347(x76231),x76232),f53(f869(x76231,a852),x76234)))+~P85(f784(f784(f347(f869(x76231,a852)),x76233),x76234))
% 11.41/11.19 [7624]P85(f784(f784(f347(x76241),x76242),x76243))+~P85(f784(f784(f347(x76241),x76242),f53(f869(x76241,a852),x76244)))+~P85(f784(f784(f347(f869(x76241,a852)),x76243),x76244))
% 11.41/11.19 [7640]~P85(f784(x76401,f736(x76401,x76403,x76402)))+P85(f784(x76401,f784(f784(f155(x76402),x76403),x76404)))+~P85(f784(f784(f243(a859),x76404),f784(f188(f860(x76402)),x76403)))
% 11.41/11.19 [7644]P85(f784(x76441,x76442))+~P85(f784(f784(f347(x76444),x76442),f784(f164(x76444),x76443)))+P85(f784(f784(f243(a859),f737(x76441,x76443,x76444)),f784(f188(f860(x76444)),x76443)))
% 11.41/11.19 [7663]~P85(f784(f784(f194(x76632),x76633),x76634))+~P85(f784(f784(f194(f37(x76631,x76632)),x76634),x76633))+P85(f784(f784(f194(f37(x76631,x76632)),x76633),x76633))
% 11.41/11.19 [7690]~P103(x76901)+~P85(f784(f784(f242(f869(x76902,x76901)),x76904),x76903))+~P85(f784(f784(f243(f869(x76902,x76901)),x76903),x76904))
% 11.41/11.19 [7733]~P85(f784(x77334,x77332))+~P85(f784(f784(f347(x77331),x77332),x77333))+P85(f784(f784(f347(x77331),x77332),f784(f784(f111(f869(x77331,a852)),x77333),f784(f266(x77331),x77334))))
% 11.41/11.19 [7752]P85(f784(f784(f347(x77521),x77522),x77523))+~P85(f784(f784(f242(f869(x77521,a852)),x77523),x77524))+P85(f784(f784(f242(f869(x77521,a852)),x77523),f784(f784(f312(x77521),x77522),x77524)))
% 11.41/11.19 [7753]P85(f784(f784(f347(x77531),x77532),x77533))+~P85(f784(f784(f242(f869(x77531,a852)),x77533),x77534))+P85(f784(f784(f242(f869(x77531,a852)),x77533),f784(f784(f312(x77531),x77532),x77534)))
% 11.41/11.19 [7882]~P85(f784(f784(f347(x78821),x78823),x78824))+~P85(f784(f784(f243(f869(x78821,a852)),x78822),x78824))+P85(f784(f784(f243(f869(x78821,a852)),x78822),f784(f784(f312(x78821),x78823),x78824)))
% 11.41/11.19 [7884]E(f784(f784(f111(f869(x78841,a852)),x78842),x78843),f187(f869(x78841,a852)))+~E(f784(f784(f111(f869(x78841,a852)),f52(f869(x78841,a852),x78844)),x78843),f187(f869(x78841,a852)))+~P85(f784(f784(f347(f869(x78841,a852)),x78842),x78844))
% 11.41/11.19 [7959]P85(f784(f784(f347(x79591),x79592),x79593))+~P85(f784(f784(f242(f869(x79591,a852)),x79593),f784(f784(f312(x79591),x79592),x79594)))+P85(f784(f784(f242(f869(x79591,a852)),x79593),x79594))
% 11.41/11.19 [7960]P85(f784(f784(f347(x79601),x79602),x79603))+~P85(f784(f784(f242(f869(x79601,a852)),x79603),f784(f784(f312(x79601),x79602),x79604)))+P85(f784(f784(f242(f869(x79601,a852)),x79603),x79604))
% 11.41/11.19 [7980]P85(f784(f784(f347(x79802),f736(x79801,x79803,x79802)),f784(f164(x79802),x79803)))+P85(f784(x79801,f784(f784(f155(x79802),x79803),x79804)))+~P85(f784(f784(f243(a859),x79804),f784(f188(f860(x79802)),x79803)))
% 11.41/11.19 [7988]~P85(f784(f784(f243(f869(x79881,a852)),x79882),x79884))+P85(f784(f784(f243(f869(x79881,a852)),x79882),x79883))+~P85(f784(f784(f243(f869(x79881,a852)),x79884),x79883))
% 11.41/11.19 [7989]~P85(f784(f784(f242(f869(x79891,a852)),x79892),x79894))+P85(f784(f784(f243(f869(x79891,a852)),x79892),x79893))+~P85(f784(f784(f243(f869(x79891,a852)),x79894),x79893))
% 11.41/11.19 [7990]~P85(f784(f784(f242(f869(x79901,a852)),x79904),x79903))+~P85(f784(f784(f243(f869(x79901,a852)),x79902),x79904))+P85(f784(f784(f243(f869(x79901,a852)),x79902),x79903))
% 11.41/11.19 [7991]~P85(f784(f784(f242(f869(x79911,a852)),x79912),x79914))+P85(f784(f784(f242(f869(x79911,a852)),x79912),x79913))+~P85(f784(f784(f242(f869(x79911,a852)),x79914),x79913))
% 11.41/11.19 [8026]~P85(f784(f784(f347(x80261),x80264),x80263))+~P85(f784(f784(f243(f869(x80261,a852)),x80262),f784(f784(f312(x80261),x80264),x80263)))+P85(f784(f784(f243(f869(x80261,a852)),x80262),x80263))
% 11.41/11.19 [8038]~P74(x80381)+P85(f784(f784(f243(x80381),x80382),x80383))+~P85(f784(f784(f243(x80381),f784(f784(f89(x80381),x80384),x80382)),f784(f784(f89(x80381),x80384),x80383)))
% 11.41/11.19 [8039]~P74(x80391)+P85(f784(f784(f243(x80391),x80392),x80393))+~P85(f784(f784(f243(x80391),f784(f784(f89(x80391),x80394),x80392)),f784(f784(f89(x80391),x80394),x80393)))
% 11.41/11.19 [8040]~P74(x80401)+P85(f784(f784(f243(x80401),x80402),x80403))+~P85(f784(f784(f243(x80401),f784(f784(f89(x80401),x80402),x80404)),f784(f784(f89(x80401),x80403),x80404)))
% 11.41/11.19 [8041]~P74(x80411)+P85(f784(f784(f243(x80411),x80412),x80413))+~P85(f784(f784(f243(x80411),f784(f784(f89(x80411),x80412),x80414)),f784(f784(f89(x80411),x80413),x80414)))
% 11.41/11.19 [8042]~P74(x80421)+P85(f784(f784(f242(x80421),x80422),x80423))+~P85(f784(f784(f242(x80421),f784(f784(f89(x80421),x80424),x80422)),f784(f784(f89(x80421),x80424),x80423)))
% 11.41/11.19 [8043]~P74(x80431)+P85(f784(f784(f242(x80431),x80432),x80433))+~P85(f784(f784(f242(x80431),f784(f784(f89(x80431),x80434),x80432)),f784(f784(f89(x80431),x80434),x80433)))
% 11.41/11.19 [8044]~P74(x80441)+P85(f784(f784(f242(x80441),x80442),x80443))+~P85(f784(f784(f242(x80441),f784(f784(f89(x80441),x80442),x80444)),f784(f784(f89(x80441),x80443),x80444)))
% 11.41/11.19 [8045]~P74(x80451)+P85(f784(f784(f242(x80451),x80452),x80453))+~P85(f784(f784(f242(x80451),f784(f784(f89(x80451),x80452),x80454)),f784(f784(f89(x80451),x80453),x80454)))
% 11.41/11.19 [8207]P85(f784(x82071,x82072))+~P85(f784(f784(f347(x82073),x82072),f784(f164(x82073),x82074)))+P85(f784(f784(f243(a859),f784(f188(f860(x82073)),f784(f131(x82073,x82071),x82074))),f784(f188(f860(x82073)),x82074)))
% 11.41/11.19 [8338]E(x83381,x83382)+P85(f784(f784(f194(x83383),x83381),f374(x83382,x83381,x83383,x83384)))+~P85(f784(f784(f194(f37(x83384,x83383)),x83381),x83382))
% 11.41/11.19 [8339]E(x83391,x83392)+P85(f784(f784(f194(x83393),x83391),f528(x83392,x83391,x83393,x83394)))+~P85(f784(f784(f194(f37(x83394,x83393)),x83391),x83392))
% 11.41/11.19 [8366]~P85(f784(x83664,x83662))+P85(f784(f784(f194(x83661),x83662),f374(x83663,x83662,x83661,x83664)))+~P85(f784(f784(f194(f37(x83664,x83661)),x83662),x83663))
% 11.41/11.19 [8367]~P85(f784(x83674,x83672))+P85(f784(f784(f194(x83671),x83672),f528(x83673,x83672,x83671,x83674)))+~P85(f784(f784(f194(f37(x83674,x83671)),x83672),x83673))
% 11.41/11.19 [8690]~P26(x86904,x86903,x86901,f249(f869(x86904,a852)))+E(f784(x86901,f534(x86902,x86901,x86903,x86904)),x86902)+~P85(f784(f784(f347(x86903),x86902),f784(f313(x86904,x86903,x86901),f249(f869(x86904,a852)))))
% 11.41/11.19 [8831]~P85(f784(f71(x88311),x88314))+P85(f784(f784(f347(x88311),f553(x88312,x88313,x88314,x88311)),x88314))+P85(f784(f71(f868(x88311,x88313)),f784(f784(f258(x88311,x88313),x88314),x88312)))
% 11.41/11.19 [8874]E(x88741,x88742)+P85(f784(f784(f194(f37(x88743,x88744)),f374(x88741,x88742,x88744,x88743)),x88741))+~P85(f784(f784(f194(f37(x88743,x88744)),x88742),x88741))
% 11.41/11.19 [8875]E(x88751,x88752)+P85(f784(f784(f194(f37(x88753,x88754)),f528(x88751,x88752,x88754,x88753)),x88751))+~P85(f784(f784(f194(f37(x88753,x88754)),x88752),x88751))
% 11.41/11.19 [8895]~P85(f784(x88951,x88954))+P85(f784(f784(f194(f37(x88951,x88952)),f374(x88953,x88954,x88952,x88951)),x88953))+~P85(f784(f784(f194(f37(x88951,x88952)),x88954),x88953))
% 11.41/11.19 [8896]~P85(f784(x88961,x88964))+P85(f784(f784(f194(f37(x88961,x88962)),f528(x88963,x88964,x88962,x88961)),x88963))+~P85(f784(f784(f194(f37(x88961,x88962)),x88964),x88963))
% 11.41/11.19 [9136]~P85(f784(f71(x91361),x91363))+~P85(f784(f71(x91362),f784(x91364,f553(x91364,x91362,x91363,x91361))))+P85(f784(f71(f868(x91361,x91362)),f784(f784(f258(x91361,x91362),x91363),x91364)))
% 11.41/11.19 [9151]~E(f784(f188(f860(x91514)),x91512),f784(f188(f860(x91514)),x91513))+P85(f784(f784(f347(f868(f860(x91514),f860(x91514))),f784(f784(f251(f860(x91514),f860(x91514)),x91513),x91512)),f150(x91514,x91511)))+P85(f784(f784(f243(a859),f745(x91511,x91512,x91513,x91514)),f784(f188(f860(x91514)),x91513)))
% 11.41/11.19 [9261]E(f784(f784(f165(x92611),f746(x92612,x92613,x92614,x92611)),x92613),f784(f784(f165(x92611),f746(x92612,x92613,x92614,x92611)),x92614))+~P85(f784(f784(f347(f868(f860(x92611),f860(x92611))),f784(f784(f251(f860(x92611),f860(x92611)),x92614),x92613)),f141(x92611,x92612)))+P85(f784(f784(f243(a859),f784(f188(f860(x92611)),x92614)),f784(f188(f860(x92611)),x92613)))
% 11.41/11.19 [9320]~P85(f784(f784(f243(a859),f2(a859)),x93203))+~P85(f784(f784(f243(a859),x93204),x93201))+P85(f784(f784(f243(a859),f784(f784(f89(a859),f784(f784(f90(a859),x93201),f60(a859,x93202,x93203))),x93204)),f784(f784(f90(a859),x93201),x93203)))
% 11.41/11.19 [9503]~P103(x95032)+~P85(f784(f784(f242(x95032),f784(x95033,f716(x95034,x95033,x95031,x95032))),f784(x95034,f716(x95034,x95033,x95031,x95032))))+P85(f784(f784(f242(f869(x95031,x95032)),x95033),x95034))
% 11.41/11.19 [9601]~P3(x96011)+E(f784(f784(f8(a859,x96011),f784(f784(f20(a859,x96011,x96011),f784(f784(f10(x96011,f869(x96011,x96011),a859),f3(x96011)),x96012)),f784(f784(f10(a859,x96011,a859),x96012),f784(f784(f9(a859,a859,a859),f89(a859)),f87(a859))))),f305(a859,x96013,x96014)),f784(f784(f3(x96011),f784(x96012,x96013)),f784(x96012,f784(f784(f89(a859),x96014),f87(a859)))))+~P85(f784(f784(f242(a859),x96013),x96014))
% 11.41/11.19 [6647]~P4(x66471)+E(f784(f784(f51(x66471),f784(f784(f90(x66471),x66472),x66473)),x66474),f784(f784(f90(x66471),x66472),f784(f784(f51(x66471),x66473),x66474)))+~P85(f784(f784(f289(x66471),x66474),x66473))
% 11.41/11.19 [6736]E(f784(f784(f130(x67361),x67362),x67363),x67364)+~E(x67363,f784(f784(f133(x67361),f784(f188(f860(x67361)),x67362)),x67364))+~E(f784(f784(f165(x67361),f784(f188(f860(x67361)),x67362)),x67364),x67362)
% 11.41/11.19 [6796]~P60(x67962)+E(x67961,f2(x67962))+E(f784(f784(f293(x67962),f784(f784(f252(x67962),x67963),x67964)),f784(f784(f252(x67962),x67961),x67964)),f784(f784(f252(x67962),f784(f784(f293(x67962),x67963),x67961)),x67964))
% 11.41/11.19 [6944]~P4(x69441)+E(f784(f784(f51(x69441),f784(f784(f90(x69441),x69442),x69443)),x69444),f784(f784(f90(x69441),f784(f784(f51(x69441),x69442),x69444)),x69443))+~P85(f784(f784(f289(x69441),x69444),x69442))
% 11.41/11.19 [6953]~P101(x69531)+~P85(f784(f784(f243(x69531),x69533),x69534))+P85(f784(f784(f243(x69531),f784(f784(f246(x69531),x69532),x69533)),x69534))
% 11.41/11.19 [6954]~P101(x69541)+~P85(f784(f784(f243(x69541),x69543),x69544))+P85(f784(f784(f243(x69541),f784(f784(f246(x69541),x69542),x69543)),x69544))
% 11.41/11.19 [6955]~P101(x69551)+~P85(f784(f784(f243(x69551),x69552),x69554))+P85(f784(f784(f243(x69551),f784(f784(f246(x69551),x69552),x69553)),x69554))
% 11.41/11.19 [6956]~P101(x69561)+~P85(f784(f784(f243(x69561),x69562),x69564))+P85(f784(f784(f243(x69561),f784(f784(f246(x69561),x69562),x69563)),x69564))
% 11.41/11.19 [6957]~P99(x69571)+~P85(f784(f784(f243(x69571),x69573),x69574))+P85(f784(f784(f243(x69571),f784(f784(f111(x69571),x69572),x69573)),x69574))
% 11.41/11.19 [6958]~P99(x69581)+~P85(f784(f784(f243(x69581),x69582),x69584))+P85(f784(f784(f243(x69581),f784(f784(f111(x69581),x69582),x69583)),x69584))
% 11.41/11.19 [6959]~P101(x69591)+~P85(f784(f784(f242(x69591),x69593),x69594))+P85(f784(f784(f242(x69591),f784(f784(f246(x69591),x69592),x69593)),x69594))
% 11.41/11.19 [6960]~P101(x69601)+~P85(f784(f784(f242(x69601),x69603),x69604))+P85(f784(f784(f242(x69601),f784(f784(f246(x69601),x69602),x69603)),x69604))
% 11.41/11.19 [6961]~P101(x69611)+~P85(f784(f784(f242(x69611),x69612),x69614))+P85(f784(f784(f242(x69611),f784(f784(f246(x69611),x69612),x69613)),x69614))
% 11.41/11.19 [6962]~P101(x69621)+~P85(f784(f784(f242(x69621),x69622),x69624))+P85(f784(f784(f242(x69621),f784(f784(f246(x69621),x69622),x69623)),x69624))
% 11.41/11.19 [6963]~P99(x69631)+~P85(f784(f784(f242(x69631),x69633),x69634))+P85(f784(f784(f242(x69631),f784(f784(f111(x69631),x69632),x69633)),x69634))
% 11.41/11.19 [6964]~P99(x69641)+~P85(f784(f784(f242(x69641),x69642),x69644))+P85(f784(f784(f242(x69641),f784(f784(f111(x69641),x69642),x69643)),x69644))
% 11.41/11.19 [6981]~P85(f784(x69813,x69814))+~P85(f784(x69812,x69814))+P85(f784(f784(f784(f111(f869(x69811,a852)),x69812),x69813),x69814))
% 11.41/11.19 [7013]~E(f784(f188(f860(x70131)),x70133),f784(f188(f860(x70132)),x70134))+~P85(f784(f132(x70131),x70133))+E(f175(x70131,x70132,f172(x70131,x70132,f784(f784(f173(x70131,x70132),x70133),x70134))),f784(f164(x70131),x70133))
% 11.41/11.19 [7107]P25(x71071,x71072,x71073)+~P25(x71071,x71072,x71074)+~P85(f784(f784(f242(f869(f858(x71071),a852)),x71073),x71074))
% 11.41/11.19 [7245]~P4(x72451)+E(f784(f784(f51(x72451),f784(f784(f252(x72451),x72452),x72453)),f784(f784(f252(x72451),x72454),x72453)),f784(f784(f252(x72451),f784(f784(f51(x72451),x72452),x72454)),x72453))+~P85(f784(f784(f289(x72451),x72454),x72452))
% 11.41/11.19 [7499]~P68(x74991)+E(f784(f784(f89(x74991),f784(x74992,x74993)),f784(f784(f8(a859,x74991),x74992),f784(f304(a859,f784(a160,x74993)),x74994))),f784(f784(f8(a859,x74991),x74992),f784(f304(a859,x74993),x74994)))+~P85(f784(f784(f243(a859),x74993),x74994))
% 11.41/11.19 [7527]~P101(x75271)+P85(f784(f784(f243(x75271),x75272),x75273))+~P85(f784(f784(f243(x75271),f784(f784(f186(x75271),x75274),x75272)),x75273))
% 11.41/11.19 [7528]~P101(x75281)+P85(f784(f784(f243(x75281),x75282),x75283))+~P85(f784(f784(f243(x75281),f784(f784(f186(x75281),x75282),x75284)),x75283))
% 11.41/11.19 [7529]~P101(x75291)+P85(f784(f784(f242(x75291),x75292),x75293))+~P85(f784(f784(f242(x75291),f784(f784(f186(x75291),x75294),x75292)),x75293))
% 11.41/11.19 [7530]~P101(x75301)+P85(f784(f784(f242(x75301),x75302),x75303))+~P85(f784(f784(f242(x75301),f784(f784(f186(x75301),x75304),x75302)),x75303))
% 11.41/11.19 [7531]~P101(x75311)+P85(f784(f784(f242(x75311),x75312),x75313))+~P85(f784(f784(f242(x75311),f784(f784(f186(x75311),x75312),x75314)),x75313))
% 11.41/11.19 [7532]~P101(x75321)+P85(f784(f784(f242(x75321),x75322),x75323))+~P85(f784(f784(f242(x75321),f784(f784(f186(x75321),x75322),x75324)),x75323))
% 11.41/11.19 [7533]~P98(x75331)+P85(f784(f784(f242(x75331),x75332),x75333))+~P85(f784(f784(f242(x75331),f784(f784(f110(x75331),x75334),x75332)),x75333))
% 11.41/11.19 [7534]~P98(x75341)+P85(f784(f784(f242(x75341),x75342),x75343))+~P85(f784(f784(f242(x75341),f784(f784(f110(x75341),x75344),x75342)),x75343))
% 11.41/11.19 [7535]~P98(x75351)+P85(f784(f784(f242(x75351),x75352),x75353))+~P85(f784(f784(f242(x75351),f784(f784(f110(x75351),x75352),x75354)),x75353))
% 11.41/11.19 [7536]~P98(x75361)+P85(f784(f784(f242(x75361),x75362),x75363))+~P85(f784(f784(f242(x75361),f784(f784(f110(x75361),x75362),x75364)),x75363))
% 11.41/11.19 [7537]~P86(x75371)+P85(f784(f784(f289(x75371),x75372),x75373))+~P85(f784(f784(f289(x75371),f784(f784(f90(x75371),x75374),x75372)),x75373))
% 11.41/11.19 [7538]~P86(x75381)+P85(f784(f784(f289(x75381),x75382),x75383))+~P85(f784(f784(f289(x75381),f784(f784(f90(x75381),x75382),x75384)),x75383))
% 11.41/11.19 [7615]~P85(f784(f784(f347(x76151),x76152),x76154))+P85(f784(f784(f347(x76151),x76152),x76153))+P85(f784(f784(f347(x76151),x76152),f784(f784(f3(f869(x76151,a852)),x76154),x76153)))
% 11.41/11.19 [7616]~P85(f784(f784(f347(x76161),x76162),x76164))+P85(f784(f784(f347(x76161),x76162),x76163))+P85(f784(f784(f347(x76161),x76162),f784(f784(f3(f869(x76161,a852)),x76164),x76163)))
% 11.41/11.19 [7695]P85(f784(x76951,x76952))+P85(f784(x76953,x76952))+~P85(f784(f784(f784(f110(f869(x76954,a852)),x76953),x76951),x76952))
% 11.41/11.19 [7704]~P85(f784(f784(f347(x77041),x77042),x77044))+~P85(f784(f784(f347(x77041),x77042),x77043))+P85(f784(f784(f347(x77041),x77042),f784(f784(f111(f869(x77041,a852)),x77043),x77044)))
% 11.41/11.19 [7705]~P85(f784(f784(f347(x77051),x77052),x77054))+~P85(f784(f784(f347(x77051),x77052),x77053))+P85(f784(f784(f347(x77051),x77052),f784(f784(f111(f869(x77051,a852)),x77053),x77054)))
% 11.41/11.19 [7761]~P101(x77611)+~P85(f784(f71(x77611),x77614))+E(f784(f784(f74(x77611,x77611,f246(x77611)),x77612),f784(f784(f312(x77611),x77613),x77614)),f784(f784(f246(x77611),x77613),f784(f784(f74(x77611,x77611,f246(x77611)),x77612),x77614)))
% 11.41/11.19 [7762]~P101(x77621)+~P85(f784(f71(x77621),x77624))+E(f784(f784(f74(x77621,x77621,f186(x77621)),x77622),f784(f784(f312(x77621),x77623),x77624)),f784(f784(f186(x77621),x77623),f784(f784(f74(x77621,x77621,f186(x77621)),x77622),x77624)))
% 11.41/11.19 [7763]~P98(x77631)+~P85(f784(f71(x77631),x77634))+E(f784(f784(f74(x77631,x77631,f110(x77631)),x77632),f784(f784(f312(x77631),x77633),x77634)),f784(f784(f110(x77631),x77633),f784(f784(f74(x77631,x77631,f110(x77631)),x77632),x77634)))
% 11.41/11.19 [7764]~P99(x77641)+~P85(f784(f71(x77641),x77644))+E(f784(f784(f74(x77641,x77641,f111(x77641)),x77642),f784(f784(f312(x77641),x77643),x77644)),f784(f784(f111(x77641),x77643),f784(f784(f74(x77641,x77641,f111(x77641)),x77642),x77644)))
% 11.41/11.19 [7766]~P138(x77661)+~P90(x77661)+E(f784(f784(f89(x77661),f784(f784(f90(x77661),f784(f113(x77661),x77662)),x77663)),f784(f784(f90(x77661),f784(f113(x77661),x77662)),x77664)),f784(f784(f90(x77661),f784(f113(x77661),x77662)),f784(f784(f89(x77661),x77663),x77664)))
% 11.41/11.19 [7767]~P123(x77671)+~P90(x77671)+E(f784(f784(f3(x77671),f784(f784(f90(x77671),f784(f113(x77671),x77672)),x77673)),f784(f784(f90(x77671),f784(f113(x77671),x77672)),x77674)),f784(f784(f90(x77671),f784(f113(x77671),x77672)),f784(f784(f3(x77671),x77673),x77674)))
% 11.41/11.19 [7880]E(x78801,x78802)+P85(f784(f784(f347(x78803),x78801),f784(f164(x78803),x78804)))+~P85(f784(f784(f347(x78803),x78801),f784(f164(x78803),f784(f784(f144(x78803),x78802),x78804))))
% 11.41/11.19 [8049]P52(x80491,x80492,x80493)+~P52(x80491,x80492,x80494)+~P85(f784(f784(f242(f869(f868(x80491,x80492),a852)),x80493),x80494))
% 11.41/11.19 [8091]P85(f784(f784(f347(x80911),x80912),x80913))+P85(f784(f784(f347(x80911),x80912),x80914))+~P85(f784(f784(f347(x80911),x80912),f784(f784(f110(f869(x80911,a852)),x80914),x80913)))
% 11.41/11.19 [8092]P85(f784(f784(f347(x80921),x80922),x80923))+P85(f784(f784(f347(x80921),x80922),x80924))+~P85(f784(f784(f347(x80921),x80922),f784(f784(f110(f869(x80921,a852)),x80924),x80923)))
% 11.41/11.19 [8101]~P46(x81011,x81014,x81013)+~P85(f784(f784(f347(x81011),x81012),x81014))+P85(f784(f784(f347(f868(x81011,x81011)),f784(f784(f251(x81011,x81011),x81012),x81012)),x81013))
% 11.41/11.19 [8102]~P46(x81021,x81024,x81023)+~P85(f784(f784(f347(x81021),x81022),x81024))+P85(f784(f784(f347(f868(x81021,x81021)),f784(f784(f251(x81021,x81021),x81022),x81022)),x81023))
% 11.41/11.19 [8103]~P46(x81031,x81034,x81033)+~P85(f784(f784(f347(x81031),x81032),x81034))+P85(f784(f784(f347(f868(x81031,x81031)),f784(f784(f251(x81031,x81031),x81032),x81032)),x81033))
% 11.41/11.19 [8115]~P85(f784(f71(x81152),x81154))+~P85(f784(f71(x81151),x81153))+P85(f784(f71(f868(x81151,x81152)),f784(f784(f258(x81151,x81152),x81153),f784(f18(f869(x81152,a852),x81151),x81154))))
% 11.41/11.19 [8116]~P85(f784(f784(f347(x81161),x81162),x81164))+~P85(f784(f784(f242(f869(x81161,a852)),x81163),x81164))+P85(f784(f784(f242(f869(x81161,a852)),f784(f784(f312(x81161),x81162),x81163)),x81164))
% 11.41/11.19 [8124]~P112(x81242)+~P71(x81242)+E(f784(f784(f11(x81241,x81242),f784(f784(f10(a859,x81242,x81241),f109(x81242)),x81243)),x81244),f784(f109(x81242),f784(f784(f11(x81241,a859),x81243),x81244)))
% 11.41/11.19 [8125]~P136(x81252)+~P71(x81252)+E(f784(f784(f11(x81251,x81252),f784(f784(f10(a1,x81252,x81251),f112(x81252)),x81253)),x81254),f784(f112(x81252),f784(f784(f11(x81251,a1),x81253),x81254)))
% 11.41/11.19 [8149]E(f784(f784(f3(f869(x81491,a852)),x81492),f784(f784(f3(f869(x81491,a852)),x81493),x81494)),x81494)+~P85(f784(f784(f242(f869(x81491,a852)),x81492),x81493))+~P85(f784(f784(f242(f869(x81491,a852)),x81494),x81492))
% 11.41/11.19 [8241]~P85(f784(f71(x82411),x82414))+E(f784(f784(f3(a859),f784(f784(f8(x82411,a859),x82412),x82413)),f784(f784(f8(x82411,a859),x82412),x82414)),f784(f784(f8(x82411,a859),x82412),f784(f784(f3(f869(x82411,a852)),x82413),x82414)))+~P85(f784(f784(f242(f869(x82411,a852)),x82414),x82413))
% 11.41/11.19 [8399]~P9(x83991,x83994,x83993)+~P85(f784(f784(f347(x83991),x83992),x83994))+P85(f784(f784(f347(x83991),x83992),f784(f287(x83991,x83991,x83993),f784(f784(f312(x83991),x83992),f187(f869(x83991,a852))))))
% 11.41/11.19 [8461]~P85(f784(f784(f242(f869(x84611,a852)),x84612),x84613))+~P85(f784(f784(f242(f869(x84611,a852)),x84612),x84614))+P85(f784(f784(f242(f869(x84611,a852)),x84612),f784(f784(f111(f869(x84611,a852)),x84613),x84614)))
% 11.41/11.19 [8552]E(x85521,f187(f869(x85522,a852)))+P85(f784(f71(x85523),x85524))+~P85(f784(f71(f868(x85523,x85522)),f784(f784(f258(x85523,x85522),x85524),f784(f18(f869(x85522,a852),x85523),x85521))))
% 11.41/11.19 [8553]E(x85531,f187(f869(x85532,a852)))+P85(f784(f71(x85533),x85534))+~P85(f784(f71(f868(x85532,x85533)),f784(f784(f258(x85532,x85533),x85531),f784(f18(f869(x85533,a852),x85532),x85534))))
% 11.41/11.19 [8611]P85(f784(f784(f347(x86111),x86112),f335(x86111,x86113)))+~P85(f784(f784(f347(x86111),x86114),f335(x86111,x86113)))+~P85(f784(f784(f347(f868(x86111,x86111)),f784(f784(f251(x86111,x86111),x86112),x86114)),x86113))
% 11.41/11.19 [8612]P85(f784(f784(f347(x86121),x86122),f335(x86121,x86123)))+~P85(f784(f784(f347(x86121),x86124),f335(x86121,x86123)))+~P85(f784(f784(f347(f868(x86121,x86121)),f784(f784(f251(x86121,x86121),x86122),x86124)),x86123))
% 11.41/11.19 [8664]~P35(x86641,x86644)+P85(f784(f784(f347(f868(x86641,x86641)),f784(f784(f251(x86641,x86641),x86643),x86642)),f310(x86641,x86644)))+P35(x86641,f784(f784(f312(f868(x86641,x86641)),f784(f784(f251(x86641,x86641),x86642),x86643)),x86644))
% 11.41/11.19 [8665]~P55(x86651,x86654)+P85(f784(f784(f347(f868(x86651,x86651)),f784(f784(f251(x86651,x86651),x86653),x86652)),f310(x86651,x86654)))+P55(x86651,f784(f784(f312(f868(x86651,x86651)),f784(f784(f251(x86651,x86651),x86652),x86653)),x86654))
% 11.41/11.19 [8736]~E(x87362,x87363)+~P85(f784(f784(f347(x87361),x87362),f784(f164(x87361),x87364)))+P85(f784(f784(f347(f868(x87361,x87361)),f784(f784(f251(x87361,x87361),x87362),x87363)),f784(f164(f868(x87361,x87361)),f784(f784(f173(x87361,x87361),x87364),x87364))))
% 11.41/11.19 [8808]~E(x88083,x88084)+P85(f784(f784(f261(x88081,x88081,a852),a343),x88082))+~P85(f784(f784(f347(f868(x88081,x88081)),x88082),f784(f164(f868(x88081,x88081)),f784(f784(f173(x88081,x88081),x88083),x88084))))
% 11.41/11.19 [8846]P85(f784(f784(f347(f868(f860(x88461),f860(x88461))),f784(f784(f251(f860(x88461),f860(x88461)),x88462),x88463)),f141(x88461,x88464)))+~E(f784(f784(f165(x88461),f784(f188(f860(x88461)),x88462)),x88463),x88462)+~P85(f784(f784(f243(a859),f784(f188(f860(x88461)),x88462)),f784(f188(f860(x88461)),x88463)))
% 11.41/11.19 [8940]~P85(f784(f71(x89401),x89404))+P85(f784(f784(f347(x89401),f423(x89402,x89403,x89404,x89401)),x89404))+P85(f784(f71(x89403),f784(f784(f54(x89401,f869(x89403,a852)),x89404),x89402)))
% 11.41/11.19 [8941]~P85(f784(f71(x89411),x89414))+P85(f784(f784(f347(x89411),f620(x89412,x89413,x89414,x89411)),x89414))+P85(f784(f71(x89413),f784(f784(f54(x89411,f869(x89413,a852)),x89414),x89412)))
% 11.41/11.19 [9021]P85(f784(f784(f347(f868(x90211,x90211)),x90212),f784(f784(f291(x90211,x90211,x90211),x90213),f310(x90211,x90213))))+~P85(f784(f784(f243(a859),f2(a859)),x90214))+~P85(f784(f784(f347(f868(x90211,x90211)),x90212),f784(f784(f180(f868(x90211,x90211),a852),x90214),x90213)))
% 11.41/11.19 [9028]~P35(x90281,x90282)+~P85(f784(f784(f347(f868(x90281,x90281)),f784(f784(f251(x90281,x90281),x90284),x90283)),x90282))+~P85(f784(f784(f347(f868(x90281,x90281)),f784(f784(f251(x90281,x90281),x90283),x90284)),x90282))
% 11.41/11.19 [9029]~P35(x90291,x90292)+~P85(f784(f784(f347(f868(x90291,x90291)),f784(f784(f251(x90291,x90291),x90294),x90293)),x90292))+~P85(f784(f784(f347(f868(x90291,x90291)),f784(f784(f251(x90291,x90291),x90293),x90294)),x90292))
% 11.41/11.19 [9147]~P85(f784(f71(x91471),x91474))+E(f784(f784(f8(x91471,a859),f784(f784(f10(f869(x91472,a852),a859,x91471),f50(x91472)),x91473)),x91474),f784(f50(f868(x91471,x91472)),f784(f784(f258(x91471,x91472),x91474),x91473)))+P85(f784(f784(f347(x91471),f555(x91473,x91472,x91474,x91471)),x91474))
% 11.41/11.19 [9149]~P85(f784(f132(x91491),x91492))+P85(f784(f132(x91491),f784(f784(f151(x91491,x91492),x91493),x91494)))+P85(f784(f784(f347(x91491),x91494),f784(f784(f3(f869(x91491,a852)),f784(f164(x91491),x91492)),f784(f784(f312(x91491),f784(f784(f155(x91491),x91492),x91493)),f187(f869(x91491,a852))))))
% 11.41/11.19 [9158]~P85(f784(f71(x91582),x91583))+~P85(f784(f71(x91581),f784(x91584,f423(x91584,x91581,x91583,x91582))))+P85(f784(f71(x91581),f784(f784(f54(x91582,f869(x91581,a852)),x91583),x91584)))
% 11.41/11.19 [9159]~P85(f784(f71(x91592),x91593))+~P85(f784(f71(x91591),f784(x91594,f620(x91594,x91591,x91593,x91592))))+P85(f784(f71(x91591),f784(f784(f54(x91592,f869(x91591,a852)),x91593),x91594)))
% 11.41/11.19 [9222]~P85(f784(f784(f347(f868(x92221,x92221)),x92222),f784(f784(f291(x92221,x92221,x92221),x92224),f310(x92221,x92224))))+P85(f784(f784(f347(f868(x92221,x92221)),x92222),f784(f784(f291(x92221,x92221,x92221),x92223),f310(x92221,x92223))))+~P85(f784(f784(f242(f869(f868(x92221,x92221),a852)),x92224),x92223))
% 11.41/11.19 [9230]E(f784(f784(f165(x92301),f746(x92304,x92303,x92302,x92301)),x92303),f784(f784(f165(x92301),f746(x92304,x92303,x92302,x92301)),x92302))+~P85(f784(f784(f347(f868(f860(x92301),f860(x92301))),f784(f784(f251(f860(x92301),f860(x92301)),x92302),x92303)),f141(x92301,x92304)))+E(f784(f784(f165(x92301),f784(f188(f860(x92301)),x92302)),x92303),x92302)
% 11.41/11.19 [9246]~P85(f784(f71(x92461),x92464))+E(f784(f784(f8(x92461,a859),f784(f784(f10(f869(x92462,a852),a859,x92461),f50(x92462)),x92463)),x92464),f784(f50(f868(x92461,x92462)),f784(f784(f258(x92461,x92462),x92464),x92463)))+~P85(f784(f71(x92462),f784(x92463,f555(x92463,x92462,x92464,x92461))))
% 11.41/11.19 [9250]~E(f784(f188(f860(x92501)),x92503),f784(f188(f860(x92501)),x92502))+P85(f784(f784(f347(f868(f860(x92501),f860(x92501))),f784(f784(f251(f860(x92501),f860(x92501)),x92502),x92503)),f150(x92501,x92504)))+P85(f784(f784(f347(f868(x92501,x92501)),f728(x92504,x92503,x92502,x92501)),f784(f164(f868(x92501,x92501)),f784(f784(f173(x92501,x92501),x92502),x92503))))
% 11.41/11.19 [9332]~P85(f784(f784(f347(f868(f860(x93321),f860(x93321))),f784(f784(f251(f860(x93321),f860(x93321)),x93322),x93323)),f141(x93321,x93324)))+E(f784(f784(f165(x93321),f784(f188(f860(x93321)),x93322)),x93323),x93322)+P85(f784(f784(f243(a859),f746(x93324,x93323,x93322,x93321)),f784(f784(f246(a859),f784(f188(f860(x93321)),x93322)),f784(f188(f860(x93321)),x93323))))
% 11.41/11.19 [9352]~P85(f784(f784(f347(f868(f860(x93521),f860(x93521))),f784(f784(f251(f860(x93521),f860(x93521)),x93522),x93523)),f141(x93521,x93524)))+P85(f784(f784(f243(a859),f784(f188(f860(x93521)),x93522)),f784(f188(f860(x93521)),x93523)))+P85(f784(f784(f243(a859),f746(x93524,x93523,x93522,x93521)),f784(f784(f246(a859),f784(f188(f860(x93521)),x93522)),f784(f188(f860(x93521)),x93523))))
% 11.41/11.19 [9638]~P85(f784(f784(f784(x96381,f720(x96381,x96384,x96383,x96382)),f722(x96381,x96384,x96383,x96382)),f723(x96381,x96384,x96383,x96382)))+P85(f784(f784(f784(x96381,x96382),x96383),x96384))+~P85(f784(f334(f868(f869(a1,f864(f860(a851))),f868(a1,a1)),a321),f784(f784(f251(f869(a1,f864(f860(a851))),f868(a1,a1)),x96382),f784(f784(f251(a1,a1),x96383),x96384))))
% 11.41/11.19 [9697]P85(f784(f784(f784(x96971,x96972),x96973),x96974))+P85(f784(f334(f868(f869(a1,f864(f860(a851))),f868(a1,a1)),a321),f784(f784(f251(f869(a1,f864(f860(a851))),f868(a1,a1)),f720(x96971,x96974,x96973,x96972)),f784(f784(f251(a1,a1),f722(x96971,x96974,x96973,x96972)),f723(x96971,x96974,x96973,x96972)))))+~P85(f784(f334(f868(f869(a1,f864(f860(a851))),f868(a1,a1)),a321),f784(f784(f251(f869(a1,f864(f860(a851))),f868(a1,a1)),x96972),f784(f784(f251(a1,a1),x96973),x96974))))
% 11.41/11.19 [9735]~P85(f784(f784(f347(f868(f860(x97351),f860(x97351))),f784(f784(f251(f860(x97351),f860(x97351)),x97352),x97353)),f141(x97351,x97354)))+E(f784(f784(f165(x97351),f784(f188(f860(x97351)),x97352)),x97353),x97352)+P85(f784(f784(f347(f868(x97351,x97351)),f784(f784(f251(x97351,x97351),f784(f784(f155(x97351),x97352),f746(x97354,x97353,x97352,x97351))),f784(f784(f155(x97351),x97353),f746(x97354,x97353,x97352,x97351)))),x97354))
% 11.41/11.19 [9738]~P85(f784(f784(f347(f868(f860(x97381),f860(x97381))),f784(f784(f251(f860(x97381),f860(x97381)),x97382),x97383)),f141(x97381,x97384)))+P85(f784(f784(f243(a859),f784(f188(f860(x97381)),x97382)),f784(f188(f860(x97381)),x97383)))+P85(f784(f784(f347(f868(x97381,x97381)),f784(f784(f251(x97381,x97381),f784(f784(f155(x97381),x97382),f746(x97384,x97383,x97382,x97381))),f784(f784(f155(x97381),x97383),f746(x97384,x97383,x97382,x97381)))),x97384))
% 11.41/11.19 [9808]~E(f784(f188(f860(x98081)),x98082),f784(f188(f860(x98081)),x98083))+P85(f784(f784(f347(f868(f860(x98081),f860(x98081))),f784(f784(f251(f860(x98081),f860(x98081)),x98082),x98083)),f150(x98081,x98084)))+~P85(f784(f784(f347(f868(x98081,x98081)),f784(f784(f251(x98081,x98081),f784(f784(f155(x98081),x98082),f745(x98084,x98083,x98082,x98081))),f784(f784(f155(x98081),x98083),f745(x98084,x98083,x98082,x98081)))),x98084))
% 11.41/11.19 [9948]~P68(x99481)+~P85(f784(f71(x99482),x99484))+E(f784(f157(x99481),f784(f784(f146(x99482,x99481),x99483),f99(f860(x99482),f784(f784(f20(f860(x99482),a852,a852),f784(f784(f10(a852,f869(a852,a852),f860(x99482)),a344),f784(f784(f9(f860(x99482),f869(x99482,a852),a852),f784(f784(f10(f869(x99482,a852),f869(f869(x99482,a852),a852),f860(x99482)),a343),f164(x99482))),x99484))),f132(x99482))))),f235(x99482,x99481,x99483,x99484))
% 11.41/11.19 [7336]~P59(x73362)+E(x73361,f2(x73362))+E(f784(f784(f293(x73362),f784(f784(f89(x73362),x73363),f784(f784(f90(x73362),x73364),x73361))),x73361),f784(f784(f89(x73362),x73364),f784(f784(f293(x73362),x73363),x73361)))
% 11.41/11.19 [7337]~P4(x73372)+E(x73371,f2(x73372))+E(f784(f784(f51(x73372),f784(f784(f89(x73372),x73373),f784(f784(f90(x73372),x73374),x73371))),x73371),f784(f784(f89(x73372),x73374),f784(f784(f51(x73372),x73373),x73371)))
% 11.41/11.19 [7338]~P4(x73382)+E(x73381,f2(x73382))+E(f784(f784(f51(x73382),f784(f784(f89(x73382),x73383),f784(f784(f90(x73382),x73381),x73384))),x73381),f784(f784(f89(x73382),x73384),f784(f784(f51(x73382),x73383),x73381)))
% 11.41/11.19 [7578]~P59(x75782)+E(x75781,f2(x75782))+E(f784(f784(f293(x75782),f784(f784(f89(x75782),x75783),f784(f784(f90(x75782),x75784),x75781))),x75781),f784(f784(f89(x75782),f784(f784(f293(x75782),x75783),x75781)),x75784))
% 11.41/11.19 [7579]~P60(x75792)+E(x75791,f2(x75792))+E(f784(f784(f293(x75792),f784(f784(f89(x75792),x75793),f784(f784(f90(x75792),x75791),x75794))),x75791),f784(f784(f89(x75792),f784(f784(f293(x75792),x75793),x75791)),x75794))
% 11.41/11.19 [7580]~P60(x75802)+E(x75801,f2(x75802))+E(f784(f784(f293(x75802),f784(f784(f3(x75802),x75803),f784(f784(f90(x75802),x75801),x75804))),x75801),f784(f784(f3(x75802),f784(f784(f293(x75802),x75803),x75801)),x75804))
% 11.41/11.19 [8626]~E(f784(f784(f291(x86261,x86261,x86261),x86262),x86264),f187(f869(f868(x86261,x86261),a852)))+~E(f784(f784(f291(x86261,x86261,x86261),x86262),x86263),f187(f869(f868(x86261,x86261),a852)))+E(f784(f784(f291(x86261,x86261,x86261),x86262),f784(f784(f110(f869(f868(x86261,x86261),a852)),x86263),x86264)),f187(f869(f868(x86261,x86261),a852)))
% 11.41/11.19 [8737]~P85(f784(f784(f242(f869(x87371,a852)),x87373),x87374))+~P85(f784(f784(f242(f869(x87371,a852)),x87372),x87374))+P85(f784(f784(f242(f869(x87371,a852)),f784(f784(f110(f869(x87371,a852)),x87372),x87373)),x87374))
% 11.41/11.19 [9081]~P85(f784(f71(x90811),x90814))+~P85(f784(f71(x90811),x90813))+E(f784(f784(f3(a859),f784(f784(f89(a859),f784(f784(f8(x90811,a859),x90812),x90813)),f784(f784(f8(x90811,a859),x90812),x90814))),f784(f784(f8(x90811,a859),x90812),f784(f784(f111(f869(x90811,a852)),x90813),x90814))),f784(f784(f8(x90811,a859),x90812),f784(f784(f110(f869(x90811,a852)),x90813),x90814)))
% 11.41/11.19 [9156]~P85(f784(f784(f347(x91561),x91563),x91562))+~P85(f784(f784(f242(f869(x91561,a852)),x91562),f784(f784(f312(x91561),x91563),x91564)))+P85(f784(f784(f242(f869(x91561,a852)),f784(f784(f3(f869(x91561,a852)),x91562),f784(f784(f312(x91561),x91563),f187(f869(x91561,a852))))),x91564))
% 11.41/11.19 [9305]~P85(f784(f784(f347(x93051),x93053),x93052))+P85(f784(f784(f242(f869(x93051,a852)),x93052),f784(f784(f312(x93051),x93053),x93054)))+~P85(f784(f784(f242(f869(x93051,a852)),f784(f784(f3(f869(x93051,a852)),x93052),f784(f784(f312(x93051),x93053),f187(f869(x93051,a852))))),x93054))
% 11.41/11.19 [9306]~P85(f784(f784(f347(x93061),x93063),x93062))+P85(f784(f784(f242(f869(x93061,a852)),x93062),f784(f784(f312(x93061),x93063),x93064)))+~P85(f784(f784(f242(f869(x93061,a852)),f784(f784(f3(f869(x93061,a852)),x93062),f784(f784(f312(x93061),x93063),f187(f869(x93061,a852))))),x93064))
% 11.41/11.19 [9331]~P85(f784(f784(f242(f869(x93311,a852)),x93312),x93314))+P85(f784(f784(f242(f869(x93311,a852)),x93312),f784(f784(f312(x93311),x93313),x93314)))+~P85(f784(f784(f242(f869(x93311,a852)),f784(f784(f3(f869(x93311,a852)),x93312),f784(f784(f312(x93311),x93313),f187(f869(x93311,a852))))),x93314))
% 11.41/11.19 [9389]~P85(f784(f784(f243(a859),x93892),x93894))+~P85(f784(f784(f242(a859),x93891),x93893))+P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),f784(f784(f251(a859,a859),x93891),x93892)),f784(f784(f251(a859,a859),x93893),x93894))),a47))
% 11.41/11.19 [9390]~P85(f784(f784(f242(a859),x93902),x93904))+~P85(f784(f784(f242(a859),x93901),x93903))+P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),f784(f784(f251(a859,a859),x93901),x93902)),f784(f784(f251(a859,a859),x93903),x93904))),a79))
% 11.41/11.19 [9773]~P26(x97731,f869(f869(x97731,a852),a852),f784(f784(f9(x97731,f869(f868(x97731,x97731),a852),f869(f869(x97731,a852),a852)),f784(f784(f10(f869(x97731,a852),f869(f869(f868(x97731,x97731),a852),f869(f869(x97731,a852),a852)),x97731),f69(x97731)),f784(f784(f9(x97731,f869(x97731,a852),f869(x97731,a852)),f312(x97731)),f187(f869(x97731,a852))))),x97733),x97732)+~P85(f784(f784(f347(x97731),x97734),x97732))+E(f784(f784(f3(f869(f869(x97731,a852),a852)),f784(f784(f69(x97731),x97732),x97733)),f784(f784(f69(x97731),f784(f784(f312(x97731),x97734),f187(f869(x97731,a852)))),x97733)),f784(f784(f69(x97731),f784(f784(f3(f869(x97731,a852)),x97732),f784(f784(f312(x97731),x97734),f187(f869(x97731,a852))))),x97733))
% 11.41/11.19 [9914]~P46(x99141,x99142,x99144)+~P85(f784(f784(f347(f868(x99141,x99141)),x99143),x99144))+P85(f784(f784(f261(x99141,x99141,a852),f784(f784(f9(x99141,f869(x99141,a852),f869(x99141,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x99141,a852),f869(x99141,a852)),x99141),f10(a852,a852,x99141)),f784(f784(f10(a852,f869(a852,a852),x99141),a344),f784(f784(f9(x99141,f869(x99141,a852),a852),f347(x99141)),x99142)))),f784(f784(f9(x99141,f869(x99141,a852),a852),f347(x99141)),x99142))),x99143))
% 11.41/11.19 [9922]P85(f784(f71(x99221),x99222))+~P85(f784(f71(x99223),f784(f313(x99221,x99223,x99224),x99222)))+~P85(f784(f71(x99221),f784(f266(x99221),f784(f784(f20(x99221,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99221),a344),f784(f784(f9(x99221,f869(x99221,a852),a852),f347(x99221)),x99222))),f784(f784(f9(x99221,x99223,a852),f784(f784(f10(x99223,f869(x99223,a852),x99221),a343),x99224)),f784(x99224,f607(x99224,x99223,x99222,x99221)))))))
% 11.41/11.19 [8032]~P60(x80322)+E(x80321,f2(x80322))+E(f784(f784(f293(x80322),f784(f784(f89(x80322),f784(f784(f90(x80322),x80321),x80323)),x80324)),x80321),f784(f784(f89(x80322),x80323),f784(f784(f293(x80322),x80324),x80321)))
% 11.41/11.19 [8033]~P60(x80332)+E(x80331,f2(x80332))+E(f784(f784(f293(x80332),f784(f784(f3(x80332),f784(f784(f90(x80332),x80331),x80333)),x80334)),x80331),f784(f784(f3(x80332),x80333),f784(f784(f293(x80332),x80334),x80331)))
% 11.41/11.19 [8873]~E(f784(f784(f291(x88731,x88731,x88731),x88733),x88734),f187(f869(f868(x88731,x88731),a852)))+~E(f784(f784(f291(x88731,x88731,x88731),x88732),x88734),f187(f869(f868(x88731,x88731),a852)))+E(f784(f784(f291(x88731,x88731,x88731),f784(f784(f110(f869(f868(x88731,x88731),a852)),x88732),x88733)),x88734),f187(f869(f868(x88731,x88731),a852)))
% 11.41/11.19 [9860]~P141(x98601)+~P141(x98602)+E(f784(f784(f320(x98601),f784(f784(f9(x98601,a108,f864(f860(a851))),f784(f784(f10(f869(x98602,f864(f860(a851))),f869(a108,f864(f860(a851))),x98601),f320(x98602)),f784(f784(f10(f869(x98602,f868(x98601,x98602)),f869(x98602,f864(f860(a851))),x98601),f784(f10(f868(x98601,x98602),f864(f860(a851)),x98602),x98603)),f251(x98601,x98602)))),x98604)),x98604),f784(f784(f320(f868(x98601,x98602)),x98603),x98604))
% 11.41/11.19 [9852]P85(f784(x98521,f589(x98522,x98523,x98521,x98524)))+~P85(f784(f71(x98524),f784(f266(x98524),x98521)))+P85(f784(f71(x98523),f784(f266(x98523),f784(f784(f10(f869(x98524,a852),a852,x98523),f96(x98524)),f784(f784(f10(f869(x98524,a852),f869(x98524,a852),x98523),f784(f20(x98524,a852,a852),f784(f784(f10(a852,f869(a852,a852),x98524),a344),x98521))),x98522)))))
% 11.41/11.19 [9873]~P85(f784(f71(x98732),f784(f266(x98732),x98733)))+~P85(f784(f71(x98731),f784(f266(x98731),f784(f784(f9(x98731,x98732,a852),x98734),f589(x98734,x98731,x98733,x98732)))))+P85(f784(f71(x98731),f784(f266(x98731),f784(f784(f10(f869(x98732,a852),a852,x98731),f96(x98732)),f784(f784(f10(f869(x98732,a852),f869(x98732,a852),x98731),f784(f20(x98732,a852,a852),f784(f784(f10(a852,f869(a852,a852),x98732),a344),x98733))),x98734)))))
% 11.41/11.19 [5731]~E(x57315,x57312)+P38(f37(x57311,x57313),x57312,x57314,x57315)+P85(f784(x57311,x57312))
% 11.41/11.19 [6293]E(x62931,x62932)+~P38(f37(x62933,x62934),x62931,x62935,x62932)+P85(f784(x62933,x62931))
% 11.41/11.19 [6294]E(x62941,x62942)+~P38(f37(x62943,x62944),x62941,x62945,x62942)+P85(f784(x62943,x62941))
% 11.41/11.19 [7840]~P38(x78402,x78403,x78404,x78405)+~P38(f37(x78401,x78402),x78405,x78404,x78403)+P38(f37(x78401,x78402),x78403,x78404,x78403)
% 11.41/11.19 [8994]E(x89941,x89942)+~P38(f37(x89945,x89943),x89941,x89944,x89942)+P38(x89943,x89941,x89944,f365(x89942,x89944,x89941,x89943,x89945))
% 11.41/11.19 [8995]E(x89951,x89952)+~P38(f37(x89955,x89953),x89951,x89954,x89952)+P38(x89953,x89951,x89954,f540(x89952,x89954,x89951,x89953,x89955))
% 11.41/11.19 [8997]E(x89971,x89972)+P38(f37(x89973,x89974),f365(x89971,x89975,x89972,x89974,x89973),x89975,x89971)+~P38(f37(x89973,x89974),x89972,x89975,x89971)
% 11.41/11.19 [8998]E(x89981,x89982)+P38(f37(x89983,x89984),f540(x89981,x89985,x89982,x89984,x89983),x89985,x89981)+~P38(f37(x89983,x89984),x89982,x89985,x89981)
% 11.41/11.19 [9000]~P38(f37(x90005,x90001),x90002,x90003,x90004)+P38(x90001,x90002,x90003,f365(x90004,x90003,x90002,x90001,x90005))+~P85(f784(x90005,x90002))
% 11.41/11.19 [9001]~P38(f37(x90015,x90011),x90012,x90013,x90014)+P38(x90011,x90012,x90013,f540(x90014,x90013,x90012,x90011,x90015))+~P85(f784(x90015,x90012))
% 11.41/11.19 [9005]~P38(f37(x90051,x90052),x90055,x90054,x90053)+P38(f37(x90051,x90052),f365(x90053,x90054,x90055,x90052,x90051),x90054,x90053)+~P85(f784(x90051,x90055))
% 11.41/11.19 [9006]~P38(f37(x90061,x90062),x90065,x90064,x90063)+P38(f37(x90061,x90062),f540(x90063,x90064,x90065,x90062,x90061),x90064,x90063)+~P85(f784(x90061,x90065))
% 11.41/11.19 [6443]E(x64431,x64432)+~E(f784(x64433,x64431),f784(x64433,x64432))+~P26(x64434,x64435,x64433,f249(f869(x64434,a852)))
% 11.41/11.19 [6444]E(x64441,x64442)+~E(f784(x64443,x64441),f784(x64443,x64442))+~P26(x64444,x64445,x64443,f249(f869(x64444,a852)))
% 11.41/11.19 [6607]~E(f784(x66073,x66075),f190(x66072))+~E(f784(x66074,x66075),f190(x66072))+E(f784(f176(x66071,x66072,x66073,x66074),x66075),f190(x66072))
% 11.41/11.19 [7377]E(x73771,x73772)+~P26(x73773,x73774,x73775,f249(f869(x73773,a852)))+~E(f784(f313(x73773,x73774,x73775),x73771),f784(f313(x73773,x73774,x73775),x73772))
% 11.41/11.19 [7634]P26(x76342,x76343,f529(x76344,x76343,x76342,x76341),x76341)+~E(f784(f313(x76343,x76342,x76345),x76344),x76341)+E(x76341,f187(f869(x76342,a852)))
% 11.41/11.19 [8160]~P85(f784(f784(x81603,x81602),x81605))+~P85(f784(f784(x81603,x81604),x81602))+P85(f784(f784(f347(x81601),x81602),f292(x81601,x81603,x81604,x81605)))
% 11.41/11.19 [8161]~P85(f784(f784(x81613,x81612),x81615))+~P85(f784(f784(x81613,x81614),x81612))+P85(f784(f784(f347(x81611),x81612),f301(x81611,x81613,x81614,x81615)))
% 11.41/11.19 [8699]~P26(x86991,x86993,x86995,f249(f869(x86991,a852)))+~P26(x86993,x86992,x86994,f249(f869(x86993,a852)))+P26(x86991,x86992,f784(f82(x86993,x86992,x86991,x86994),x86995),f249(f869(x86991,a852)))
% 11.41/11.19 [9200]P85(f784(f784(f347(f868(x92001,x92001)),f784(f784(f251(x92001,x92001),x92002),x92003)),f310(x92001,x92004)))+~P85(f784(f784(f347(f868(x92001,x92001)),f784(f784(f251(x92001,x92001),x92002),x92005)),f310(x92001,x92004)))+~P85(f784(f784(f347(f868(x92001,x92001)),f784(f784(f251(x92001,x92001),x92005),x92003)),f310(x92001,x92004)))
% 11.41/11.19 [9237]~P101(x92372)+~P85(f784(f132(x92371),x92375))+P85(f784(f132(x92371),f143(x92371,x92372,x92373,x92374,x92375)))
% 11.41/11.19 [5262]~E(x52622,f120(x52621))+E(f784(f784(f130(x52621),x52622),x52623),f784(f784(f144(x52621),x52624),x52625))+~E(x52623,f784(f784(f144(x52621),x52624),x52625))
% 11.41/11.19 [5263]~E(x52632,f120(x52631))+E(f784(f784(f130(x52631),x52632),x52633),f784(f784(f144(x52631),x52634),x52635))+~E(f784(f784(f144(x52631),x52634),x52635),x52633)
% 11.41/11.19 [6400]~E(f784(f188(f860(x64001)),x64005),f784(f188(f860(x64002)),x64004))+E(f784(f784(f146(f868(x64001,x64002),x64002),f260(x64001,x64002)),x64003),x64004)+~E(f784(f784(f173(x64001,x64002),x64005),x64004),x64003)
% 11.41/11.19 [6401]~E(f784(f188(f860(x64011)),x64014),f784(f188(f860(x64012)),x64015))+E(f784(f784(f146(f868(x64011,x64012),x64011),f250(x64011,x64012)),x64013),x64014)+~E(f784(f784(f173(x64011,x64012),x64014),x64015),x64013)
% 11.41/11.19 [6894]~P101(x68941)+~P15(x68941,f784(f784(f146(x68942,x68941),x68943),x68945))+P15(x68941,f784(f784(f146(x68942,x68941),x68943),f784(f131(x68942,x68944),x68945)))
% 11.41/11.19 [6939]~P85(f784(x69393,x69395))+~P85(f784(f784(x69392,x69394),x69395))+P85(f784(f784(f101(x69391,x69392,x69393),x69394),x69395))
% 11.41/11.19 [7036]~P101(x70361)+P15(x70361,f784(f784(f146(x70362,x70361),x70363),f154(x70362,x70364,x70365)))+~P15(x70361,f784(f784(f146(x70362,x70361),x70363),x70365))
% 11.41/11.19 [7059]~P52(x70593,x70592,x70595)+~P52(x70591,x70593,x70594)+P52(x70591,x70592,f784(f784(f291(x70591,x70593,x70592),x70594),x70595))
% 11.41/11.19 [7148]E(x71481,x71482)+~P26(x71483,x71484,x71485,f249(f869(x71483,a852)))+~E(f784(f784(f146(x71483,x71484),x71485),x71481),f784(f784(f146(x71483,x71484),x71485),x71482))
% 11.41/11.19 [7149]E(x71491,x71492)+~P26(x71493,x71494,x71495,f249(f869(x71493,a852)))+~E(f784(f784(f146(x71493,x71494),x71495),x71491),f784(f784(f146(x71493,x71494),x71495),x71492))
% 11.41/11.19 [7232]P38(x72321,x72322,x72323,x72324)+~P38(x72321,x72322,x72325,x72324)+~P85(f784(f784(f242(a859),x72325),x72323))
% 11.41/11.19 [7322]~P85(f784(f784(f243(a859),x73221),f784(x73223,x73225)))+P85(f784(f784(f243(a859),x73221),f147(x73222,x73223,x73224)))+~P85(f784(f784(f347(x73222),x73225),f784(f164(x73222),x73224)))
% 11.41/11.19 [7323]~P85(f784(f784(f242(a859),x73231),f784(x73233,x73235)))+P85(f784(f784(f242(a859),x73231),f147(x73232,x73233,x73234)))+~P85(f784(f784(f347(x73232),x73235),f784(f164(x73232),x73234)))
% 11.41/11.19 [7732]~P100(x77321)+P85(f784(f784(f242(f869(x77321,a852)),f305(x77321,x77322,x77323)),f305(x77321,x77324,x77325)))+P85(f784(f784(f242(x77321),x77322),x77323))
% 11.41/11.19 [7759]~P6(x77591)+P85(f784(f784(f242(x77591),f784(f784(f55(x77592,x77591),x77593),x77594)),f784(x77594,x77595)))+~P85(f784(f784(f347(x77592),x77595),x77593))
% 11.41/11.19 [7827]~P26(x78271,x78272,x78274,x78273)+E(f784(f86(x78271,x78272,x78273,x78274),f784(x78274,x78275)),x78275)+~P85(f784(f784(f347(x78271),x78275),x78273))
% 11.41/11.19 [8021]~P85(f784(x80211,x80215))+P85(f784(x80211,f392(x80211,x80212,x80213,x80214)))+~P85(f784(f784(f347(x80214),x80215),x80213))
% 11.41/11.19 [8022]~P85(f784(x80221,x80225))+P85(f784(x80221,f392(x80221,x80222,x80223,x80224)))+~P85(f784(f784(f347(x80224),x80225),x80222))
% 11.41/11.19 [8113]P85(f784(f71(x81131),x81132))+~P85(f784(f71(x81133),x81134))+~P85(f784(f784(f242(f869(x81131,a852)),x81132),f784(f313(x81133,x81131,x81135),x81134)))
% 11.41/11.19 [8123]~P26(x81234,x81231,x81232,f249(f869(x81234,a852)))+~P85(f784(f784(f347(x81234),x81233),x81235))+P85(f784(f784(f347(x81231),f784(x81232,x81233)),f784(f313(x81234,x81231,x81232),x81235)))
% 11.41/11.19 [8272]E(x82721,x82722)+~P26(x82723,x82724,x82725,f784(f784(f110(f869(x82723,a852)),f784(f164(x82723),x82721)),f784(f164(x82723),x82722)))+~E(f784(f784(f146(x82723,x82724),x82725),x82721),f784(f784(f146(x82723,x82724),x82725),x82722))
% 11.41/11.19 [8273]E(x82731,x82732)+~P26(x82733,x82734,x82735,f784(f784(f110(f869(x82733,a852)),f784(f164(x82733),x82731)),f784(f164(x82733),x82732)))+~E(f784(f784(f146(x82733,x82734),x82735),x82731),f784(f784(f146(x82733,x82734),x82735),x82732))
% 11.41/11.19 [8330]~P100(x83301)+~P85(f784(f784(f243(f869(x83301,a852)),f305(x83301,x83304,x83305)),f305(x83301,x83302,x83303)))+P85(f784(f784(f242(x83301),x83302),x83303))
% 11.41/11.19 [8398]~P26(x83981,x83984,x83985,f249(f869(x83981,a852)))+~P85(f784(f784(f347(x83984),f784(x83985,x83982)),f784(f313(x83981,x83984,x83985),x83983)))+P85(f784(f784(f347(x83981),x83982),x83983))
% 11.41/11.19 [8476]P85(f784(x84761,x84762))+~P85(f784(x84761,f393(x84761,x84763,x84764,x84765)))+~P85(f784(f784(f347(x84765),x84762),x84764))
% 11.41/11.19 [8477]P85(f784(x84771,x84772))+~P85(f784(x84771,f393(x84771,x84773,x84774,x84775)))+~P85(f784(f784(f347(x84775),x84772),x84773))
% 11.41/11.19 [8734]~P26(x87342,x87343,x87341,x87344)+E(f784(x87341,f784(f86(x87342,x87343,x87344,x87341),x87345)),x87345)+~P85(f784(f784(f347(x87343),x87345),f784(f313(x87342,x87343,x87341),x87344)))
% 11.41/11.19 [8821]E(x88211,f120(x88212))+E(f784(f784(f144(x88212),x88213),f743(x88214,x88213,x88215,x88211,x88212)),x88211)+~E(f784(f784(f130(x88212),x88211),x88215),f784(f784(f144(x88212),x88213),x88214))
% 11.41/11.19 [8822]E(x88221,f120(x88222))+E(f784(f784(f144(x88222),x88223),f744(x88224,x88221,x88225,x88223,x88222)),x88221)+~E(f784(f784(f130(x88222),x88221),x88224),f784(f784(f144(x88222),x88223),x88225))
% 11.41/11.19 [8837]E(f784(f784(f144(x88372),x88373),f743(x88374,x88373,x88371,x88375,x88372)),x88375)+~E(f784(f784(f130(x88372),x88375),x88371),f784(f784(f144(x88372),x88373),x88374))+E(x88371,f784(f784(f144(x88372),x88373),x88374))
% 11.41/11.19 [8838]E(f784(f784(f144(x88381),x88382),f744(x88384,x88385,x88383,x88382,x88381)),x88385)+~E(f784(f784(f130(x88381),x88385),x88384),f784(f784(f144(x88381),x88382),x88383))+E(f784(f784(f144(x88381),x88382),x88383),x88384)
% 11.41/11.19 [8913]~E(f784(f313(x89133,x89132,x89134),f249(f869(x89133,a852))),f249(f869(x89132,a852)))+~E(f784(f313(x89131,x89133,x89135),f249(f869(x89131,a852))),f249(f869(x89133,a852)))+E(f784(f313(x89131,x89132,f784(f82(x89133,x89132,x89131,x89134),x89135)),f249(f869(x89131,a852))),f249(f869(x89132,a852)))
% 11.41/11.19 [9243]E(x92431,f120(x92432))+~E(f784(f784(f130(x92432),x92431),x92433),f784(f784(f144(x92432),x92435),x92434))+E(f784(f784(f130(x92432),f744(x92433,x92431,x92434,x92435,x92432)),x92433),x92434)
% 11.41/11.19 [9244]E(x92441,f120(x92442))+~E(f784(f784(f130(x92442),x92441),x92445),f784(f784(f144(x92442),x92444),x92443))+E(f784(f784(f130(x92442),f743(x92443,x92444,x92445,x92441,x92442)),x92445),x92443)
% 11.41/11.19 [9251]E(f784(f784(f130(x92512),f743(x92514,x92513,x92511,x92515,x92512)),x92511),x92514)+~E(f784(f784(f130(x92512),x92515),x92511),f784(f784(f144(x92512),x92513),x92514))+E(x92511,f784(f784(f144(x92512),x92513),x92514))
% 11.41/11.19 [9252]~E(f784(f784(f130(x92521),x92525),x92524),f784(f784(f144(x92521),x92522),x92523))+E(f784(f784(f130(x92521),f744(x92524,x92525,x92523,x92522,x92521)),x92524),x92523)+E(f784(f784(f144(x92521),x92522),x92523),x92524)
% 11.41/11.19 [9253]E(f784(f784(f130(x92531),x92535),f748(x92533,x92532,x92534,x92535,x92531)),x92532)+E(f784(f784(f130(x92531),x92532),f747(x92533,x92532,x92534,x92535,x92531)),x92535)+~E(f784(f784(f130(x92531),x92535),x92534),f784(f784(f130(x92531),x92532),x92533))
% 11.41/11.19 [9285]~P101(x92851)+P15(x92851,f784(f784(f146(x92852,x92851),x92853),f143(x92852,x92851,x92853,x92854,x92855)))+~P15(x92851,f784(f784(f146(x92852,x92851),x92853),x92855))
% 11.41/11.19 [9301]~P56(x93015,x93011,x93014,x93013)+P85(f784(f784(x93011,x93012),f546(x93013,x93014,x93011,x93015,x93012)))+~P85(f784(f784(f347(x93015),x93012),x93014))
% 11.41/11.19 [9398]~P85(f784(f784(f347(f868(x93981,x93981)),f784(f784(f251(x93981,x93981),x93985),x93983)),f310(x93981,x93984)))+P85(f784(f784(f347(f868(x93981,x93981)),f784(f784(f251(x93981,x93981),x93982),x93983)),f784(f784(f291(x93981,x93981,x93981),x93984),f310(x93981,x93984))))+~P85(f784(f784(f347(f868(x93981,x93981)),f784(f784(f251(x93981,x93981),x93982),x93985)),f784(f784(f291(x93981,x93981,x93981),x93984),f310(x93981,x93984))))
% 11.41/11.19 [9399]~P85(f784(f784(f347(f868(x93991,x93991)),f784(f784(f251(x93991,x93991),x93992),x93995)),f310(x93991,x93994)))+P85(f784(f784(f347(f868(x93991,x93991)),f784(f784(f251(x93991,x93991),x93992),x93993)),f784(f784(f291(x93991,x93991,x93991),x93994),f310(x93991,x93994))))+~P85(f784(f784(f347(f868(x93991,x93991)),f784(f784(f251(x93991,x93991),x93995),x93993)),f784(f784(f291(x93991,x93991,x93991),x93994),f310(x93991,x93994))))
% 11.41/11.19 [9401]P85(f784(f784(f347(f868(f860(x94011),f860(x94011))),f784(f784(f251(f860(x94011),f860(x94011)),x94012),x94013)),f150(x94011,f310(x94011,x94014))))+~P85(f784(f784(f347(f868(f860(x94011),f860(x94011))),f784(f784(f251(f860(x94011),f860(x94011)),x94012),x94015)),f150(x94011,f310(x94011,x94014))))+~P85(f784(f784(f347(f868(f860(x94011),f860(x94011))),f784(f784(f251(f860(x94011),f860(x94011)),x94015),x94013)),f150(x94011,f310(x94011,x94014))))
% 11.41/11.19 [9406]E(f784(f784(f130(x94061),x94062),f747(x94063,x94062,x94064,x94065,x94061)),x94065)+E(f784(f784(f130(x94061),f748(x94063,x94062,x94064,x94065,x94061)),x94063),x94064)+~E(f784(f784(f130(x94061),x94062),x94063),f784(f784(f130(x94061),x94065),x94064))
% 11.41/11.19 [9407]E(f784(f784(f130(x94071),x94072),f748(x94073,x94074,x94075,x94072,x94071)),x94074)+E(f784(f784(f130(x94071),f747(x94073,x94074,x94075,x94072,x94071)),x94075),x94073)+~E(f784(f784(f130(x94071),x94072),x94075),f784(f784(f130(x94071),x94074),x94073))
% 11.41/11.19 [9464]P85(f784(f784(f347(f868(x94641,x94641)),f784(f784(f251(x94641,x94641),x94642),x94643)),f784(f784(f291(x94641,x94641,x94641),x94644),f310(x94641,x94644))))+~P85(f784(f784(f347(f868(x94641,x94641)),f784(f784(f251(x94641,x94641),x94642),x94645)),f784(f784(f291(x94641,x94641,x94641),x94644),f310(x94641,x94644))))+~P85(f784(f784(f347(f868(x94641,x94641)),f784(f784(f251(x94641,x94641),x94645),x94643)),f784(f784(f291(x94641,x94641,x94641),x94644),f310(x94641,x94644))))
% 11.41/11.19 [9498]E(f784(f784(f130(x94981),f747(x94982,x94983,x94984,x94985,x94981)),x94984),x94982)+~E(f784(f784(f130(x94981),x94983),x94982),f784(f784(f130(x94981),x94985),x94984))+E(f784(f784(f130(x94981),f748(x94982,x94983,x94984,x94985,x94981)),x94982),x94984)
% 11.41/11.19 [9513]~P56(x95131,x95134,x95133,x95132)+~P85(f784(f784(f347(x95131),x95135),x95133))+P85(f784(f784(f347(x95131),f546(x95132,x95133,x95134,x95131,x95135)),x95132))
% 11.41/11.19 [9629]~P85(f784(f784(f347(f868(f869(x96291,a852),f869(x96291,a852))),f784(f784(f251(f869(x96291,a852),f869(x96291,a852)),x96294),x96293)),f338(x96291,x96292)))+~P85(f784(f784(f347(x96291),x96295),x96294))+P85(f784(f784(f347(x96291),f636(x96292,x96293,x96294,x96291,x96295)),x96293))
% 11.41/11.19 [6476]~P18(x64762,x64765,x64761)+~P85(f784(f71(x64762),x64764))+E(f784(x64761,f784(f784(f312(x64762),x64763),x64764)),f784(f784(f74(x64762,x64762,x64765),x64763),x64764))
% 11.41/11.19 [6477]~E(x64773,x64774)+~E(x64772,x64775)+E(f784(f784(f312(x64771),x64772),f784(f784(f312(x64771),x64773),f187(f869(x64771,a852)))),f784(f784(f312(x64771),x64774),f784(f784(f312(x64771),x64775),f187(f869(x64771,a852)))))
% 11.41/11.19 [6523]E(f784(x65231,x65232),f249(f869(x65233,a852)))+~E(f784(f784(f55(x65234,f869(x65233,a852)),x65235),x65231),f249(f869(x65233,a852)))+~P85(f784(f784(f347(x65234),x65232),x65235))
% 11.41/11.19 [6524]E(f784(x65241,x65242),f187(f869(x65243,a852)))+~E(f784(f784(f54(x65244,f869(x65243,a852)),x65245),x65241),f187(f869(x65243,a852)))+~P85(f784(f784(f347(x65244),x65242),x65245))
% 11.41/11.19 [6525]E(f784(x65251,x65252),f249(f869(x65253,a852)))+~E(f784(f784(f55(x65254,f869(x65253,a852)),x65255),x65251),f249(f869(x65253,a852)))+~P85(f784(f784(f347(x65254),x65252),x65255))
% 11.41/11.19 [6526]E(f784(x65261,x65262),f187(f869(x65263,a852)))+~E(f784(f784(f54(x65264,f869(x65263,a852)),x65265),x65261),f187(f869(x65263,a852)))+~P85(f784(f784(f347(x65264),x65262),x65265))
% 11.41/11.19 [6843]~P85(f784(f784(f194(x68431),x68433),x68435))+~P85(f784(f784(f194(x68432),x68435),x68434))+P85(f784(f784(f194(f38(x68431,x68432)),x68433),x68434))
% 11.41/11.19 [6844]~P85(f784(f784(f194(x68441),x68443),x68445))+~P85(f784(f784(f194(x68442),x68445),x68444))+P85(f784(f784(f194(f38(x68441,x68442)),x68443),x68444))
% 11.41/11.19 [7045]~E(x70452,x70454)+~P111(x70451)+E(f784(f784(f89(x70451),f784(f784(f90(x70451),x70452),x70453)),f784(f784(f90(x70451),x70454),x70455)),f784(f784(f89(x70451),f784(f784(f90(x70451),x70452),x70455)),f784(f784(f90(x70451),x70454),x70453)))
% 11.41/11.19 [7046]~E(x70462,x70464)+~P111(x70461)+E(f784(f784(f89(x70461),f784(f784(f90(x70461),x70462),x70463)),f784(f784(f90(x70461),x70464),x70465)),f784(f784(f89(x70461),f784(f784(f90(x70461),x70462),x70465)),f784(f784(f90(x70461),x70464),x70463)))
% 11.41/11.19 [7106]~P6(x71061)+~P85(f784(f784(f347(x71064),x71063),x71065))+P85(f784(f784(f242(x71061),f784(x71062,x71063)),f784(f784(f54(x71064,x71061),x71065),x71062)))
% 11.41/11.19 [7152]~P103(x71521)+P85(f784(f784(f242(x71521),f784(x71522,x71523)),f784(x71524,x71523)))+~P85(f784(f784(f242(f869(x71525,x71521)),x71522),x71524))
% 11.41/11.19 [7153]~P103(x71531)+P85(f784(f784(f242(x71531),f784(x71532,x71533)),f784(x71534,x71533)))+~P85(f784(f784(f242(f869(x71535,x71531)),x71532),x71534))
% 11.41/11.19 [7154]~P103(x71541)+P85(f784(f784(f242(x71541),f784(x71542,x71543)),f784(x71544,x71543)))+~P85(f784(f784(f242(f869(x71545,x71541)),x71542),x71544))
% 11.41/11.19 [7290]E(x72901,x72902)+E(x72903,x72901)+~E(f784(f784(f312(x72904),x72901),f784(f784(f312(x72904),x72905),f187(f869(x72904,a852)))),f784(f784(f312(x72904),x72902),f784(f784(f312(x72904),x72903),f187(f869(x72904,a852)))))
% 11.41/11.19 [7291]E(x72911,x72912)+E(x72913,x72911)+~E(f784(f784(f312(x72914),x72913),f784(f784(f312(x72914),x72912),f187(f869(x72914,a852)))),f784(f784(f312(x72914),x72915),f784(f784(f312(x72914),x72911),f187(f869(x72914,a852)))))
% 11.41/11.19 [7292]E(x72921,x72922)+E(x72921,x72923)+~E(f784(f784(f312(x72924),x72923),f784(f784(f312(x72924),x72922),f187(f869(x72924,a852)))),f784(f784(f312(x72924),x72925),f784(f784(f312(x72924),x72921),f187(f869(x72924,a852)))))
% 11.41/11.19 [7293]E(x72931,x72932)+E(x72931,x72933)+~E(f784(f784(f312(x72934),x72931),f784(f784(f312(x72934),x72935),f187(f869(x72934,a852)))),f784(f784(f312(x72934),x72932),f784(f784(f312(x72934),x72933),f187(f869(x72934,a852)))))
% 11.41/11.19 [7837]P26(x78371,x78372,x78373,x78374)+~P26(x78371,x78372,x78373,x78375)+~P85(f784(f784(f242(f869(x78371,a852)),x78374),x78375))
% 11.41/11.19 [7937]P85(f784(x79371,x79372))+~P85(f784(f784(f194(x79374),x79372),x79375))+P85(f784(f784(f194(f35(x79371,x79373,x79374)),x79372),x79375))
% 11.41/11.19 [7938]P85(f784(x79381,x79382))+~P85(f784(f784(f194(x79384),x79382),x79385))+P85(f784(f784(f194(f35(x79381,x79383,x79384)),x79382),x79385))
% 11.41/11.19 [7939]P85(f784(x79391,x79392))+~P85(f784(f784(f194(x79394),x79392),x79395))+P85(f784(f784(f194(f35(x79391,x79393,x79394)),x79392),x79395))
% 11.41/11.19 [7965]~P85(f784(x79651,x79654))+~P85(f784(f784(f194(x79652),x79654),x79655))+P85(f784(f784(f194(f35(x79651,x79652,x79653)),x79654),x79655))
% 11.41/11.19 [7966]~P85(f784(x79661,x79664))+~P85(f784(f784(f194(x79662),x79664),x79665))+P85(f784(f784(f194(f35(x79661,x79662,x79663)),x79664),x79665))
% 11.41/11.19 [7967]~P85(f784(x79671,x79674))+~P85(f784(f784(f194(x79672),x79674),x79675))+P85(f784(f784(f194(f35(x79671,x79672,x79673)),x79674),x79675))
% 11.41/11.19 [8012]E(x80121,x80122)+~E(f784(f313(x80123,x80124,x80125),x80121),f784(f313(x80123,x80124,x80125),x80122))+~P26(x80123,x80124,x80125,f784(f784(f110(f869(x80123,a852)),x80121),x80122))
% 11.41/11.19 [8111]~P26(x81111,x81112,x81113,x81115)+~P26(x81111,x81112,x81113,x81114)+P26(x81111,x81112,x81113,f784(f784(f111(f869(x81111,a852)),x81114),x81115))
% 11.41/11.19 [8214]~P68(x82141)+E(f784(f784(f89(x82141),f784(x82142,x82143)),f784(f157(x82141),f784(f784(f146(x82144,x82141),x82142),f154(x82144,x82143,x82145)))),f784(f157(x82141),f784(f784(f146(x82144,x82141),x82142),x82145)))+~P85(f784(f784(f347(x82144),x82143),f784(f164(x82144),x82145)))
% 11.41/11.19 [8302]~P101(x83021)+~P15(x83021,f784(f784(f146(x83022,x83021),x83023),x83025))+P15(x83021,f784(f784(f146(x83022,x83021),x83023),f784(f784(f142(x83022,x83021,x83023),x83024),x83025)))
% 11.41/11.19 [8381]P85(f784(x83811,x83812))+P85(f784(f784(f194(x83813),x83812),x83814))+~P85(f784(f784(f194(f35(x83811,x83815,x83813)),x83812),x83814))
% 11.41/11.19 [8382]P85(f784(x83821,x83822))+P85(f784(f784(f194(x83823),x83822),x83824))+~P85(f784(f784(f194(f35(x83821,x83825,x83823)),x83822),x83824))
% 11.41/11.19 [8383]P85(f784(x83831,x83832))+P85(f784(f784(f194(x83833),x83832),x83834))+~P85(f784(f784(f194(f35(x83831,x83835,x83833)),x83832),x83834))
% 11.41/11.19 [8394]~P6(x83941)+P85(f784(f784(f242(x83941),f784(f784(f54(x83942,x83941),x83943),x83944)),f784(f784(f54(x83942,x83941),x83945),x83944)))+~P85(f784(f784(f242(f869(x83942,a852)),x83943),x83945))
% 11.41/11.19 [8395]~P6(x83951)+P85(f784(f784(f242(x83951),f784(f784(f55(x83952,x83951),x83953),x83954)),f784(f784(f55(x83952,x83951),x83955),x83954)))+~P85(f784(f784(f242(f869(x83952,a852)),x83955),x83953))
% 11.41/11.19 [8402]~P85(f784(x84024,x84022))+P85(f784(f784(f194(x84021),x84022),x84023))+~P85(f784(f784(f194(f35(x84024,x84021,x84025)),x84022),x84023))
% 11.41/11.19 [8403]~P85(f784(x84034,x84032))+P85(f784(f784(f194(x84031),x84032),x84033))+~P85(f784(f784(f194(f35(x84034,x84031,x84035)),x84032),x84033))
% 11.41/11.19 [8404]~P85(f784(x84044,x84042))+P85(f784(f784(f194(x84041),x84042),x84043))+~P85(f784(f784(f194(f35(x84044,x84041,x84045)),x84042),x84043))
% 11.41/11.19 [8427]~P101(x84273)+P85(f784(f132(x84271),x84272))+~P85(f784(f132(x84271),f784(f784(f142(x84271,x84273,x84274),x84275),x84272)))
% 11.41/11.19 [8435]P85(f784(f784(f194(x84351),x84352),x84353))+P85(f784(f784(f194(x84354),x84352),x84353))+~P85(f784(f784(f194(f35(x84355,x84351,x84354)),x84352),x84353))
% 11.41/11.19 [8436]P85(f784(f784(f194(x84361),x84362),x84363))+P85(f784(f784(f194(x84364),x84362),x84363))+~P85(f784(f784(f194(f35(x84365,x84361,x84364)),x84362),x84363))
% 11.41/11.19 [8437]P85(f784(f784(f194(x84371),x84372),x84373))+P85(f784(f784(f194(x84374),x84372),x84373))+~P85(f784(f784(f194(f35(x84375,x84371,x84374)),x84372),x84373))
% 11.41/11.19 [8560]~P101(x85601)+~P85(f784(f784(f347(x85602),x85603),f784(f164(x85602),x85604)))+~P85(f784(f132(x85602),f784(f784(f142(x85602,x85601,x85605),x85603),x85604)))
% 11.41/11.19 [8636]~P101(x86361)+P15(x86361,f784(f784(f146(x86362,x86361),x86363),x86364))+~P15(x86361,f784(f784(f146(x86362,x86361),x86363),f784(f784(f142(x86362,x86361,x86363),x86365),x86364)))
% 11.41/11.19 [8721]~P101(x87212)+E(f784(f784(f142(x87211,x87212,x87213),x87214),x87215),f143(x87211,x87212,x87213,x87214,x87215))+P85(f784(f784(f347(x87212),f784(x87213,x87214)),f784(f313(x87211,x87212,x87213),f784(f164(x87211),x87215))))
% 11.41/11.19 [8788]~P101(x87882)+E(f143(x87881,x87882,x87883,x87884,x87885),x87885)+~P85(f784(f784(f347(x87882),f784(x87883,x87884)),f784(f313(x87881,x87882,x87883),f784(f164(x87881),x87885))))
% 11.41/11.19 [8802]~P26(x88022,x88021,x88023,x88025)+P85(f784(f784(f243(f869(x88021,a852)),f784(f313(x88022,x88021,x88023),x88024)),f784(f313(x88022,x88021,x88023),x88025)))+~P85(f784(f784(f243(f869(x88022,a852)),x88024),x88025))
% 11.41/11.19 [8828]~P26(x88282,x88281,x88283,f249(f869(x88282,a852)))+P85(f784(f784(f242(f869(x88281,a852)),f784(f313(x88282,x88281,x88283),x88284)),f784(f313(x88282,x88281,x88283),x88285)))+~P85(f784(f784(f242(f869(x88282,a852)),x88284),x88285))
% 11.41/11.19 [8951]~P26(x89511,x89512,x89513,f249(f869(x89511,a852)))+~P85(f784(f784(f242(f869(x89512,a852)),x89514),f784(f313(x89511,x89512,x89513),x89515)))+P85(f784(f784(f242(f869(x89511,a852)),f784(f315(x89511,x89512,x89513),x89514)),x89515))
% 11.41/11.19 [8969]~E(f784(f313(x89693,x89691,x89694),f249(f869(x89693,a852))),f249(f869(x89691,a852)))+P85(f784(f784(f242(f869(x89691,a852)),x89692),f784(f313(x89693,x89691,x89694),x89695)))+~P85(f784(f784(f242(f869(x89693,a852)),f784(f315(x89693,x89691,x89694),x89692)),x89695))
% 11.41/11.19 [9007]~E(f784(f237(x90072),x90074),f784(f172(x90071,x90072,x90075),x90073))+~P85(f784(f132(x90071),f784(f784(f146(f868(x90071,x90072),x90071),f250(x90071,x90072)),x90075)))+P85(f784(f784(f347(f868(x90071,x90072)),f784(f784(f251(x90071,x90072),x90073),x90074)),f784(f164(f868(x90071,x90072)),x90075)))
% 11.41/11.19 [9008]~E(f784(f172(x90081,x90082,x90085),x90083),f784(f237(x90082),x90084))+~P85(f784(f132(x90081),f784(f784(f146(f868(x90081,x90082),x90081),f250(x90081,x90082)),x90085)))+P85(f784(f784(f347(f868(x90081,x90082)),f784(f784(f251(x90081,x90082),x90083),x90084)),f784(f164(f868(x90081,x90082)),x90085)))
% 11.41/11.19 [9073]~P26(x90731,x90734,x90735,f249(f869(x90731,a852)))+~P85(f784(f784(f242(f869(x90734,a852)),f784(f313(x90731,x90734,x90735),x90732)),f784(f313(x90731,x90734,x90735),x90733)))+P85(f784(f784(f242(f869(x90731,a852)),x90732),x90733))
% 11.41/11.19 [9139]E(f784(f237(x91391),x91392),f784(f172(x91393,x91391,x91394),x91395))+~P85(f784(f132(x91393),f784(f784(f146(f868(x91393,x91391),x91393),f250(x91393,x91391)),x91394)))+~P85(f784(f784(f347(f868(x91393,x91391)),f784(f784(f251(x91393,x91391),x91395),x91392)),f784(f164(f868(x91393,x91391)),x91394)))
% 11.41/11.19 [9140]E(f784(f172(x91401,x91402,x91403),x91404),f784(f237(x91402),x91405))+~P85(f784(f132(x91401),f784(f784(f146(f868(x91401,x91402),x91401),f250(x91401,x91402)),x91403)))+~P85(f784(f784(f347(f868(x91401,x91402)),f784(f784(f251(x91401,x91402),x91404),x91405)),f784(f164(f868(x91401,x91402)),x91403)))
% 11.41/11.19 [9141]E(f784(f172(x91411,x91412,x91413),x91414),f784(f237(x91412),x91415))+~P85(f784(f132(x91411),f784(f784(f146(f868(x91411,x91412),x91411),f250(x91411,x91412)),x91413)))+~P85(f784(f784(f347(f868(x91411,x91412)),f784(f784(f251(x91411,x91412),x91414),x91415)),f784(f164(f868(x91411,x91412)),x91413)))
% 11.41/11.19 [9347]~P17(x93471,x93472,x93473)+~P85(f784(f71(x93471),x93475))+P85(f784(f76(x93471,x93472,x93473,x93474,x93475),f784(f784(f74(x93471,x93472,x93473),x93474),x93475)))
% 11.41/11.19 [9421]P85(f784(x94211,f711(x94212,x94211,x94213,x94214,x94215)))+~P85(f784(f784(f242(f869(x94215,a852)),x94214),x94213))+P85(f784(f784(f242(f869(x94215,a852)),f784(f784(f111(f869(x94215,a852)),x94214),f784(f266(x94215),x94211))),f784(f784(f111(f869(x94215,a852)),x94213),f784(f266(x94215),x94212))))
% 11.41/11.19 [9511]~P6(x95115)+P85(f784(f784(f347(x95111),f674(x95112,x95113,x95111,x95114,x95115)),x95113))+P85(f784(f784(f242(x95115),x95114),f784(f784(f55(x95111,x95115),x95113),x95112)))
% 11.41/11.19 [9523]~P85(f784(x95235,f711(x95235,x95233,x95234,x95232,x95231)))+~P85(f784(f784(f242(f869(x95231,a852)),x95232),x95234))+P85(f784(f784(f242(f869(x95231,a852)),f784(f784(f111(f869(x95231,a852)),x95232),f784(f266(x95231),x95233))),f784(f784(f111(f869(x95231,a852)),x95234),f784(f266(x95231),x95235))))
% 11.41/11.19 [9591]P85(f784(f784(f347(x95911),f711(x95912,x95913,x95914,x95915,x95911)),x95915))+~P85(f784(f784(f242(f869(x95911,a852)),x95915),x95914))+P85(f784(f784(f242(f869(x95911,a852)),f784(f784(f111(f869(x95911,a852)),x95915),f784(f266(x95911),x95913))),f784(f784(f111(f869(x95911,a852)),x95914),f784(f266(x95911),x95912))))
% 11.41/11.19 [9640]~P6(x96401)+~P85(f784(f784(f242(x96401),x96402),f784(x96405,f674(x96405,x96404,x96403,x96402,x96401))))+P85(f784(f784(f242(x96401),x96402),f784(f784(f55(x96403,x96401),x96404),x96405)))
% 11.41/11.19 [9670]~P71(x96701)+~P85(f784(f71(x96702),x96705))+E(f784(f784(f784(f75(x96701,x96702,f90(x96701)),f784(f784(f20(x96702,x96701,x96701),f784(f784(f10(x96701,f869(x96701,x96701),x96702),f90(x96701)),x96703)),x96704)),f87(x96701)),x96705),f784(f784(f90(x96701),f784(f784(f784(f75(x96701,x96702,f90(x96701)),x96703),f87(x96701)),x96705)),f784(f784(f784(f75(x96701,x96702,f90(x96701)),x96704),f87(x96701)),x96705)))
% 11.41/11.19 [9718]~P85(f784(f784(f347(f868(f869(x97181,a852),f869(x97181,a852))),f784(f784(f251(f869(x97181,a852),f869(x97181,a852)),x97185),x97184)),f338(x97181,x97183)))+~P85(f784(f784(f347(x97181),x97182),x97185))+P85(f784(f784(f347(f868(x97181,x97181)),f784(f784(f251(x97181,x97181),x97182),f636(x97183,x97184,x97185,x97181,x97182))),x97183))
% 11.41/11.19 [9870]~P85(f784(f784(f347(f868(f860(x98701),f860(x98701))),f784(f784(f251(f860(x98701),f860(x98701)),f784(f784(f130(x98701),x98705),x98702)),f784(f784(f130(x98701),x98705),x98703))),f141(x98701,x98704)))+P85(f784(f784(f347(f868(f860(x98701),f860(x98701))),f784(f784(f251(f860(x98701),f860(x98701)),x98702),x98703)),f141(x98701,x98704)))+P85(f784(f784(f347(f868(x98701,x98701)),f784(f784(f251(x98701,x98701),f752(x98704,x98703,x98702,x98705,x98701)),f752(x98704,x98703,x98702,x98705,x98701))),x98704))
% 11.41/11.19 [7157]~E(x71573,x71575)+E(f784(f784(f155(x71571),f784(f784(f151(x71571,x71572),x71573),x71574)),x71575),x71574)+~P85(f784(f784(f243(a859),x71573),f784(f188(f860(x71571)),x71572)))
% 11.41/11.19 [7166]~E(f784(f188(f860(x71661)),x71663),f784(f188(f860(x71662)),x71664))+E(f784(f172(x71661,x71662,f784(f784(f173(x71661,x71662),x71663),x71664)),x71665),f190(x71662))+P85(f784(f784(f347(x71661),x71665),f784(f164(x71661),x71663)))
% 11.41/11.19 [7286]~E(f784(f784(f130(x72861),x72862),x72864),f784(f784(f130(x72861),x72863),x72865))+E(f784(f784(f165(x72861),f784(f188(f860(x72861)),x72862)),x72863),x72862)+P85(f784(f784(f242(a859),f784(f188(f860(x72861)),x72863)),f784(f188(f860(x72861)),x72862)))
% 11.41/11.19 [7287]E(x72871,x72872)+E(f784(f784(f155(x72873),f784(f784(f151(x72873,x72874),x72871),x72875)),x72872),f784(f784(f155(x72873),x72874),x72872))+~P85(f784(f784(f243(a859),x72871),f784(f188(f860(x72873)),x72874)))
% 11.41/11.19 [7798]~E(f784(f784(f130(x77981),x77982),x77984),f784(f784(f130(x77981),x77983),x77985))+E(f784(f784(f165(x77981),f784(f188(f860(x77981)),x77982)),x77983),x77982)+~P85(f784(f784(f242(a859),f784(f188(f860(x77981)),x77982)),f784(f188(f860(x77981)),x77983)))
% 11.41/11.19 [7822]~P85(f784(f71(x78221),f784(x78224,x78225)))+~P85(f784(f784(f347(x78222),x78225),x78223))+P85(f784(f71(x78221),f784(f784(f55(x78222,f869(x78221,a852)),x78223),x78224)))
% 11.41/11.19 [7933]~E(f784(f188(f860(x79331)),x79332),f784(f188(f860(x79333)),x79334))+~E(f784(f172(x79331,x79333,f784(f784(f173(x79331,x79333),x79332),x79334)),x79335),f190(x79333))+~P85(f784(f784(f347(x79331),x79335),f784(f164(x79331),x79332)))
% 11.41/11.19 [7999]~P46(x79991,x79993,x79995)+~P46(x79991,x79992,x79994)+P46(x79991,f784(f784(f110(f869(x79991,a852)),x79992),x79993),f784(f784(f110(f869(f868(x79991,x79991),a852)),x79994),x79995))
% 11.41/11.19 [8000]~P46(x80001,x80003,x80005)+~P46(x80001,x80002,x80004)+P46(x80001,f784(f784(f111(f869(x80001,a852)),x80002),x80003),f784(f784(f111(f869(f868(x80001,x80001),a852)),x80004),x80005))
% 11.41/11.19 [8346]E(f784(f784(f251(x83461,x83462),f784(f784(f155(x83461),x83463),x83464)),f784(f784(f155(x83462),x83465),x83464)),f784(f784(f155(f868(x83461,x83462)),f784(f784(f173(x83461,x83462),x83463),x83465)),x83464))+~P85(f784(f784(f243(a859),x83464),f784(f188(f860(x83461)),x83463)))+~P85(f784(f784(f243(a859),x83464),f784(f188(f860(x83462)),x83465)))
% 11.41/11.19 [8504]~P46(x85041,x85043,x85044)+P85(f784(f784(f347(x85041),x85042),x85043))+~P85(f784(f784(f347(f868(x85041,x85041)),f784(f784(f251(x85041,x85041),x85045),x85042)),x85044))
% 11.41/11.19 [8505]~P46(x85051,x85053,x85054)+P85(f784(f784(f347(x85051),x85052),x85053))+~P85(f784(f784(f347(f868(x85051,x85051)),f784(f784(f251(x85051,x85051),x85052),x85055)),x85054))
% 11.41/11.19 [8506]~P9(x85061,x85063,x85064)+P85(f784(f784(f347(x85061),x85062),x85063))+~P85(f784(f784(f347(f868(x85061,x85061)),f784(f784(f251(x85061,x85061),x85065),x85062)),x85064))
% 11.41/11.19 [8507]~P9(x85071,x85073,x85074)+P85(f784(f784(f347(x85071),x85072),x85073))+~P85(f784(f784(f347(f868(x85071,x85071)),f784(f784(f251(x85071,x85071),x85072),x85075)),x85074))
% 11.41/11.19 [8743]~P9(x87431,x87435,x87432)+E(f784(f287(x87431,x87431,x87432),f784(f784(f312(x87431),x87433),f187(f869(x87431,a852)))),f784(f287(x87431,x87431,x87432),f784(f784(f312(x87431),x87434),f187(f869(x87431,a852)))))+~P85(f784(f784(f347(f868(x87431,x87431)),f784(f784(f251(x87431,x87431),x87433),x87434)),x87432))
% 11.41/11.19 [8744]~P9(x87441,x87445,x87442)+E(f784(f287(x87441,x87441,x87442),f784(f784(f312(x87441),x87443),f187(f869(x87441,a852)))),f784(f287(x87441,x87441,x87442),f784(f784(f312(x87441),x87444),f187(f869(x87441,a852)))))+~P85(f784(f784(f347(f868(x87441,x87441)),f784(f784(f251(x87441,x87441),x87443),x87444)),x87442))
% 11.41/11.19 [8910]P85(f784(x89101,x89102))+~P85(f784(f784(f347(x89103),x89102),x89105))+P85(f784(f784(f347(x89103),f393(x89101,x89104,x89105,x89103)),f784(f784(f110(f869(x89103,a852)),x89105),x89104)))
% 11.41/11.19 [8911]P85(f784(x89111,x89112))+~P85(f784(f784(f347(x89113),x89112),x89114))+P85(f784(f784(f347(x89113),f393(x89111,x89114,x89115,x89113)),f784(f784(f110(f869(x89113,a852)),x89115),x89114)))
% 11.41/11.19 [8919]~P85(f784(x89192,x89195))+~P85(f784(f784(f347(x89191),x89195),x89194))+P85(f784(f784(f347(x89191),f392(x89192,x89193,x89194,x89191)),f784(f784(f110(f869(x89191,a852)),x89194),x89193)))
% 11.41/11.19 [8920]~P85(f784(x89202,x89205))+~P85(f784(f784(f347(x89201),x89205),x89203))+P85(f784(f784(f347(x89201),f392(x89202,x89203,x89204,x89201)),f784(f784(f110(f869(x89201,a852)),x89204),x89203)))
% 11.41/11.19 [8933]~P85(f784(f784(f242(f869(x89331,a852)),x89335),x89333))+~P85(f784(f784(f242(f869(x89331,a852)),x89332),x89334))+P85(f784(f784(f242(f869(x89331,a852)),f784(f784(f3(f869(x89331,a852)),x89332),x89333)),f784(f784(f3(f869(x89331,a852)),x89334),x89335)))
% 11.41/11.19 [8934]~P85(f784(f784(f242(f869(x89341,a852)),x89343),x89345))+~P85(f784(f784(f242(f869(x89341,a852)),x89342),x89344))+P85(f784(f784(f242(f869(x89341,a852)),f784(f784(f110(f869(x89341,a852)),x89342),x89343)),f784(f784(f110(f869(x89341,a852)),x89344),x89345)))
% 11.41/11.19 [8935]~P85(f784(f784(f242(f869(x89351,a852)),x89353),x89355))+~P85(f784(f784(f242(f869(x89351,a852)),x89352),x89354))+P85(f784(f784(f242(f869(x89351,a852)),f784(f784(f111(f869(x89351,a852)),x89352),x89353)),f784(f784(f111(f869(x89351,a852)),x89354),x89355)))
% 11.41/11.19 [9024]P85(f784(f784(f347(f868(x90241,x90241)),f784(f784(f251(x90241,x90241),x90242),x90243)),f340(x90241,x90244,x90245)))+~P85(f784(f784(f242(a859),f784(x90244,x90242)),f784(x90244,x90243)))+~P85(f784(f784(f347(f868(x90241,x90241)),f784(f784(f251(x90241,x90241),x90242),x90243)),x90245))
% 11.41/11.19 [9031]~E(f784(f188(f860(x90311)),x90313),f784(f188(f860(x90312)),x90314))+E(f784(f172(x90311,x90312,f784(f784(f173(x90311,x90312),x90313),x90314)),x90315),f784(f237(x90312),f727(x90315,x90314,x90312,x90313,x90311)))+~P85(f784(f784(f347(x90311),x90315),f784(f164(x90311),x90313)))
% 11.41/11.19 [9181]P85(f784(f784(f347(f868(x91811,x91811)),f784(f784(f251(x91811,x91811),x91812),x91813)),f310(x91811,x91814)))+~P85(f784(f784(f347(f868(x91811,x91811)),f784(f784(f251(x91811,x91811),x91812),x91815)),f310(x91811,x91814)))+~P85(f784(f784(f347(f868(x91811,x91811)),f784(f784(f251(x91811,x91811),x91815),x91813)),x91814))
% 11.41/11.19 [9182]P85(f784(f784(f347(f868(x91821,x91821)),f784(f784(f251(x91821,x91821),x91822),x91823)),f310(x91821,x91824)))+~P85(f784(f784(f347(f868(x91821,x91821)),f784(f784(f251(x91821,x91821),x91825),x91823)),f310(x91821,x91824)))+~P85(f784(f784(f347(f868(x91821,x91821)),f784(f784(f251(x91821,x91821),x91822),x91825)),x91824))
% 11.41/11.19 [9275]E(x92751,x92752)+E(f784(a160,f654(x92753,x92754,x92751,x92752,x92755)),x92754)+~P85(f784(f784(f347(f868(x92755,x92755)),f784(f784(f251(x92755,x92755),x92752),x92751)),f784(f784(f180(f868(x92755,x92755),a852),x92754),x92753)))
% 11.41/11.19 [9276]E(x92761,x92762)+E(f784(a160,f656(x92763,x92764,x92761,x92762,x92765)),x92764)+~P85(f784(f784(f347(f868(x92765,x92765)),f784(f784(f251(x92765,x92765),x92762),x92761)),f784(f784(f180(f868(x92765,x92765),a852),x92764),x92763)))
% 11.41/11.19 [9277]E(x92771,f2(a859))+E(f784(a160,f654(x92772,x92771,x92773,x92774,x92775)),x92771)+~P85(f784(f784(f347(f868(x92775,x92775)),f784(f784(f251(x92775,x92775),x92774),x92773)),f784(f784(f180(f868(x92775,x92775),a852),x92771),x92772)))
% 11.41/11.19 [9278]E(x92781,f2(a859))+E(f784(a160,f656(x92782,x92781,x92783,x92784,x92785)),x92781)+~P85(f784(f784(f347(f868(x92785,x92785)),f784(f784(f251(x92785,x92785),x92784),x92783)),f784(f784(f180(f868(x92785,x92785),a852),x92781),x92782)))
% 11.41/11.19 [9297]P85(f784(f784(f347(f868(x92971,x92971)),f784(f784(f251(x92971,x92971),x92972),x92973)),f784(f784(f291(x92971,x92971,x92971),x92974),f310(x92971,x92974))))+~P85(f784(f784(f347(f868(x92971,x92971)),f784(f784(f251(x92971,x92971),x92972),x92975)),x92974))+~P85(f784(f784(f347(f868(x92971,x92971)),f784(f784(f251(x92971,x92971),x92975),x92973)),x92974))
% 11.41/11.19 [9307]~P85(f784(f784(f347(f868(x93071,x93071)),f784(f784(f251(x93071,x93071),x93072),x93075)),f310(x93071,x93074)))+P85(f784(f784(f347(f868(x93071,x93071)),f784(f784(f251(x93071,x93071),x93072),x93073)),f784(f784(f291(x93071,x93071,x93071),x93074),f310(x93071,x93074))))+~P85(f784(f784(f347(f868(x93071,x93071)),f784(f784(f251(x93071,x93071),x93075),x93073)),x93074))
% 11.41/11.19 [9308]~P85(f784(f784(f347(f868(x93081,x93081)),f784(f784(f251(x93081,x93081),x93085),x93083)),f310(x93081,x93084)))+P85(f784(f784(f347(f868(x93081,x93081)),f784(f784(f251(x93081,x93081),x93082),x93083)),f784(f784(f291(x93081,x93081,x93081),x93084),f310(x93081,x93084))))+~P85(f784(f784(f347(f868(x93081,x93081)),f784(f784(f251(x93081,x93081),x93082),x93085)),x93084))
% 11.41/11.19 [9343]~P9(x93431,x93435,x93432)+~P85(f784(f784(f347(f868(x93431,x93431)),f784(f784(f251(x93431,x93431),x93433),x93434)),x93432))+P85(f784(f784(f242(f869(x93431,a852)),f784(f287(x93431,x93431,x93432),f784(f784(f312(x93431),x93433),f187(f869(x93431,a852))))),f784(f287(x93431,x93431,x93432),f784(f784(f312(x93431),x93434),f187(f869(x93431,a852))))))
% 11.41/11.19 [9394]P85(f784(f784(f347(f868(x93941,x93941)),f784(f784(f251(x93941,x93941),x93942),x93943)),f784(f784(f291(x93941,x93941,x93941),x93944),f310(x93941,x93944))))+~P85(f784(f784(f347(f868(x93941,x93941)),f784(f784(f251(x93941,x93941),x93942),x93945)),f784(f784(f291(x93941,x93941,x93941),x93944),f310(x93941,x93944))))+~P85(f784(f784(f347(f868(x93941,x93941)),f784(f784(f251(x93941,x93941),x93945),x93943)),x93944))
% 11.41/11.19 [9395]P85(f784(f784(f347(f868(x93951,x93951)),f784(f784(f251(x93951,x93951),x93952),x93953)),f784(f784(f291(x93951,x93951,x93951),x93954),f310(x93951,x93954))))+~P85(f784(f784(f347(f868(x93951,x93951)),f784(f784(f251(x93951,x93951),x93955),x93953)),f784(f784(f291(x93951,x93951,x93951),x93954),f310(x93951,x93954))))+~P85(f784(f784(f347(f868(x93951,x93951)),f784(f784(f251(x93951,x93951),x93952),x93955)),x93954))
% 11.41/11.19 [9441]~P85(f784(f76(x94411,x94411,x94414,x94412,x94413),x94415))+P85(f784(f784(f347(x94411),x94412),x94413))+P85(f784(f72(x94411,x94414,f784(f784(f312(x94411),x94412),x94413)),x94415))
% 11.41/11.19 [9486]~E(f784(f313(x94863,x94862,x94865),x94864),x94861)+E(x94861,f187(f869(x94862,a852)))+P85(f784(f784(f242(f869(x94863,a852)),f784(f313(x94862,x94863,f529(x94864,x94863,x94862,x94861)),x94861)),x94864))
% 11.41/11.19 [9526]~P6(x95265)+P85(f784(f784(f347(x95261),f404(x95262,x95263,x95264,x95261,x95265)),x95264))+P85(f784(f784(f242(x95265),f784(f784(f54(x95261,x95265),x95264),x95263)),x95262))
% 11.41/11.19 [9695]E(x96951,x96952)+P85(f784(f784(f347(f868(x96953,x96953)),f784(f784(f251(x96953,x96953),x96951),f657(x96954,x96955,x96952,x96951,x96953))),x96954))+~P85(f784(f784(f347(f868(x96953,x96953)),f784(f784(f251(x96953,x96953),x96951),x96952)),f784(f784(f180(f868(x96953,x96953),a852),x96955),x96954)))
% 11.41/11.19 [9696]E(x96961,f2(a859))+P85(f784(f784(f347(f868(x96962,x96962)),f784(f784(f251(x96962,x96962),x96963),f657(x96964,x96961,x96965,x96963,x96962))),x96964))+~P85(f784(f784(f347(f868(x96962,x96962)),f784(f784(f251(x96962,x96962),x96963),x96965)),f784(f784(f180(f868(x96962,x96962),a852),x96961),x96964)))
% 11.41/11.19 [9740]~P6(x97401)+~P85(f784(f784(f242(x97401),f784(x97404,f404(x97405,x97404,x97403,x97402,x97401))),x97405))+P85(f784(f784(f242(x97401),f784(f784(f54(x97402,x97401),x97403),x97404)),x97405))
% 11.41/11.19 [9795]E(x97951,x97952)+P85(f784(f784(f347(f868(x97953,x97953)),f784(f784(f251(x97953,x97953),f655(x97954,x97955,x97951,x97952,x97953)),x97951)),x97954))+~P85(f784(f784(f347(f868(x97953,x97953)),f784(f784(f251(x97953,x97953),x97952),x97951)),f784(f784(f180(f868(x97953,x97953),a852),x97955),x97954)))
% 11.41/11.19 [9796]E(x97961,f2(a859))+P85(f784(f784(f347(f868(x97962,x97962)),f784(f784(f251(x97962,x97962),f655(x97963,x97961,x97964,x97965,x97962)),x97964)),x97963))+~P85(f784(f784(f347(f868(x97962,x97962)),f784(f784(f251(x97962,x97962),x97965),x97964)),f784(f784(f180(f868(x97962,x97962),a852),x97961),x97963)))
% 11.41/11.19 [9800]E(x98001,x98002)+P85(f784(f784(f347(f868(x98003,x98003)),f784(f784(f251(x98003,x98003),x98001),f655(x98004,x98005,x98002,x98001,x98003))),f784(f784(f180(f868(x98003,x98003),a852),f654(x98004,x98005,x98002,x98001,x98003)),x98004)))+~P85(f784(f784(f347(f868(x98003,x98003)),f784(f784(f251(x98003,x98003),x98001),x98002)),f784(f784(f180(f868(x98003,x98003),a852),x98005),x98004)))
% 11.41/11.19 [9801]E(x98011,f2(a859))+P85(f784(f784(f347(f868(x98012,x98012)),f784(f784(f251(x98012,x98012),x98013),f655(x98014,x98011,x98015,x98013,x98012))),f784(f784(f180(f868(x98012,x98012),a852),f654(x98014,x98011,x98015,x98013,x98012)),x98014)))+~P85(f784(f784(f347(f868(x98012,x98012)),f784(f784(f251(x98012,x98012),x98013),x98015)),f784(f784(f180(f868(x98012,x98012),a852),x98011),x98014)))
% 11.41/11.19 [9861]E(x98611,x98612)+P85(f784(f784(f347(f868(x98613,x98613)),f784(f784(f251(x98613,x98613),f657(x98614,x98615,x98611,x98612,x98613)),x98611)),f784(f784(f180(f868(x98613,x98613),a852),f656(x98614,x98615,x98611,x98612,x98613)),x98614)))+~P85(f784(f784(f347(f868(x98613,x98613)),f784(f784(f251(x98613,x98613),x98612),x98611)),f784(f784(f180(f868(x98613,x98613),a852),x98615),x98614)))
% 11.41/11.19 [9862]E(x98621,f2(a859))+P85(f784(f784(f347(f868(x98622,x98622)),f784(f784(f251(x98622,x98622),f657(x98623,x98621,x98624,x98625,x98622)),x98624)),f784(f784(f180(f868(x98622,x98622),a852),f656(x98623,x98621,x98624,x98625,x98622)),x98623)))+~P85(f784(f784(f347(f868(x98622,x98622)),f784(f784(f251(x98622,x98622),x98625),x98624)),f784(f784(f180(f868(x98622,x98622),a852),x98621),x98623)))
% 11.41/11.19 [9893]~P68(x98932)+~P85(f784(f71(x98931),x98935))+E(f784(f784(f8(x98931,x98932),f784(f784(f9(x98931,x98932,x98932),f784(f784(f20(x98931,x98932,f869(x98932,x98932)),f784(f784(f10(a852,f869(x98932,f869(x98932,x98932)),x98931),f105(x98932)),f784(f784(f9(x98931,f869(x98931,a852),a852),f347(x98931)),x98933))),x98934)),f2(x98932))),x98935),f784(f784(f8(x98931,x98932),x98934),f784(f784(f111(f869(x98931,a852)),x98935),x98933)))
% 11.41/11.19 [8558]~P68(x85581)+~P85(f784(f71(x85584),x85585))+E(f784(f784(f89(x85581),f784(x85582,x85583)),f784(f784(f8(x85584,x85581),x85582),f784(f784(f3(f869(x85584,a852)),x85585),f784(f784(f312(x85584),x85583),f187(f869(x85584,a852)))))),f784(f784(f8(x85584,x85581),x85582),f784(f784(f312(x85584),x85583),x85585)))
% 11.41/11.19 [8559]~P71(x85591)+~P85(f784(f71(x85594),x85595))+E(f784(f784(f90(x85591),f784(x85592,x85593)),f784(f784(f11(x85594,x85591),x85592),f784(f784(f3(f869(x85594,a852)),x85595),f784(f784(f312(x85594),x85593),f187(f869(x85594,a852)))))),f784(f784(f11(x85594,x85591),x85592),f784(f784(f312(x85594),x85593),x85595)))
% 11.41/11.19 [8863]~P68(x88631)+E(f784(f784(f89(x88631),f784(f784(f8(a859,x88631),x88632),f305(a859,x88633,x88634))),f784(f784(f8(a859,x88631),x88632),f305(a859,f784(f784(f89(a859),x88634),f87(a859)),f784(f784(f89(a859),x88634),x88635)))),f784(f784(f8(a859,x88631),x88632),f305(a859,x88633,f784(f784(f89(a859),x88634),x88635))))+~P85(f784(f784(f242(a859),x88633),f784(f784(f89(a859),x88634),f87(a859))))
% 11.41/11.19 [8864]~P85(f784(f784(f347(x88641),x88644),x88645))+~P85(f784(f784(f242(f869(x88641,a852)),f784(f164(x88641),x88642)),x88645))+P85(f784(f784(f242(f869(x88641,a852)),f784(f164(x88641),f784(f784(f151(x88641,x88642),x88643),x88644))),x88645))
% 11.41/11.19 [9083]~P6(x90832)+~P85(f784(f71(x90831),x90835))+E(f784(f784(f74(x90831,x90832,f784(f784(f10(x90832,f869(x90832,x90832),x90831),f110(x90832)),x90833)),x90834),x90835),f784(f784(f110(x90832),x90834),f784(f784(f54(x90831,x90832),x90835),x90833)))
% 11.41/11.19 [9084]~P6(x90842)+~P85(f784(f71(x90841),x90845))+E(f784(f784(f74(x90841,x90842,f784(f784(f10(x90842,f869(x90842,x90842),x90841),f111(x90842)),x90843)),x90844),x90845),f784(f784(f111(x90842),x90844),f784(f784(f55(x90841,x90842),x90845),x90843)))
% 11.41/11.19 [9168]~P26(x91681,x91682,x91683,x91685)+P26(x91681,x91682,x91683,f784(f784(f312(x91681),x91684),x91685))+P85(f784(f784(f347(x91682),f784(x91683,x91684)),f784(f313(x91681,x91682,x91683),f784(f784(f3(f869(x91681,a852)),x91685),f784(f784(f312(x91681),x91684),f187(f869(x91681,a852)))))))
% 11.41/11.19 [9368]~P85(f784(f784(f347(f868(f860(x93681),f860(x93681))),f784(f784(f251(f860(x93681),f860(x93681)),x93682),x93684)),f150(x93681,x93685)))+~P85(f784(f784(f243(a859),x93683),f784(f188(f860(x93681)),x93682)))+P85(f784(f784(f347(f868(x93681,x93681)),f784(f784(f251(x93681,x93681),f784(f784(f155(x93681),x93682),x93683)),f784(f784(f155(x93681),x93684),x93683))),x93685))
% 11.41/11.19 [9602]E(x96021,f2(a1))+~P85(f784(f64(x96023,x96021),f784(f784(f251(a1,a1),x96024),x96025)))+P85(f784(f64(f784(f784(f90(a1),x96022),x96023),x96021),f784(f784(f251(a1,a1),f784(f784(f89(a1),f784(f784(f90(a1),x96022),x96024)),f784(f784(f51(a1),f784(f784(f90(a1),x96022),x96025)),x96021))),f60(a1,f784(f784(f90(a1),x96022),x96025),x96021))))
% 11.41/11.19 [9607]~P85(f784(f784(f243(a859),f2(a859)),x96073))+~P85(f784(f63(x96072,x96073),f784(f784(f251(a859,a859),x96074),x96075)))+P85(f784(f63(f784(f784(f90(a859),x96071),x96072),x96073),f784(f784(f251(a859,a859),f784(f784(f89(a859),f784(f784(f90(a859),x96071),x96074)),f784(f784(f51(a859),f784(f784(f90(a859),x96071),x96075)),x96073))),f60(a859,f784(f784(f90(a859),x96071),x96075),x96073))))
% 11.41/11.19 [9915]~P68(x99152)+~P85(f784(f71(x99151),x99154))+E(f784(f784(f8(x99151,x99152),x99153),f784(f266(x99151),f784(f784(f20(x99151,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99151),a344),f784(f784(f9(x99151,f869(x99151,a852),a852),f347(x99151)),x99154))),f784(f784(f9(x99151,f869(x99151,a852),a852),f347(x99151)),x99155)))),f784(f784(f8(x99151,x99152),f784(f784(f9(x99151,x99152,x99152),f784(f784(f20(x99151,x99152,f869(x99152,x99152)),f784(f784(f10(a852,f869(x99152,f869(x99152,x99152)),x99151),f105(x99152)),f784(f784(f9(x99151,f869(x99151,a852),a852),f347(x99151)),x99155))),x99153)),f2(x99152))),x99154))
% 11.41/11.19 [8197]~E(f784(f784(f130(x81971),x81972),x81975),f784(f784(f130(x81971),x81973),x81974))+E(f784(f784(f130(x81971),f784(f784(f133(x81971),f784(f188(f860(x81971)),x81972)),x81973)),x81974),x81975)+P85(f784(f784(f242(a859),f784(f188(f860(x81971)),x81973)),f784(f188(f860(x81971)),x81972)))
% 11.41/11.19 [8397]~E(f784(f784(f130(x83972),x83973),x83971),f784(f784(f130(x83972),x83974),x83975))+E(x83971,f784(f784(f130(x83972),f784(f784(f133(x83972),f784(f188(f860(x83972)),x83973)),x83974)),x83975))+~P85(f784(f784(f242(a859),f784(f188(f860(x83972)),x83973)),f784(f188(f860(x83972)),x83974)))
% 11.41/11.19 [8487]~E(f784(f784(f89(a859),f784(f784(f90(a859),x84873),x84874)),x84871),f784(f784(f89(a859),f784(f784(f90(a859),x84872),x84874)),x84875))+~P85(f784(f784(f242(a859),x84873),x84872))+E(x84871,f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x84872),x84873)),x84874)),x84875))
% 11.41/11.19 [8488]~E(f784(f784(f89(a859),f784(f784(f90(a859),x84881),x84883)),x84884),f784(f784(f89(a859),f784(f784(f90(a859),x84882),x84883)),x84885))+~P85(f784(f784(f242(a859),x84882),x84881))+E(f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x84881),x84882)),x84883)),x84884),x84885)
% 11.41/11.19 [8629]E(f784(f784(f89(a859),f784(f784(f90(a859),x86291),x86292)),x86293),f784(f784(f89(a859),f784(f784(f90(a859),x86294),x86292)),x86295))+~P85(f784(f784(f242(a859),x86294),x86291))+~E(x86295,f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x86291),x86294)),x86292)),x86293))
% 11.41/11.19 [8630]E(f784(f784(f89(a859),f784(f784(f90(a859),x86301),x86302)),x86303),f784(f784(f89(a859),f784(f784(f90(a859),x86304),x86302)),x86305))+~P85(f784(f784(f242(a859),x86304),x86301))+~E(f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x86301),x86304)),x86302)),x86303),x86305)
% 11.41/11.19 [8965]~P85(f784(f784(f289(a1),x89651),x89654))+~P85(f784(f784(f289(a1),x89651),f784(f784(f89(a1),x89652),x89655)))+P85(f784(f784(f289(a1),x89651),f784(f784(f89(a1),f784(f784(f89(a1),x89652),f784(f784(f90(a1),x89653),x89654))),x89655)))
% 11.41/11.19 [9169]~P85(f784(f784(f289(a1),x91691),x91694))+P85(f784(f784(f289(a1),x91691),f784(f784(f89(a1),x91692),x91693)))+~P85(f784(f784(f289(a1),x91691),f784(f784(f89(a1),f784(f784(f89(a1),x91692),f784(f784(f90(a1),x91695),x91694))),x91693)))
% 11.41/11.19 [9417]~P68(x94172)+~P85(f784(f71(x94171),x94175))+E(f784(f784(f8(x94171,x94172),f784(f784(f20(x94171,x94172,x94172),f784(f784(f10(x94172,f869(x94172,x94172),x94171),f89(x94172)),x94173)),x94174)),x94175),f784(f784(f89(x94172),f784(f784(f8(x94171,x94172),x94173),x94175)),f784(f784(f8(x94171,x94172),x94174),x94175)))
% 11.41/11.19 [9418]~P71(x94182)+~P85(f784(f71(x94181),x94185))+E(f784(f784(f11(x94181,x94182),f784(f784(f20(x94181,x94182,x94182),f784(f784(f10(x94182,f869(x94182,x94182),x94181),f90(x94182)),x94183)),x94184)),x94185),f784(f784(f90(x94182),f784(f784(f11(x94181,x94182),x94183),x94185)),f784(f784(f11(x94181,x94182),x94184),x94185)))
% 11.41/11.19 [9419]~P59(x94192)+~P85(f784(f71(x94191),x94195))+E(f784(f784(f11(x94191,x94192),f784(f784(f20(x94191,x94192,x94192),f784(f784(f10(x94192,f869(x94192,x94192),x94191),f293(x94192)),x94193)),x94194)),x94195),f784(f784(f293(x94192),f784(f784(f11(x94191,x94192),x94193),x94195)),f784(f784(f11(x94191,x94192),x94194),x94195)))
% 11.41/11.19 [9541]~E(f659(x95415,x95414,x95413,x95412,x95411),f660(x95415,x95414,x95413,x95412,x95411))+P85(f784(f784(f347(f868(x95411,x95411)),f784(f784(f251(x95411,x95411),x95412),x95413)),f310(x95411,x95414)))+~P85(f784(f784(f347(f868(x95411,x95411)),f784(f784(f251(x95411,x95411),x95412),x95413)),f310(x95411,f784(f784(f110(f869(f868(x95411,x95411),a852)),x95414),x95415))))
% 11.41/11.19 [9542]~E(f669(x95425,x95424,x95423,x95422,x95421),f670(x95425,x95424,x95423,x95422,x95421))+P85(f784(f784(f347(f868(x95421,x95421)),f784(f784(f251(x95421,x95421),x95422),x95423)),f310(x95421,x95424)))+~P85(f784(f784(f347(f868(x95421,x95421)),f784(f784(f251(x95421,x95421),x95422),x95423)),f310(x95421,f784(f784(f110(f869(f868(x95421,x95421),a852)),x95424),x95425))))
% 11.41/11.19 [9728]P85(f784(f784(f347(f868(x97281,x97281)),f784(f784(f251(x97281,x97281),x97282),f670(x97285,x97284,x97283,x97282,x97281))),f310(x97281,x97284)))+P85(f784(f784(f347(f868(x97281,x97281)),f784(f784(f251(x97281,x97281),x97282),x97283)),f310(x97281,x97284)))+~P85(f784(f784(f347(f868(x97281,x97281)),f784(f784(f251(x97281,x97281),x97282),x97283)),f310(x97281,f784(f784(f110(f869(f868(x97281,x97281),a852)),x97284),x97285))))
% 11.41/11.19 [9822]P85(f784(f784(f347(f868(x98221,x98221)),f784(f784(f251(x98221,x98221),f660(x98225,x98224,x98223,x98222,x98221)),x98223)),f310(x98221,x98224)))+P85(f784(f784(f347(f868(x98221,x98221)),f784(f784(f251(x98221,x98221),x98222),x98223)),f310(x98221,x98224)))+~P85(f784(f784(f347(f868(x98221,x98221)),f784(f784(f251(x98221,x98221),x98222),x98223)),f310(x98221,f784(f784(f110(f869(f868(x98221,x98221),a852)),x98224),x98225))))
% 11.41/11.19 [9868]P85(f784(f784(f347(f868(x98681,x98681)),f784(f784(f251(x98681,x98681),x98682),x98683)),f310(x98681,x98684)))+P85(f784(f784(f347(f868(x98681,x98681)),f784(f784(f251(x98681,x98681),f659(x98685,x98684,x98683,x98682,x98681)),f660(x98685,x98684,x98683,x98682,x98681))),x98685))+~P85(f784(f784(f347(f868(x98681,x98681)),f784(f784(f251(x98681,x98681),x98682),x98683)),f310(x98681,f784(f784(f110(f869(f868(x98681,x98681),a852)),x98684),x98685))))
% 11.41/11.19 [9869]P85(f784(f784(f347(f868(x98691,x98691)),f784(f784(f251(x98691,x98691),x98692),x98693)),f310(x98691,x98694)))+P85(f784(f784(f347(f868(x98691,x98691)),f784(f784(f251(x98691,x98691),f670(x98695,x98694,x98693,x98692,x98691)),f669(x98695,x98694,x98693,x98692,x98691))),x98695))+~P85(f784(f784(f347(f868(x98691,x98691)),f784(f784(f251(x98691,x98691),x98692),x98693)),f310(x98691,f784(f784(f110(f869(f868(x98691,x98691),a852)),x98694),x98695))))
% 11.41/11.19 [9992]~P85(f784(f784(f347(f868(f860(x99921),f860(x99921))),f784(f784(f251(f860(x99921),f860(x99921)),x99924),x99925)),f150(x99921,x99922)))+~P85(f784(f784(f347(f868(x99921,x99921)),x99923),f784(f164(f868(x99921,x99921)),f784(f784(f173(x99921,x99921),x99924),x99925))))+P85(f784(f784(f261(x99921,x99921,a852),f784(f784(f9(x99921,f869(f868(x99921,x99921),a852),f869(x99921,a852)),f784(f784(f10(f869(x99921,f869(f869(f868(x99921,x99921),a852),a852)),f869(f869(f868(x99921,x99921),a852),f869(x99921,a852)),x99921),f9(x99921,f869(f868(x99921,x99921),a852),a852)),f784(f784(f10(f869(x99921,f868(x99921,x99921)),f869(x99921,f869(f869(f868(x99921,x99921),a852),a852)),x99921),f784(f10(f868(x99921,x99921),f869(f869(f868(x99921,x99921),a852),a852),x99921),f347(f868(x99921,x99921)))),f251(x99921,x99921)))),x99922)),x99923))
% 11.41/11.19 [9445]~P85(f784(f784(f242(a859),x94453),x94452))+~P85(f784(f784(f243(a859),f784(f784(f89(a859),f784(f784(f90(a859),x94453),x94454)),x94451)),f784(f784(f89(a859),f784(f784(f90(a859),x94452),x94454)),x94455)))+P85(f784(f784(f243(a859),x94451),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x94452),x94453)),x94454)),x94455)))
% 11.41/11.19 [9446]~P85(f784(f784(f242(a859),x94463),x94462))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),f784(f784(f90(a859),x94463),x94464)),x94461)),f784(f784(f89(a859),f784(f784(f90(a859),x94462),x94464)),x94465)))+P85(f784(f784(f242(a859),x94461),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x94462),x94463)),x94464)),x94465)))
% 11.41/11.19 [9468]~P85(f784(f784(f242(a859),x94681),x94684))+P85(f784(f784(f243(a859),f784(f784(f89(a859),f784(f784(f90(a859),x94681),x94682)),x94683)),f784(f784(f89(a859),f784(f784(f90(a859),x94684),x94682)),x94685)))+~P85(f784(f784(f243(a859),x94683),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x94684),x94681)),x94682)),x94685)))
% 11.41/11.19 [9469]~P85(f784(f784(f242(a859),x94691),x94694))+P85(f784(f784(f242(a859),f784(f784(f89(a859),f784(f784(f90(a859),x94691),x94692)),x94693)),f784(f784(f89(a859),f784(f784(f90(a859),x94694),x94692)),x94695)))+~P85(f784(f784(f242(a859),x94693),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x94694),x94691)),x94692)),x94695)))
% 11.41/11.19 [9579]~P85(f784(f784(f242(a859),x95792),x95791))+~P85(f784(f784(f243(a859),f784(f784(f89(a859),f784(f784(f90(a859),x95791),x95793)),x95794)),f784(f784(f89(a859),f784(f784(f90(a859),x95792),x95793)),x95795)))+P85(f784(f784(f243(a859),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x95791),x95792)),x95793)),x95794)),x95795))
% 11.41/11.19 [9580]~P85(f784(f784(f242(a859),x95802),x95801))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),f784(f784(f90(a859),x95801),x95803)),x95804)),f784(f784(f89(a859),f784(f784(f90(a859),x95802),x95803)),x95805)))+P85(f784(f784(f242(a859),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x95801),x95802)),x95803)),x95804)),x95805))
% 11.41/11.19 [9626]~P85(f784(f784(f242(a859),x96264),x96261))+P85(f784(f784(f243(a859),f784(f784(f89(a859),f784(f784(f90(a859),x96261),x96262)),x96263)),f784(f784(f89(a859),f784(f784(f90(a859),x96264),x96262)),x96265)))+~P85(f784(f784(f243(a859),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x96261),x96264)),x96262)),x96263)),x96265))
% 11.41/11.19 [9627]~P85(f784(f784(f242(a859),x96274),x96271))+P85(f784(f784(f242(a859),f784(f784(f89(a859),f784(f784(f90(a859),x96271),x96272)),x96273)),f784(f784(f89(a859),f784(f784(f90(a859),x96274),x96272)),x96275)))+~P85(f784(f784(f242(a859),f784(f784(f89(a859),f784(f784(f90(a859),f784(f784(f3(a859),x96271),x96274)),x96272)),x96273)),x96275))
% 11.41/11.19 [9853]~P13(x98531,x98532,x98535,x98533)+~P85(f784(f784(f347(f868(x98531,x98531)),x98534),x98535))+P85(f784(f784(f261(x98531,x98531,a852),f784(f784(f9(x98531,f869(x98531,x98532),f869(x98531,a852)),f784(f784(f10(f869(x98532,a852),f869(f869(x98531,x98532),f869(x98531,a852)),x98531),f10(x98532,a852,x98531)),f784(f784(f10(x98532,f869(x98532,a852),x98531),a343),x98533))),x98533)),x98534))
% 11.41/11.19 [7170]~P38(x71704,x71702,x71705,x71706)+P38(f35(x71701,x71703,x71704),x71702,x71705,x71706)+P85(f784(x71701,x71702))
% 11.41/11.19 [7171]~P38(x71714,x71712,x71715,x71716)+P38(f35(x71711,x71713,x71714),x71712,x71715,x71716)+P85(f784(x71711,x71712))
% 11.41/11.19 [7172]~P38(x71724,x71722,x71725,x71726)+P38(f35(x71721,x71723,x71724),x71722,x71725,x71726)+P85(f784(x71721,x71722))
% 11.41/11.19 [7250]~P38(x72502,x72504,x72505,x72506)+P38(f35(x72501,x72502,x72503),x72504,x72505,x72506)+~P85(f784(x72501,x72504))
% 11.41/11.19 [7251]~P38(x72512,x72514,x72515,x72516)+P38(f35(x72511,x72512,x72513),x72514,x72515,x72516)+~P85(f784(x72511,x72514))
% 11.41/11.19 [7252]~P38(x72522,x72524,x72525,x72526)+P38(f35(x72521,x72522,x72523),x72524,x72525,x72526)+~P85(f784(x72521,x72524))
% 11.41/11.19 [7341]P38(x73413,x73412,x73414,x73415)+~P38(f35(x73411,x73416,x73413),x73412,x73414,x73415)+P85(f784(x73411,x73412))
% 11.41/11.19 [7342]P38(x73423,x73422,x73424,x73425)+~P38(f35(x73421,x73426,x73423),x73422,x73424,x73425)+P85(f784(x73421,x73422))
% 11.41/11.19 [7343]P38(x73433,x73432,x73434,x73435)+~P38(f35(x73431,x73436,x73433),x73432,x73434,x73435)+P85(f784(x73431,x73432))
% 11.41/11.19 [7374]P38(x73741,x73742,x73743,x73744)+~P38(f35(x73745,x73741,x73746),x73742,x73743,x73744)+~P85(f784(x73745,x73742))
% 11.41/11.19 [7375]P38(x73751,x73752,x73753,x73754)+~P38(f35(x73755,x73751,x73756),x73752,x73753,x73754)+~P85(f784(x73755,x73752))
% 11.41/11.19 [7376]P38(x73761,x73762,x73763,x73764)+~P38(f35(x73765,x73761,x73766),x73762,x73763,x73764)+~P85(f784(x73765,x73762))
% 11.41/11.19 [7745]~P38(x77451,x77453,x77454,x77456)+~P38(x77452,x77456,x77454,x77455)+P38(f38(x77451,x77452),x77453,x77454,x77455)
% 11.41/11.19 [7746]~P38(x77461,x77463,x77464,x77466)+~P38(x77462,x77466,x77464,x77465)+P38(f38(x77461,x77462),x77463,x77464,x77465)
% 11.41/11.19 [7747]P38(x77471,x77472,x77473,x77474)+P38(x77475,x77472,x77473,x77474)+~P38(f35(x77476,x77471,x77475),x77472,x77473,x77474)
% 11.41/11.19 [7748]P38(x77481,x77482,x77483,x77484)+P38(x77485,x77482,x77483,x77484)+~P38(f35(x77486,x77481,x77485),x77482,x77483,x77484)
% 11.41/11.19 [7749]P38(x77491,x77492,x77493,x77494)+P38(x77495,x77492,x77493,x77494)+~P38(f35(x77496,x77491,x77495),x77492,x77493,x77494)
% 11.41/11.19 [6726]~E(f784(x67264,x67265),f190(x67262))+E(f784(f176(x67261,x67262,x67263,x67264),x67265),f784(f237(x67262),x67266))+~E(f784(x67263,x67265),f784(f237(x67262),x67266))
% 11.41/11.19 [6832]~E(f784(x68323,x68326),f190(x68321))+E(f784(f239(f864(x68321),x68322,f190(x68321),x68323),f784(x68324,x68325)),f190(x68321))+~E(f784(x68324,x68325),f784(f237(x68322),x68326))
% 11.41/11.19 [7433]E(f784(x74331,x74332),f190(x74333))+~E(f784(f176(x74335,x74333,x74336,x74331),x74332),f784(f237(x74333),x74334))+E(f784(x74331,x74332),f784(f237(x74333),x74334))
% 11.41/11.19 [7434]E(f784(x74341,x74342),f190(x74343))+~E(f784(f176(x74345,x74343,x74346,x74341),x74342),f784(f237(x74343),x74344))+E(f784(x74341,x74342),f784(f237(x74343),x74344))
% 11.41/11.19 [7470]~E(f784(f176(x74706,x74703,x74705,x74701),x74702),f784(f237(x74703),x74704))+E(f784(x74701,x74702),f784(f237(x74703),x74704))+E(f784(x74705,x74702),f784(f237(x74703),x74704))
% 11.41/11.19 [7471]~E(f784(f176(x74716,x74713,x74715,x74711),x74712),f784(f237(x74713),x74714))+E(f784(x74711,x74712),f784(f237(x74713),x74714))+E(f784(x74715,x74712),f784(f237(x74713),x74714))
% 11.41/11.19 [8358]~P20(x83586,x83581,x83582,x83584)+E(f784(f82(x83581,x83581,x83581,f784(x83582,x83583)),f784(x83584,x83585)),f784(f82(x83581,x83581,x83581,f784(x83584,x83585)),f784(x83582,x83583)))+~P85(f784(f71(x83586),x83585))
% 11.41/11.19 [8753]~P26(x87531,x87533,x87535,x87536)+~P26(x87533,x87532,x87534,f784(f313(x87531,x87533,x87535),x87536))+P26(x87531,x87532,f784(f82(x87533,x87532,x87531,x87534),x87535),x87536)
% 11.41/11.19 [8754]~P26(x87541,x87543,x87545,x87546)+~P26(x87543,x87542,x87544,f784(f313(x87541,x87543,x87545),x87546))+P26(x87541,x87542,f784(f82(x87543,x87542,x87541,x87544),x87545),x87546)
% 11.41/11.19 [8915]~P26(x89154,x89151,x89155,x89156)+~P26(x89154,x89152,f784(f82(x89151,x89152,x89154,x89153),x89155),x89156)+P26(x89151,x89152,x89153,f784(f313(x89154,x89151,x89155),x89156))
% 11.41/11.19 [9259]~P85(f784(f784(x92593,x92592),x92596))+~P85(f784(f784(x92594,x92595),x92592))+P85(f784(f784(f347(x92591),x92592),f302(x92591,x92593,x92594,x92595,x92596)))
% 11.41/11.19 [9260]~P85(f784(f784(x92604,x92602),x92606))+~P85(f784(f784(x92603,x92605),x92602))+P85(f784(f784(f347(x92601),x92602),f299(x92601,x92603,x92604,x92605,x92606)))
% 11.41/11.19 [9369]E(x93691,x93692)+E(x93693,x93694)+~P85(f784(f784(f347(f868(f860(x93695),f860(x93695))),f784(f784(f251(f860(x93695),f860(x93695)),f784(f784(f144(x93695),x93693),x93691)),f784(f784(f144(x93695),x93694),x93692))),f149(x93695,x93696)))
% 11.41/11.19 [9378]~E(x93782,x93784)+P85(f784(f784(f347(f868(f860(x93781),f860(x93781))),f784(f784(f251(f860(x93781),f860(x93781)),f784(f784(f144(x93781),x93782),x93783)),f784(f784(f144(x93781),x93784),x93785))),f139(x93781,x93786)))+~P85(f784(f784(f347(f868(f860(x93781),f860(x93781))),f784(f784(f251(f860(x93781),f860(x93781)),x93783),x93785)),f139(x93781,x93786)))
% 11.41/11.19 [9379]~E(x93792,x93794)+P85(f784(f784(f347(f868(f860(x93791),f860(x93791))),f784(f784(f251(f860(x93791),f860(x93791)),f784(f784(f144(x93791),x93792),x93793)),f784(f784(f144(x93791),x93794),x93795))),f141(x93791,x93796)))+~P85(f784(f784(f347(f868(f860(x93791),f860(x93791))),f784(f784(f251(f860(x93791),f860(x93791)),x93793),x93795)),f141(x93791,x93796)))
% 11.41/11.19 [9380]~E(x93802,x93804)+P85(f784(f784(f347(f868(f860(x93801),f860(x93801))),f784(f784(f251(f860(x93801),f860(x93801)),f784(f784(f144(x93801),x93802),x93803)),f784(f784(f144(x93801),x93804),x93805))),f149(x93801,x93806)))+~P85(f784(f784(f347(f868(f860(x93801),f860(x93801))),f784(f784(f251(f860(x93801),f860(x93801)),x93803),x93805)),f149(x93801,x93806)))
% 11.41/11.19 [9381]~E(x93812,x93814)+P85(f784(f784(f347(f868(f860(x93811),f860(x93811))),f784(f784(f251(f860(x93811),f860(x93811)),f784(f784(f130(x93811),x93812),x93813)),f784(f784(f130(x93811),x93814),x93815))),f149(x93811,x93816)))+~P85(f784(f784(f347(f868(f860(x93811),f860(x93811))),f784(f784(f251(f860(x93811),f860(x93811)),x93813),x93815)),f149(x93811,x93816)))
% 11.41/11.19 [9382]~E(x93823,x93825)+P85(f784(f784(f347(f868(f860(x93821),f860(x93821))),f784(f784(f251(f860(x93821),f860(x93821)),f784(f784(f130(x93821),x93822),x93823)),f784(f784(f130(x93821),x93824),x93825))),f149(x93821,x93826)))+~P85(f784(f784(f347(f868(f860(x93821),f860(x93821))),f784(f784(f251(f860(x93821),f860(x93821)),x93822),x93824)),f149(x93821,x93826)))
% 11.41/11.19 [9434]E(x94341,x94342)+P85(f784(f784(f347(f868(f860(x94343),f860(x94343))),f784(f784(f251(f860(x94343),f860(x94343)),x94341),x94342)),f149(x94343,x94344)))+~P85(f784(f784(f347(f868(f860(x94343),f860(x94343))),f784(f784(f251(f860(x94343),f860(x94343)),f784(f784(f144(x94343),x94345),x94341)),f784(f784(f144(x94343),x94346),x94342))),f149(x94343,x94344)))
% 11.41/11.19 [9581]~E(x95813,x95815)+P85(f784(f784(f347(f868(f860(x95811),f860(x95811))),f784(f784(f251(f860(x95811),f860(x95811)),f784(f784(f130(x95811),x95812),f784(f784(f144(x95811),x95813),f120(x95811)))),f784(f784(f130(x95811),x95814),f784(f784(f144(x95811),x95815),f120(x95811))))),f149(x95811,x95816)))+~P85(f784(f784(f347(f868(f860(x95811),f860(x95811))),f784(f784(f251(f860(x95811),f860(x95811)),x95812),x95814)),f149(x95811,x95816)))
% 11.41/11.19 [9594]E(f784(x95941,x95942),f190(x95943))+~E(f784(f239(f864(x95946),x95943,f190(x95946),x95944),f784(x95941,x95942)),f190(x95946))+E(f784(x95944,f719(x95942,x95941,x95944,x95945,x95946,x95943)),f190(x95946))
% 11.41/11.19 [9595]E(f784(x95951,x95952),f190(x95953))+~E(f784(f239(f864(x95956),x95953,f190(x95956),x95954),f784(x95951,x95952)),f190(x95956))+E(f784(f237(x95953),f719(x95952,x95951,x95954,x95955,x95956,x95953)),f784(x95951,x95952))
% 11.41/11.19 [9630]E(x96301,x96302)+E(x96303,x96304)+~P85(f784(f784(f347(f868(f860(x96305),f860(x96305))),f784(f784(f251(f860(x96305),f860(x96305)),f784(f784(f130(x96305),x96303),f784(f784(f144(x96305),x96301),f120(x96305)))),f784(f784(f130(x96305),x96304),f784(f784(f144(x96305),x96302),f120(x96305))))),f149(x96305,x96306)))
% 11.41/11.19 [9652]E(x96521,x96522)+~P85(f784(f784(f347(f868(f860(x96523),f860(x96523))),f784(f784(f251(f860(x96523),f860(x96523)),f784(f784(f130(x96523),x96521),f784(f784(f144(x96523),x96525),f120(x96523)))),f784(f784(f130(x96523),x96522),f784(f784(f144(x96523),x96526),f120(x96523))))),f149(x96523,x96524)))+P85(f784(f784(f347(f868(f860(x96523),f860(x96523))),f784(f784(f251(f860(x96523),f860(x96523)),x96521),x96522)),f149(x96523,x96524)))
% 11.41/11.19 [9680]~P85(f784(f784(f347(f868(f869(x96801,a852),f869(x96801,a852))),f784(f784(f251(f869(x96801,a852),f869(x96801,a852)),x96802),x96804)),f338(x96801,x96806)))+~P85(f784(f784(f347(f868(f869(x96801,a852),f869(x96801,a852))),f784(f784(f251(f869(x96801,a852),f869(x96801,a852)),x96803),x96805)),f338(x96801,x96806)))+P85(f784(f784(f347(f868(f869(x96801,a852),f869(x96801,a852))),f784(f784(f251(f869(x96801,a852),f869(x96801,a852)),f784(f784(f110(f869(x96801,a852)),x96802),x96803)),f784(f784(f110(f869(x96801,a852)),x96804),x96805))),f338(x96801,x96806)))
% 11.41/11.19 [5157]~E(f784(x51573,x51576),x51575)+~E(x51574,f784(f237(x51571),x51576))+E(f784(f784(f206(x51571,x51572),x51573),x51574),f784(f237(x51572),x51575))
% 11.41/11.19 [5554]~E(f784(f784(f130(x55541),x55546),x55543),x55545)+E(f784(f784(f130(x55541),x55542),x55543),f784(f784(f144(x55541),x55544),x55545))+~E(x55542,f784(f784(f144(x55541),x55544),x55546))
% 11.41/11.19 [5555]~E(f784(f784(f130(x55551),x55556),x55553),x55555)+E(f784(f784(f130(x55551),x55552),x55553),f784(f784(f130(x55551),x55554),x55555))+~E(x55552,f784(f784(f130(x55551),x55554),x55556))
% 11.41/11.19 [5556]E(f784(f784(f130(x55561),x55562),x55563),f784(f784(f144(x55561),x55564),x55565))+~E(f784(f784(f144(x55561),x55564),x55566),x55562)+~E(x55565,f784(f784(f130(x55561),x55566),x55563))
% 11.41/11.19 [5557]E(f784(f784(f130(x55571),x55572),x55573),f784(f784(f144(x55571),x55574),x55575))+~E(f784(f784(f144(x55571),x55574),x55576),x55572)+~E(x55575,f784(f784(f130(x55571),x55576),x55573))
% 11.41/11.19 [5558]~E(f784(f784(f130(x55581),x55582),x55586),x55584)+E(f784(f784(f130(x55581),x55582),x55583),f784(f784(f130(x55581),x55584),x55585))+~E(x55583,f784(f784(f130(x55581),x55586),x55585))
% 11.41/11.19 [5559]~E(f784(f784(f130(x55591),x55592),x55596),x55594)+E(f784(f784(f130(x55591),x55592),x55593),f784(f784(f130(x55591),x55594),x55595))+~E(x55593,f784(f784(f130(x55591),x55596),x55595))
% 11.41/11.19 [6719]E(f784(x67191,x67192),f784(x67193,x67192))+~E(f784(f784(f146(x67194,x67195),x67191),x67196),f784(f784(f146(x67194,x67195),x67193),x67196))+~P85(f784(f784(f347(x67194),x67192),f784(f164(x67194),x67196)))
% 11.41/11.19 [7108]~P20(x71084,x71085,x71086,x71081)+E(f784(f784(x71081,x71082),x71083),f784(f784(f74(x71084,x71085,x71086),x71083),x71082))+~P85(f784(f71(x71084),x71082))
% 11.41/11.19 [7175]~E(x71752,f784(x71754,x71756))+~P85(f784(f784(f347(x71753),x71756),x71755))+P85(f784(f784(f347(x71751),x71752),f784(f313(x71753,x71751,x71754),x71755)))
% 11.41/11.19 [7176]~E(x71762,f784(x71764,x71766))+~P85(f784(f784(f347(x71763),x71766),x71765))+P85(f784(f784(f347(x71761),x71762),f784(f313(x71763,x71761,x71764),x71765)))
% 11.41/11.19 [7177]~E(x71772,f784(x71774,x71776))+~P85(f784(f784(f347(x71773),x71776),x71775))+P85(f784(f784(f347(x71771),x71772),f784(f313(x71773,x71771,x71774),x71775)))
% 11.41/11.19 [7178]~E(f784(x71784,x71782),x71786)+~P85(f784(f784(f347(x71783),x71786),x71785))+P85(f784(f784(f347(x71781),x71782),f784(f315(x71781,x71783,x71784),x71785)))
% 11.41/11.19 [7652]~P33(x76521,x76522,x76524,x76526)+P33(x76521,x76522,f784(f784(f144(x76521),x76523),x76524),f784(f784(f144(x76521),x76525),x76526))+~P85(f784(f784(x76522,x76523),x76525))
% 11.41/11.19 [7653]~P33(x76531,x76532,x76534,x76536)+P33(x76531,x76532,f784(f784(f144(x76531),x76533),x76534),f784(f784(f144(x76531),x76535),x76536))+~P85(f784(f784(x76532,x76533),x76535))
% 11.41/11.19 [8637]~P54(x86374,x86375,x86371,x86372,x86376)+E(f784(x86371,f784(x86372,x86373)),x86373)+~P85(f784(f784(f347(x86375),x86373),x86376))
% 11.41/11.19 [9371]E(x93711,x93712)+E(f784(f188(f860(x93713)),x93714),f784(f188(f860(x93713)),x93715))+~P85(f784(f784(f347(f868(f860(x93713),f860(x93713))),f784(f784(f251(f860(x93713),f860(x93713)),f784(f784(f144(x93713),x93711),x93714)),f784(f784(f144(x93713),x93712),x93715))),f139(x93713,x93716)))
% 11.41/11.19 [9431]~P17(x94311,x94312,x94313)+E(f784(f784(f74(x94311,x94312,x94313),x94314),x94315),x94316)+~P85(f784(f76(x94311,x94312,x94313,x94314,x94315),x94316))
% 11.41/11.19 [9437]E(f784(f188(f860(x94371)),x94372),f784(f188(f860(x94371)),x94373))+P85(f784(f784(f347(f868(f860(x94371),f860(x94371))),f784(f784(f251(f860(x94371),f860(x94371)),x94372),x94373)),f139(x94371,x94374)))+~P85(f784(f784(f347(f868(f860(x94371),f860(x94371))),f784(f784(f251(f860(x94371),f860(x94371)),f784(f784(f144(x94371),x94375),x94372)),f784(f784(f144(x94371),x94376),x94373))),f139(x94371,x94374)))
% 11.41/11.19 [9459]~P85(f784(f784(f347(f868(x94591,x94591)),f784(f784(f251(x94591,x94591),x94592),x94594)),f310(x94591,x94596)))+P85(f784(f784(f347(f868(f860(x94591),f860(x94591))),f784(f784(f251(f860(x94591),f860(x94591)),f784(f784(f144(x94591),x94592),x94593)),f784(f784(f144(x94591),x94594),x94595))),f310(f860(x94591),f149(x94591,x94596))))+~P85(f784(f784(f347(f868(f860(x94591),f860(x94591))),f784(f784(f251(f860(x94591),f860(x94591)),x94593),x94595)),f310(f860(x94591),f149(x94591,x94596))))
% 11.41/11.19 [9941]~P68(x99412)+E(f784(f784(f8(x99411,x99412),f784(f784(f10(f869(x99413,a852),x99412,x99411),f784(f8(x99413,x99412),x99414)),f784(f784(f10(f869(x99413,a852),f869(x99413,a852),x99411),f266(x99413)),f784(f784(f10(f869(x99413,a852),f869(x99413,a852),x99411),f784(f20(x99413,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99413),a344),f784(f784(f9(x99413,f869(x99413,a852),a852),f347(x99413)),x99415)))),f784(f9(x99413,x99411,a852),f784(f784(f10(x99411,f869(x99411,a852),x99413),a343),x99416)))))),f784(f313(x99413,x99411,x99416),x99415)),f784(f784(f8(x99413,x99412),x99414),x99415))+~P85(f784(f71(x99413),x99415))
% 11.41/11.19 [6779]~P101(x67793)+P85(f784(x67792,x67795))+E(f784(f131(x67791,x67792),f784(f784(f142(x67791,x67793,x67794),x67795),x67796)),f784(f131(x67791,x67792),x67796))
% 11.41/11.19 [6781]P85(f784(x67811,x67812))+~E(f158(x67813,x67811,x67814),f784(f784(f251(f860(x67813),f860(x67813)),x67815),x67816))+~P85(f784(f784(f347(x67813),x67812),f784(f164(x67813),x67815)))
% 11.41/11.19 [6829]~P85(f784(x68292,x68296))+~E(f158(x68291,x68292,x68293),f784(f784(f251(f860(x68291),f860(x68291)),x68294),x68295))+~P85(f784(f784(f347(x68291),x68296),f784(f164(x68291),x68295)))
% 11.41/11.19 [7516]~P16(x75161,x75162,x75163)+~P85(f784(f71(x75161),x75166))+E(f784(f784(f74(x75161,x75162,x75163),x75164),f784(f784(f312(x75161),x75165),x75166)),f784(f784(f74(x75161,x75162,x75163),f784(f784(x75163,x75165),x75164)),x75166))
% 11.41/11.19 [7568]~P101(x75682)+~P85(f784(f784(f242(x75682),f784(x75683,x75684)),f784(x75683,x75685)))+E(f784(f784(f142(x75681,x75682,x75683),x75684),f784(f784(f144(x75681),x75685),x75686)),f784(f784(f144(x75681),x75684),f784(f784(f144(x75681),x75685),x75686)))
% 11.41/11.19 [7683]E(x76831,x76832)+~E(f784(f784(f258(x76833,x76834),x76831),f784(f18(f869(x76834,a852),x76833),x76835)),f784(f784(f258(x76833,x76834),x76832),f784(f18(f869(x76834,a852),x76833),x76835)))+~P85(f784(f784(f347(x76834),x76836),x76835))
% 11.41/11.19 [7751]~P16(x77511,x77512,x77513)+~P85(f784(f71(x77511),x77516))+E(f784(f784(f74(x77511,x77512,x77513),x77514),f784(f784(f312(x77511),x77515),x77516)),f784(f784(x77513,x77515),f784(f784(f74(x77511,x77512,x77513),x77514),x77516)))
% 11.41/11.19 [7867]~P17(x78671,x78672,x78673)+~P85(f784(f71(x78671),x78676))+E(f784(f784(f74(x78671,x78672,x78673),f784(f784(x78673,x78674),x78675)),x78676),f784(f784(x78673,x78674),f784(f784(f74(x78671,x78672,x78673),x78675),x78676)))
% 11.41/11.19 [7934]~P21(x79342,x79345,x79346,x79341)+~P85(f784(f71(x79342),x79344))+E(f784(x79341,f784(f784(f312(x79342),x79343),x79344)),f784(f82(x79345,x79345,x79345,f784(x79341,x79344)),f784(x79346,x79343)))
% 11.41/11.19 [7972]~P101(x79722)+P85(f784(f784(f242(x79722),f784(x79723,x79724)),f784(x79723,x79725)))+E(f784(f784(f142(x79721,x79722,x79723),x79724),f784(f784(f144(x79721),x79725),x79726)),f784(f784(f144(x79721),x79725),f784(f784(f142(x79721,x79722,x79723),x79724),x79726)))
% 11.41/11.19 [8104]~E(f784(f188(f860(x81041)),x81045),f784(f188(f860(x81042)),x81046))+~E(f784(f188(f860(x81041)),x81043),f784(f188(f860(x81042)),x81044))+E(f784(f784(f130(f868(x81041,x81042)),f784(f784(f173(x81041,x81042),x81043),x81044)),f784(f784(f173(x81041,x81042),x81045),x81046)),f784(f784(f173(x81041,x81042),f784(f784(f130(x81041),x81043),x81045)),f784(f784(f130(x81042),x81044),x81046)))
% 11.41/11.19 [8211]~E(x82112,f784(f313(x82113,x82111,x82114),x82116))+P85(f784(f784(f242(f869(x82111,a852)),x82112),f784(f313(x82113,x82111,x82114),x82115)))+~P85(f784(f784(f242(f869(x82113,a852)),x82116),x82115))
% 11.41/11.19 [8314]~P101(x83145)+E(f784(x83141,x83142),f784(x83141,x83143))+E(f784(f784(f142(x83144,x83145,x83141),x83142),f784(f784(f142(x83144,x83145,x83141),x83143),x83146)),f784(f784(f142(x83144,x83145,x83141),x83143),f784(f784(f142(x83144,x83145,x83141),x83142),x83146)))
% 11.41/11.19 [8351]~P26(x83513,x83511,x83514,x83515)+P26(x83513,x83511,f784(f784(f784(f81(x83513,x83511),x83514),x83516),x83512),x83515)+P85(f784(f784(f347(x83511),x83512),f784(f313(x83513,x83511,x83514),x83515)))
% 11.41/11.19 [8495]~P85(f784(f784(f347(x84952),x84954),f784(x84956,x84953)))+~P85(f784(f784(f347(x84951),x84953),x84955))+P85(f784(f784(f347(f868(x84951,x84952)),f784(f784(f251(x84951,x84952),x84953),x84954)),f784(f784(f258(x84951,x84952),x84955),x84956)))
% 11.41/11.19 [8496]~P85(f784(f784(f347(x84962),x84964),f784(x84966,x84963)))+~P85(f784(f784(f347(x84961),x84963),x84965))+P85(f784(f784(f347(f868(x84961,x84962)),f784(f784(f251(x84961,x84962),x84963),x84964)),f784(f784(f258(x84961,x84962),x84965),x84966)))
% 11.41/11.19 [8908]~P68(x89082)+~P26(x89084,x89081,x89085,x89086)+E(f784(f784(f8(x89081,x89082),x89083),f784(f313(x89084,x89081,x89085),x89086)),f784(f784(f8(x89084,x89082),f784(f82(x89081,x89082,x89084,x89083),x89085)),x89086))
% 11.41/11.19 [8909]~P71(x89092)+~P26(x89094,x89091,x89095,x89096)+E(f784(f784(f11(x89091,x89092),x89093),f784(f313(x89094,x89091,x89095),x89096)),f784(f784(f11(x89094,x89092),f784(f82(x89091,x89092,x89094,x89093),x89095)),x89096))
% 11.41/11.19 [9146]~E(f784(f784(f784(a196,x91465),f42(x91461)),f784(f784(a197,x91464),x91461)),f784(f784(f784(a196,x91466),f42(x91461)),f784(f784(a197,x91464),x91461)))+~P85(f784(f784(f194(x91463),f784(f784(f784(a196,x91464),f42(x91461)),f784(x91462,x91464))),x91466))+P85(f784(f784(f194(f34(x91461,x91462,x91463)),x91464),f784(f784(f784(a196,x91465),f42(x91461)),f784(f784(a197,x91464),x91461))))
% 11.41/11.19 [9150]~P20(x91503,x91501,x91506,x91502)+~P85(f784(f71(x91503),x91504))+E(f784(f82(x91501,x91501,x91501,f784(x91502,f784(f784(f3(f869(x91503,a852)),x91504),f784(f784(f312(x91503),x91505),f187(f869(x91503,a852)))))),f784(x91506,x91505)),f784(x91502,f784(f784(f312(x91503),x91505),x91504)))
% 11.41/11.19 [9535]~E(f784(f784(f784(a196,f784(f784(a198,x95355),f784(a197,x95354))),x95351),f784(f784(a197,x95355),a27)),f784(f784(f784(a196,f784(f784(a198,x95356),f784(a197,x95354))),x95351),f784(f784(a197,x95356),a27)))+~P85(f784(f784(f194(f784(a29,x95352)),f784(f784(f784(a196,f784(f784(a198,x95354),a199)),f42(a28)),f784(x95353,x95354))),x95356))+P85(f784(f784(f194(f33(x95351,x95352,x95353)),x95354),f784(f784(f784(a196,f784(f784(a198,x95355),f784(a197,x95354))),x95351),f784(f784(a197,x95355),a27))))
% 11.41/11.19 [9709]~E(f784(f313(x97092,x97094,x97096),f249(f869(x97092,a852))),f249(f869(x97094,a852)))+~E(f784(f313(x97091,x97093,x97095),f249(f869(x97091,a852))),f249(f869(x97093,a852)))+E(f784(f313(f868(x97091,x97092),f868(x97093,x97094),f262(x97091,x97093,x97092,x97094,x97095,x97096)),f249(f869(f868(x97091,x97092),a852))),f249(f869(f868(x97093,x97094),a852)))
% 11.41/11.19 [9771]~P26(x97713,x97714,x97715,f784(x97716,f703(x97716,x97715,x97714,x97713,x97712,x97711)))+P26(x97713,x97714,x97715,f784(f784(f55(x97712,f869(x97713,a852)),x97711),x97716))+E(x97711,f187(f869(x97712,a852)))
% 11.41/11.19 [9829]P26(x98296,x98295,x98294,f784(f784(f55(x98292,f869(x98296,a852)),x98291),x98293))+E(x98291,f187(f869(x98292,a852)))+P85(f784(f784(f347(x98292),f703(x98293,x98294,x98295,x98296,x98292,x98291)),x98291))
% 11.41/11.19 [9837]P85(f784(f784(f347(x98371),f632(x98372,x98373,x98374,x98375,x98376,x98371)),x98376))+P85(f784(f784(f242(f869(f868(x98371,x98374),a852)),f784(f784(f258(x98371,x98374),x98376),x98373)),f784(f784(f258(x98371,x98374),x98375),x98372)))+~P85(f784(f784(f242(f869(x98371,a852)),x98376),x98375))
% 11.41/11.19 [9958]~P85(f784(f784(f242(f869(x99582,a852)),f784(x99584,f632(x99586,x99584,x99582,x99585,x99583,x99581))),f784(x99586,f632(x99586,x99584,x99582,x99585,x99583,x99581))))+~P85(f784(f784(f242(f869(x99581,a852)),x99583),x99585))+P85(f784(f784(f242(f869(f868(x99581,x99582),a852)),f784(f784(f258(x99581,x99582),x99583),x99584)),f784(f784(f258(x99581,x99582),x99585),x99586)))
% 11.41/11.19 [7700]~P85(f784(x77001,x77005))+~P85(f784(x77006,x77004))+P85(f784(x77001,f784(f260(x77002,x77003),f784(f784(f251(x77002,x77003),x77004),x77005))))
% 11.41/11.19 [7701]~P85(f784(x77011,x77014))+~P85(f784(x77016,x77015))+P85(f784(x77011,f784(f250(x77012,x77013),f784(f784(f251(x77012,x77013),x77014),x77015))))
% 11.41/11.19 [7755]~P85(f784(f784(x77554,x77556),x77555))+~P85(f784(f784(f347(x77551),x77556),x77553))+P85(f784(f784(f784(f54(x77551,f869(x77552,a852)),x77553),x77554),x77555))
% 11.41/11.19 [7756]~P85(f784(f784(x77564,x77566),x77565))+~P85(f784(f784(f347(x77561),x77566),x77563))+P85(f784(f784(f784(f54(x77561,f869(x77562,a852)),x77563),x77564),x77565))
% 11.41/11.19 [7789]~E(f784(f188(f860(x77891)),x77893),f784(f188(f860(x77894)),x77895))+~E(f784(f172(x77891,x77894,f784(f784(f173(x77891,x77894),x77893),x77895)),x77892),f784(f237(x77894),x77896))+P85(f784(f784(f347(x77891),x77892),f784(f164(x77891),x77893)))
% 11.41/11.19 [8056]~P85(f784(f784(f347(x80561),x80562),f784(x80565,x80566)))+~P85(f784(f784(f347(x80563),x80566),x80564))+P85(f784(f784(f347(x80561),x80562),f784(f784(f54(x80563,f869(x80561,a852)),x80564),x80565)))
% 11.41/11.19 [8057]~P85(f784(f784(f347(x80571),x80572),f784(x80575,x80576)))+~P85(f784(f784(f347(x80573),x80576),x80574))+P85(f784(f784(f347(x80571),x80572),f784(f784(f54(x80573,f869(x80571,a852)),x80574),x80575)))
% 11.41/11.19 [8096]P85(f784(f784(x80961,x80962),x80963))+~P85(f784(f784(x80964,x80962),x80963))+~P85(f784(f784(f242(f869(x80965,f869(x80966,a852))),x80964),x80961))
% 11.41/11.19 [8097]P85(f784(f784(x80971,x80972),x80973))+~P85(f784(f784(x80974,x80972),x80973))+~P85(f784(f784(f242(f869(x80975,f869(x80976,a852))),x80974),x80971))
% 11.41/11.19 [8233]P85(f784(f784(x82331,x82332),x82333))+~P85(f784(f784(f347(x82334),x82332),x82335))+~P85(f784(f784(f784(f55(x82334,f869(x82336,a852)),x82335),x82331),x82333))
% 11.41/11.19 [8234]P85(f784(f784(x82341,x82342),x82343))+~P85(f784(f784(f347(x82344),x82342),x82345))+~P85(f784(f784(f784(f55(x82344,f869(x82346,a852)),x82345),x82341),x82343))
% 11.41/11.19 [8235]P85(f784(f784(x82351,x82352),x82353))+~P85(f784(f784(f347(x82354),x82352),x82355))+~P85(f784(f784(f784(f55(x82354,f869(x82356,a852)),x82355),x82351),x82353))
% 11.41/11.19 [8372]P85(f784(f784(f347(x83721),x83722),f784(x83723,x83724)))+~P85(f784(f784(f347(x83725),x83724),x83726))+~P85(f784(f784(f347(x83721),x83722),f784(f784(f55(x83725,f869(x83721,a852)),x83726),x83723)))
% 11.41/11.19 [8373]P85(f784(f784(f347(x83731),x83732),f784(x83733,x83734)))+~P85(f784(f784(f347(x83735),x83734),x83736))+~P85(f784(f784(f347(x83731),x83732),f784(f784(f55(x83735,f869(x83731,a852)),x83736),x83733)))
% 11.41/11.19 [8374]P85(f784(f784(f347(x83741),x83742),f784(x83743,x83744)))+~P85(f784(f784(f347(x83745),x83744),x83746))+~P85(f784(f784(f347(x83741),x83742),f784(f784(f55(x83745,f869(x83741,a852)),x83746),x83743)))
% 11.41/11.19 [8619]~P13(x86194,x86195,x86196,x86191)+E(f784(x86191,x86192),f784(x86191,x86193))+~P85(f784(f784(f347(f868(x86194,x86194)),f784(f784(f251(x86194,x86194),x86192),x86193)),x86196))
% 11.41/11.19 [8650]P85(f784(f784(f242(f869(x86501,a852)),x86502),f784(x86503,x86504)))+~P85(f784(f784(f347(x86505),x86504),x86506))+~P85(f784(f784(f242(f869(x86501,a852)),x86502),f784(f784(f55(x86505,f869(x86501,a852)),x86506),x86503)))
% 11.41/11.19 [8675]~P52(x86753,x86754,f784(f288(x86754,x86753),x86755))+E(x86751,f187(f869(x86752,a852)))+E(f784(f784(f55(x86752,f869(x86753,a852)),x86751),f784(f784(f10(f869(x86754,a852),f869(x86753,a852),x86752),f287(x86754,x86753,x86755)),x86756)),f784(f287(x86754,x86753,x86755),f784(f784(f55(x86752,f869(x86754,a852)),x86751),x86756)))
% 11.41/11.19 [8746]P85(f784(f784(f347(x87461),x87462),f784(f287(x87463,x87461,x87464),x87465)))+~P85(f784(f784(f347(x87463),x87466),x87465))+~P85(f784(f784(f347(f868(x87463,x87461)),f784(f784(f251(x87463,x87461),x87466),x87462)),x87464))
% 11.41/11.19 [8747]P85(f784(f784(f347(x87471),x87472),f784(f287(x87473,x87471,x87474),x87475)))+~P85(f784(f784(f347(x87473),x87476),x87475))+~P85(f784(f784(f347(f868(x87473,x87471)),f784(f784(f251(x87473,x87471),x87476),x87472)),x87474))
% 11.41/11.19 [9026]P85(f784(f784(f242(f869(x90261,a852)),f784(f287(x90262,x90261,x90263),x90264)),f784(f287(x90262,x90261,x90265),x90266)))+~P85(f784(f784(f242(f869(x90262,a852)),x90264),x90266))+~P85(f784(f784(f242(f869(f868(x90262,x90261),a852)),x90263),x90265))
% 11.41/11.19 [9183]~P85(f784(f784(f347(x91832),x91836),x91834))+~P85(f784(f784(f242(f869(x91831,a852)),x91833),x91835))+P85(f784(f784(f242(f869(f868(x91831,x91832),a852)),f784(f784(f258(x91831,x91832),x91833),f784(f18(f869(x91832,a852),x91831),x91834))),f784(f784(f258(x91831,x91832),x91835),f784(f18(f869(x91832,a852),x91831),x91834))))
% 11.41/11.19 [9330]~E(x93303,x93305)+P85(f784(f784(f347(f868(f860(x93301),f860(x93301))),f784(f784(f251(f860(x93301),f860(x93301)),f784(f784(f144(x93301),x93302),x93303)),f784(f784(f144(x93301),x93304),x93305))),f149(x93301,x93306)))+~P85(f784(f784(f347(f868(x93301,x93301)),f784(f784(f251(x93301,x93301),x93302),x93304)),x93306))
% 11.41/11.19 [9335]~E(f784(f188(f860(x93351)),x93355),f784(f188(f860(x93352)),x93356))+E(f178(x93351,x93352,f179(x93351,x93352,x93353,f784(f784(f3(f869(x93351,a852)),x93354),f784(f164(x93351),x93355))),x93355,x93356),f179(x93351,x93352,f178(x93351,x93352,x93353,x93355,x93356),x93354))+~P85(f784(f784(f242(f869(x93351,a852)),f784(f164(x93351),x93355)),x93354))
% 11.41/11.19 [9336]~E(f784(f188(f860(x93361)),x93363),f784(f188(f860(x93361)),x93365))+P85(f784(f784(f347(f868(f860(x93361),f860(x93361))),f784(f784(f251(f860(x93361),f860(x93361)),f784(f784(f144(x93361),x93362),x93363)),f784(f784(f144(x93361),x93364),x93365))),f139(x93361,x93366)))+~P85(f784(f784(f347(f868(x93361,x93361)),f784(f784(f251(x93361,x93361),x93362),x93364)),x93366))
% 11.41/11.19 [9363]P85(f784(f784(f347(f868(x93631,x93631)),f784(f784(f251(x93631,x93631),x93632),x93633)),f784(f784(f180(f868(x93631,x93631),a852),f784(a160,x93634)),x93635)))+~P85(f784(f784(f347(f868(x93631,x93631)),f784(f784(f251(x93631,x93631),x93636),x93633)),x93635))+~P85(f784(f784(f347(f868(x93631,x93631)),f784(f784(f251(x93631,x93631),x93632),x93636)),f784(f784(f180(f868(x93631,x93631),a852),x93634),x93635)))
% 11.41/11.19 [9364]P85(f784(f784(f347(f868(x93641,x93641)),f784(f784(f251(x93641,x93641),x93642),x93643)),f784(f784(f180(f868(x93641,x93641),a852),f784(a160,x93644)),x93645)))+~P85(f784(f784(f347(f868(x93641,x93641)),f784(f784(f251(x93641,x93641),x93642),x93646)),x93645))+~P85(f784(f784(f347(f868(x93641,x93641)),f784(f784(f251(x93641,x93641),x93646),x93643)),f784(f784(f180(f868(x93641,x93641),a852),x93644),x93645)))
% 11.41/11.19 [9367]~P85(f784(f784(f347(x93674),x93675),x93676))+P85(f784(f784(f242(f869(x93671,a852)),x93672),x93673))+~P85(f784(f784(f242(f869(f868(x93671,x93674),a852)),f784(f784(f258(x93671,x93674),x93672),f784(f18(f869(x93674,a852),x93671),x93676))),f784(f784(f258(x93671,x93674),x93673),f784(f18(f869(x93674,a852),x93671),x93676))))
% 11.41/11.19 [9408]E(x94081,x94082)+~P85(f784(f784(f347(f868(f860(x94083),f860(x94083))),f784(f784(f251(f860(x94083),f860(x94083)),f784(f784(f144(x94083),x94081),x94085)),f784(f784(f144(x94083),x94082),x94086))),f139(x94083,x94084)))+P85(f784(f784(f347(f868(x94083,x94083)),f784(f784(f251(x94083,x94083),x94081),x94082)),x94084))
% 11.41/11.19 [9409]E(x94091,x94092)+~P85(f784(f784(f347(f868(f860(x94093),f860(x94093))),f784(f784(f251(f860(x94093),f860(x94093)),f784(f784(f144(x94093),x94091),x94095)),f784(f784(f144(x94093),x94092),x94096))),f141(x94093,x94094)))+P85(f784(f784(f347(f868(x94093,x94093)),f784(f784(f251(x94093,x94093),x94091),x94092)),x94094))
% 11.41/11.19 [9410]E(x94101,x94102)+~P85(f784(f784(f347(f868(f860(x94103),f860(x94103))),f784(f784(f251(f860(x94103),f860(x94103)),f784(f784(f144(x94103),x94101),x94105)),f784(f784(f144(x94103),x94102),x94106))),f149(x94103,x94104)))+P85(f784(f784(f347(f868(x94103,x94103)),f784(f784(f251(x94103,x94103),x94101),x94102)),x94104))
% 11.41/11.19 [9444]P85(f784(f784(f347(f868(f860(x94441),f860(x94441))),f784(f784(f251(f860(x94441),f860(x94441)),f784(f784(f144(x94441),x94442),x94443)),f784(f784(f144(x94441),x94444),x94445))),f150(x94441,x94446)))+~P85(f784(f784(f347(f868(f860(x94441),f860(x94441))),f784(f784(f251(f860(x94441),f860(x94441)),x94443),x94445)),f150(x94441,x94446)))+~P85(f784(f784(f347(f868(x94441,x94441)),f784(f784(f251(x94441,x94441),x94442),x94444)),x94446))
% 11.41/11.19 [9466]P85(f784(x94661,x94662))+~P85(f784(x94661,f401(x94661,x94663,x94664,x94665,x94666)))+~P85(f784(f784(f347(x94666),x94662),f784(f784(f54(x94665,f869(x94666,a852)),x94664),x94663)))
% 11.41/11.19 [9471]~P85(f784(f784(f347(f868(f860(x94711),f860(x94711))),f784(f784(f251(f860(x94711),f860(x94711)),f784(f784(f144(x94711),x94712),x94715)),f784(f784(f144(x94711),x94713),x94716))),f139(x94711,x94714)))+P85(f784(f784(f347(f868(f860(x94711),f860(x94711))),f784(f784(f251(f860(x94711),f860(x94711)),x94715),x94716)),f139(x94711,x94714)))+P85(f784(f784(f347(f868(x94711,x94711)),f784(f784(f251(x94711,x94711),x94712),x94713)),x94714))
% 11.41/11.19 [9472]~P85(f784(f784(f347(f868(f860(x94721),f860(x94721))),f784(f784(f251(f860(x94721),f860(x94721)),f784(f784(f144(x94721),x94722),x94725)),f784(f784(f144(x94721),x94723),x94726))),f141(x94721,x94724)))+P85(f784(f784(f347(f868(f860(x94721),f860(x94721))),f784(f784(f251(f860(x94721),f860(x94721)),x94725),x94726)),f141(x94721,x94724)))+P85(f784(f784(f347(f868(x94721,x94721)),f784(f784(f251(x94721,x94721),x94722),x94723)),x94724))
% 11.41/11.19 [9473]~P85(f784(f784(f347(f868(f860(x94731),f860(x94731))),f784(f784(f251(f860(x94731),f860(x94731)),f784(f784(f144(x94731),x94732),x94735)),f784(f784(f144(x94731),x94733),x94736))),f149(x94731,x94734)))+P85(f784(f784(f347(f868(f860(x94731),f860(x94731))),f784(f784(f251(f860(x94731),f860(x94731)),x94735),x94736)),f149(x94731,x94734)))+P85(f784(f784(f347(f868(x94731,x94731)),f784(f784(f251(x94731,x94731),x94732),x94733)),x94734))
% 11.41/11.19 [9551]P85(f784(x95511,x95512))+P85(f784(f784(f347(x95513),f402(x95511,x95514,x95515,x95513,x95516)),x95515))+~P85(f784(f784(f347(x95516),x95512),f784(f784(f54(x95513,f869(x95516,a852)),x95515),x95514)))
% 11.41/11.19 [9557]~E(x95572,x95574)+P85(f784(f784(f347(f868(f860(x95571),f860(x95571))),f784(f784(f251(f860(x95571),f860(x95571)),f784(f784(f130(x95571),x95572),f784(f784(f144(x95571),x95573),f120(x95571)))),f784(f784(f130(x95571),x95574),f784(f784(f144(x95571),x95575),f120(x95571))))),f149(x95571,x95576)))+~P85(f784(f784(f347(f868(x95571,x95571)),f784(f784(f251(x95571,x95571),x95573),x95575)),x95576))
% 11.41/11.19 [9644]E(x96441,x96442)+~P85(f784(f784(f347(f868(f860(x96443),f860(x96443))),f784(f784(f251(f860(x96443),f860(x96443)),f784(f784(f130(x96443),x96445),f784(f784(f144(x96443),x96441),f120(x96443)))),f784(f784(f130(x96443),x96446),f784(f784(f144(x96443),x96442),f120(x96443))))),f149(x96443,x96444)))+P85(f784(f784(f347(f868(x96443,x96443)),f784(f784(f251(x96443,x96443),x96441),x96442)),x96444))
% 11.41/11.19 [9669]~P85(f784(f784(f347(f868(f860(x96691),f860(x96691))),f784(f784(f251(f860(x96691),f860(x96691)),f784(f784(f130(x96691),x96695),f784(f784(f144(x96691),x96692),f120(x96691)))),f784(f784(f130(x96691),x96696),f784(f784(f144(x96691),x96693),f120(x96691))))),f149(x96691,x96694)))+P85(f784(f784(f347(f868(f860(x96691),f860(x96691))),f784(f784(f251(f860(x96691),f860(x96691)),x96695),x96696)),f149(x96691,x96694)))+P85(f784(f784(f347(f868(x96691,x96691)),f784(f784(f251(x96691,x96691),x96692),x96693)),x96694))
% 11.41/11.19 [9681]P85(f784(x96811,x96812))+P85(f784(f784(f347(x96813),f401(x96811,x96814,x96815,x96816,x96813)),f784(x96814,f402(x96811,x96814,x96815,x96816,x96813))))+~P85(f784(f784(f347(x96813),x96812),f784(f784(f54(x96816,f869(x96813,a852)),x96815),x96814)))
% 11.41/11.19 [8760]~P17(x87603,x87604,x87601)+~P85(f784(f71(x87603),x87606))+E(f784(f784(x87601,x87602),f784(f784(f74(x87603,x87604,x87601),x87605),f784(f784(f3(f869(x87603,a852)),x87606),f784(f784(f312(x87603),x87602),f187(f869(x87603,a852)))))),f784(f784(f74(x87603,x87604,x87601),x87605),f784(f784(f312(x87603),x87602),x87606)))
% 11.41/11.19 [8859]~E(f784(f172(x88591,x88592,x88594),x88595),f784(f237(x88592),x88596))+~P85(f784(f784(x88593,x88595),x88596))+E(f784(f172(x88591,x88592,f784(f131(f868(x88591,x88592),f784(f261(x88591,x88592,a852),x88593)),x88594)),x88595),f784(f237(x88592),x88596))
% 11.41/11.19 [9032]~P85(f784(f784(f347(x90325),x90323),x90326))+P85(f784(f784(f242(f869(x90321,a852)),f784(x90322,x90323)),x90324))+~P85(f784(f784(f242(f869(x90321,a852)),f784(f784(f54(x90325,f869(x90321,a852)),x90326),x90322)),x90324))
% 11.41/11.19 [9620]~P9(x96201,x96205,x96204)+P85(f784(f784(f347(f868(x96201,x96201)),f784(f784(f251(x96201,x96201),x96202),x96203)),x96204))+~P85(f784(f784(f347(x96201),x96206),f784(f784(f111(f869(x96201,a852)),f784(f287(x96201,x96201,x96204),f784(f784(f312(x96201),x96202),f187(f869(x96201,a852))))),f784(f287(x96201,x96201,x96204),f784(f784(f312(x96201),x96203),f187(f869(x96201,a852)))))))
% 11.41/11.19 [8529]~P123(x85292)+~E(f784(f784(f89(x85292),f784(f784(f90(x85292),x85294),x85295)),x85291),f784(f784(f89(x85292),f784(f784(f90(x85292),x85293),x85295)),x85296))+E(x85291,f784(f784(f89(x85292),f784(f784(f90(x85292),f784(f784(f3(x85292),x85293),x85294)),x85295)),x85296))
% 11.41/11.19 [8530]~P123(x85301)+~E(f784(f784(f89(x85301),f784(f784(f90(x85301),x85302),x85304)),x85305),f784(f784(f89(x85301),f784(f784(f90(x85301),x85303),x85304)),x85306))+E(f784(f784(f89(x85301),f784(f784(f90(x85301),f784(f784(f3(x85301),x85302),x85303)),x85304)),x85305),x85306)
% 11.41/11.19 [8678]~P123(x86781)+E(f784(f784(f89(x86781),f784(f784(f90(x86781),x86782),x86783)),x86784),f784(f784(f89(x86781),f784(f784(f90(x86781),x86785),x86783)),x86786))+~E(x86786,f784(f784(f89(x86781),f784(f784(f90(x86781),f784(f784(f3(x86781),x86782),x86785)),x86783)),x86784))
% 11.41/11.19 [8679]~P123(x86791)+E(f784(f784(f89(x86791),f784(f784(f90(x86791),x86792),x86793)),x86794),f784(f784(f89(x86791),f784(f784(f90(x86791),x86795),x86793)),x86796))+~E(f784(f784(f89(x86791),f784(f784(f90(x86791),f784(f784(f3(x86791),x86792),x86795)),x86793)),x86794),x86796)
% 11.41/11.19 [8971]~P85(f784(f784(x89714,x89715),x89716))+~P85(f784(f784(x89713,x89715),x89716))+P85(f784(f784(f784(f784(f111(f869(x89711,f869(x89712,a852))),x89713),x89714),x89715),x89716))
% 11.41/11.19 [9201]P85(f784(f784(x92011,x92012),x92013))+P85(f784(f784(x92014,x92012),x92013))+~P85(f784(f784(f784(f784(f110(f869(x92015,f869(x92016,a852))),x92014),x92011),x92012),x92013))
% 11.41/11.19 [9488]~P131(x94881)+~P85(f784(f784(f243(x94881),f784(f784(f89(x94881),f784(f784(f90(x94881),x94884),x94885)),x94882)),f784(f784(f89(x94881),f784(f784(f90(x94881),x94883),x94885)),x94886)))+P85(f784(f784(f243(x94881),x94882),f784(f784(f89(x94881),f784(f784(f90(x94881),f784(f784(f3(x94881),x94883),x94884)),x94885)),x94886)))
% 11.41/11.19 [9489]~P131(x94891)+~P85(f784(f784(f242(x94891),f784(f784(f89(x94891),f784(f784(f90(x94891),x94894),x94895)),x94892)),f784(f784(f89(x94891),f784(f784(f90(x94891),x94893),x94895)),x94896)))+P85(f784(f784(f242(x94891),x94892),f784(f784(f89(x94891),f784(f784(f90(x94891),f784(f784(f3(x94891),x94893),x94894)),x94895)),x94896)))
% 11.41/11.19 [9507]~P131(x95071)+P85(f784(f784(f243(x95071),f784(f784(f89(x95071),f784(f784(f90(x95071),x95072),x95073)),x95074)),f784(f784(f89(x95071),f784(f784(f90(x95071),x95075),x95073)),x95076)))+~P85(f784(f784(f243(x95071),x95074),f784(f784(f89(x95071),f784(f784(f90(x95071),f784(f784(f3(x95071),x95075),x95072)),x95073)),x95076)))
% 11.41/11.19 [9508]~P131(x95081)+P85(f784(f784(f242(x95081),f784(f784(f89(x95081),f784(f784(f90(x95081),x95082),x95083)),x95084)),f784(f784(f89(x95081),f784(f784(f90(x95081),x95085),x95083)),x95086)))+~P85(f784(f784(f242(x95081),x95084),f784(f784(f89(x95081),f784(f784(f90(x95081),f784(f784(f3(x95081),x95085),x95082)),x95083)),x95086)))
% 11.41/11.19 [9613]~P131(x96131)+~P85(f784(f784(f243(x96131),f784(f784(f89(x96131),f784(f784(f90(x96131),x96132),x96134)),x96135)),f784(f784(f89(x96131),f784(f784(f90(x96131),x96133),x96134)),x96136)))+P85(f784(f784(f243(x96131),f784(f784(f89(x96131),f784(f784(f90(x96131),f784(f784(f3(x96131),x96132),x96133)),x96134)),x96135)),x96136))
% 11.41/11.19 [9614]~P131(x96141)+~P85(f784(f784(f242(x96141),f784(f784(f89(x96141),f784(f784(f90(x96141),x96142),x96144)),x96145)),f784(f784(f89(x96141),f784(f784(f90(x96141),x96143),x96144)),x96146)))+P85(f784(f784(f242(x96141),f784(f784(f89(x96141),f784(f784(f90(x96141),f784(f784(f3(x96141),x96142),x96143)),x96144)),x96145)),x96146))
% 11.41/11.19 [9654]~P131(x96541)+P85(f784(f784(f243(x96541),f784(f784(f89(x96541),f784(f784(f90(x96541),x96542),x96543)),x96544)),f784(f784(f89(x96541),f784(f784(f90(x96541),x96545),x96543)),x96546)))+~P85(f784(f784(f243(x96541),f784(f784(f89(x96541),f784(f784(f90(x96541),f784(f784(f3(x96541),x96542),x96545)),x96543)),x96544)),x96546))
% 11.41/11.19 [9655]~P131(x96551)+P85(f784(f784(f242(x96551),f784(f784(f89(x96551),f784(f784(f90(x96551),x96552),x96553)),x96554)),f784(f784(f89(x96551),f784(f784(f90(x96551),x96555),x96553)),x96556)))+~P85(f784(f784(f242(x96551),f784(f784(f89(x96551),f784(f784(f90(x96551),f784(f784(f3(x96551),x96552),x96555)),x96553)),x96554)),x96556))
% 11.41/11.19 [9823]~P68(x98232)+~P85(f784(f71(x98231),x98236))+E(f784(f784(f8(x98231,x98232),f784(f784(f20(x98231,x98232,x98232),f784(f784(f20(x98231,x98232,f869(x98232,x98232)),f784(f784(f10(a852,f869(x98232,f869(x98232,x98232)),x98231),f105(x98232)),x98233)),x98234)),x98235)),x98236),f784(f784(f89(x98232),f784(f784(f8(x98231,x98232),x98234),f784(f784(f111(f869(x98231,a852)),x98236),f784(f266(x98231),x98233)))),f784(f784(f8(x98231,x98232),x98235),f784(f784(f111(f869(x98231,a852)),x98236),f784(f88(f869(x98231,a852)),f784(f266(x98231),x98233))))))
% 11.41/11.19 [9889]P85(f784(f784(f347(x98892),x98894),x98896))+P85(f784(f784(f347(x98892),x98895),x98896))+E(f784(f315(x98891,x98892,f784(f784(f9(x98891,x98892,x98892),f784(f784(f9(x98891,x98892,f869(x98892,x98892)),f784(f784(f10(a852,f869(x98892,f869(x98892,x98892)),x98891),f105(x98892)),f784(f784(f9(x98891,f869(x98891,a852),a852),f347(x98891)),x98893))),x98894)),x98895)),x98896),f187(f869(x98891,a852)))
% 11.41/11.19 [9890]P85(f784(f784(f347(x98902),x98905),x98906))+~P85(f784(f784(f347(x98902),x98904),x98906))+E(f784(f315(x98901,x98902,f784(f784(f9(x98901,x98902,x98902),f784(f784(f9(x98901,x98902,f869(x98902,x98902)),f784(f784(f10(a852,f869(x98902,f869(x98902,x98902)),x98901),f105(x98902)),f784(f784(f9(x98901,f869(x98901,a852),a852),f347(x98901)),x98903))),x98904)),x98905)),x98906),x98903)
% 11.41/11.19 [9891]P85(f784(f784(f347(x98912),x98914),x98916))+~P85(f784(f784(f347(x98912),x98915),x98916))+E(f784(f315(x98911,x98912,f784(f784(f9(x98911,x98912,x98912),f784(f784(f9(x98911,x98912,f869(x98912,x98912)),f784(f784(f10(a852,f869(x98912,f869(x98912,x98912)),x98911),f105(x98912)),f784(f784(f9(x98911,f869(x98911,a852),a852),f347(x98911)),x98913))),x98914)),x98915)),x98916),f784(f88(f869(x98911,a852)),x98913))
% 11.41/11.19 [9892]~P85(f784(f784(f347(x98922),x98924),x98926))+~P85(f784(f784(f347(x98922),x98925),x98926))+E(f784(f315(x98921,x98922,f784(f784(f9(x98921,x98922,x98922),f784(f784(f9(x98921,x98922,f869(x98922,x98922)),f784(f784(f10(a852,f869(x98922,f869(x98922,x98922)),x98921),f105(x98922)),f784(f784(f9(x98921,f869(x98921,a852),a852),f347(x98921)),x98923))),x98924)),x98925)),x98926),f249(f869(x98921,a852)))
% 11.41/11.19 [8554]E(x85541,x85542)+~P54(x85544,x85545,x85543,x85546,x85547)+~E(f784(x85543,x85541),f784(x85543,x85542))
% 11.41/11.19 [6937]E(f784(f239(f864(x69371),x69372,f190(x69371),x69373),f784(x69374,x69375)),f784(f237(x69371),x69376))+~E(f784(x69374,x69375),f784(f237(x69372),x69377))+~E(f784(x69373,x69377),f784(f237(x69371),x69376))
% 11.41/11.19 [8575]~P12(x85756,x85755,x85757,x85754,x85751)+E(f784(f784(x85751,x85752),x85753),x85754)+P85(f784(f71(x85755),x85753))
% 11.41/11.19 [8576]~P12(x85766,x85765,x85767,x85764,x85761)+E(f784(f784(x85761,x85762),x85763),x85764)+P85(f784(f71(x85765),x85763))
% 11.41/11.19 [9355]P40(x93551,x93552,x93553,x93554,x93555,f784(f784(x93553,x93556),x93557))+~E(f784(f784(x93553,x93556),x93557),x93554)+~E(x93555,f187(f869(x93551,a852)))
% 11.41/11.19 [9527]~P85(f784(x95276,x95273))+~P85(f784(f784(f347(f868(x95272,x95272)),f784(f784(f251(x95272,x95272),x95274),x95275)),f784(x95277,x95273)))+P85(f784(f784(f347(f868(f868(x95271,x95272),f868(x95271,x95272))),f784(f784(f251(f868(x95271,x95272),f868(x95271,x95272)),f784(f784(f251(x95271,x95272),x95273),x95274)),f784(f784(f251(x95271,x95272),x95273),x95275))),f285(x95271,x95272,x95276,x95277)))
% 11.41/11.19 [9707]~P26(x97073,x97071,x97074,f249(f869(x97073,a852)))+E(f784(f172(x97071,x97072,f784(f784(f146(f868(x97073,x97072),f868(x97071,x97072)),f784(f261(x97073,x97072,f868(x97071,x97072)),f784(f784(f10(x97071,f869(x97072,f868(x97071,x97072)),x97073),f251(x97071,x97072)),x97074))),x97075)),f784(x97074,x97076)),f784(f237(x97072),x97077))+~E(f784(f172(x97073,x97072,x97075),x97076),f784(f237(x97072),x97077))
% 11.41/11.19 [9943]~P40(x99432,x99437,x99433,x99436,x99431,f784(f784(x99433,x99435),x99434))+E(f784(f784(x99433,f460(x99434,x99435,x99431,x99436,x99433,x99437,x99432)),f461(x99434,x99435,x99431,x99436,x99433,x99437,x99432)),f784(f784(x99433,x99435),x99434))+E(x99431,f187(f869(x99432,a852)))
% 11.41/11.19 [9944]~P40(x99447,x99446,x99441,x99444,x99445,f784(f784(x99441,x99442),x99443))+E(f784(f784(x99441,f460(x99443,x99442,x99445,x99444,x99441,x99446,x99447)),f461(x99443,x99442,x99445,x99444,x99441,x99446,x99447)),f784(f784(x99441,x99442),x99443))+E(f784(f784(x99441,x99442),x99443),x99444)
% 11.41/11.19 [8582]~P38(x85823,f784(f784(f784(a196,x85824),f42(x85821)),f784(x85822,x85824)),x85825,x85827)+P38(f34(x85821,x85822,x85823),x85824,x85825,f784(f784(f784(a196,x85826),f42(x85821)),f784(f784(a197,x85824),x85821)))+~E(f784(f784(f784(a196,x85826),f42(x85821)),f784(f784(a197,x85824),x85821)),f784(f784(f784(a196,x85827),f42(x85821)),f784(f784(a197,x85824),x85821)))
% 11.41/11.19 [9271]~P38(f784(a29,x92712),f784(f784(f784(a196,f784(f784(a198,x92714),a199)),f42(a28)),f784(x92713,x92714)),x92715,x92717)+P38(f33(x92711,x92712,x92713),x92714,x92715,f784(f784(f784(a196,f784(f784(a198,x92716),f784(a197,x92714))),x92711),f784(f784(a197,x92716),a27)))+~E(f784(f784(f784(a196,f784(f784(a198,x92716),f784(a197,x92714))),x92711),f784(f784(a197,x92716),a27)),f784(f784(f784(a196,f784(f784(a198,x92717),f784(a197,x92714))),x92711),f784(f784(a197,x92717),a27)))
% 11.41/11.19 [9598]~P85(f784(f76(x95981,x95984,x95985,x95986,x95983),x95987))+P85(f784(f76(x95981,x95984,x95985,x95986,f784(f784(f312(x95981),x95982),x95983)),f784(f784(x95985,x95982),x95987)))+P85(f784(f784(f347(x95981),x95982),x95983))
% 11.41/11.19 [9970]~P40(x99702,x99707,x99706,x99705,x99701,f784(f784(x99706,x99704),x99703))+E(x99701,f187(f869(x99702,a852)))+P85(f784(f784(f347(x99702),f460(x99703,x99704,x99701,x99705,x99706,x99707,x99702)),x99701))
% 11.41/11.19 [9971]~P40(x99715,x99717,x99711,x99714,x99716,f784(f784(x99711,x99712),x99713))+E(f784(f784(x99711,x99712),x99713),x99714)+P85(f784(f784(f347(x99715),f460(x99713,x99712,x99716,x99714,x99711,x99717,x99715)),x99716))
% 11.41/11.19 [6718]~E(x67185,x67187)+~E(x67186,x67184)+E(f784(f784(f784(f784(f81(x67181,f864(x67182)),x67183),x67184),f784(f237(x67182),x67185)),x67186),f784(f237(x67182),x67187))
% 11.41/11.19 [6853]E(x68531,x68532)+~E(f784(x68535,x68531),f784(f237(x68534),x68537))+E(f784(f784(f784(f784(f81(x68533,f864(x68534)),x68535),x68532),f784(f237(x68534),x68536)),x68531),f784(f237(x68534),x68537))
% 11.41/11.19 [7594]E(x75941,x75942)+~E(x75943,x75944)+~E(f784(f784(f784(f784(f81(x75945,f864(x75946)),x75947),x75944),f784(f237(x75946),x75941)),x75943),f784(f237(x75946),x75942))
% 11.41/11.19 [7659]E(x76591,x76592)+E(f784(x76593,x76594),f784(f237(x76595),x76591))+~E(f784(f784(f784(f784(f81(x76596,f864(x76595)),x76593),x76597),f784(f237(x76595),x76592)),x76594),f784(f237(x76595),x76591))
% 11.41/11.19 [7660]E(x76601,x76602)+E(f784(x76603,x76601),f784(f237(x76604),x76605))+~E(f784(f784(f784(f784(f81(x76606,f864(x76604)),x76603),x76602),f784(f237(x76604),x76607)),x76601),f784(f237(x76604),x76605))
% 11.41/11.19 [8781]~P22(x87814,x87815,x87816,x87817,x87811)+~P85(f784(f71(x87815),x87813))+E(f784(f784(x87811,x87812),x87813),f784(f784(f784(f75(x87814,x87815,x87816),x87812),x87817),x87813))
% 11.41/11.19 [8782]~P12(x87824,x87825,x87826,x87827,x87821)+~P85(f784(f71(x87825),x87823))+E(f784(f784(x87821,x87822),x87823),f784(f784(f784(f75(x87824,x87825,x87826),x87822),x87827),x87823))
% 11.41/11.19 [9323]~P25(x93231,x93232,f784(f784(f312(f858(x93231)),f784(f784(f784(f100(x93231),x93233),x93234),x93237)),f187(f869(f858(x93231),a852))))+P25(x93231,x93232,f784(f784(f312(f858(x93231)),f784(f784(f784(f100(x93231),x93233),f38(x93234,x93235)),x93236)),f187(f869(f858(x93231),a852))))+~P25(x93231,x93232,f784(f784(f312(f858(x93231)),f784(f784(f784(f100(x93231),x93237),x93235),x93236)),f187(f869(f858(x93231),a852))))
% 11.41/11.19 [9502]~P24(x95023,x95024,x95025,x95027,x95026,x95021)+~P85(f784(f71(x95024),x95022))+E(f784(x95021,x95022),f784(f784(f784(f75(x95023,x95024,x95025),x95026),x95027),x95022))
% 11.41/11.19 [9649]P40(x96491,x96492,x96493,x96494,x96495,f784(f784(x96493,x96496),x96497))+~P40(x96491,x96492,x96493,x96494,f784(f784(f3(f869(x96491,a852)),x96495),f784(f784(f312(x96491),x96496),f187(f869(x96491,a852)))),x96497)+~P85(f784(f784(f347(x96491),x96496),x96495))
% 11.41/11.19 [9918]~P25(x99181,x99182,f784(f784(f312(f858(x99181)),f784(f784(f784(f100(x99181),f101(x99181,x99183,x99184)),x99185),x99187)),f187(f869(f858(x99181),a852))))+P25(x99181,x99182,f784(f784(f312(f858(x99181)),f784(f784(f784(f100(x99181),x99183),f35(x99184,x99185,x99186)),x99187)),f187(f869(f858(x99181),a852))))+~P25(x99181,x99182,f784(f784(f312(f858(x99181)),f784(f784(f784(f100(x99181),f101(x99181,x99183,f784(f82(a852,a852,a857,a341),x99184))),x99186),x99187)),f187(f869(f858(x99181),a852))))
% 11.41/11.19 [9988]P85(f784(f784(x99887,f844(x99884,x99885,x99881,x99886,x99883,x99882,x99887)),f845(x99884,x99885,x99881,x99886,x99883,x99882,x99887)))+~P85(f784(f784(x99887,f784(f260(x99882,x99883),x99886)),f784(f250(x99882,x99883),x99886)))+P85(f784(x99881,f784(f784(f261(x99882,x99883,x99884),x99885),x99886)))
% 11.41/11.19 [9997]~P40(x99972,x99973,x99974,x99975,x99971,f784(f784(x99974,x99977),x99976))+P40(x99972,x99973,x99974,x99975,f784(f784(f3(f869(x99972,a852)),x99971),f784(f784(f312(x99972),f460(x99976,x99977,x99971,x99975,x99974,x99973,x99972)),f187(f869(x99972,a852)))),f461(x99976,x99977,x99971,x99975,x99974,x99973,x99972))+E(x99971,f187(f869(x99972,a852)))
% 11.41/11.19 [9998]~P40(x99985,x99986,x99981,x99984,x99987,f784(f784(x99981,x99982),x99983))+P40(x99985,x99986,x99981,x99984,f784(f784(f3(f869(x99985,a852)),x99987),f784(f784(f312(x99985),f460(x99983,x99982,x99987,x99984,x99981,x99986,x99985)),f187(f869(x99985,a852)))),f461(x99983,x99982,x99987,x99984,x99981,x99986,x99985))+E(f784(f784(x99981,x99982),x99983),x99984)
% 11.41/11.19 [10017]~P85(f784(x100171,f784(f784(x100175,f845(x100174,x100175,x100171,x100176,x100173,x100172,x100177)),f844(x100174,x100175,x100171,x100176,x100173,x100172,x100177))))+~P85(f784(f784(x100177,f784(f260(x100172,x100173),x100176)),f784(f250(x100172,x100173),x100176)))+P85(f784(x100171,f784(f784(f261(x100172,x100173,x100174),x100175),x100176)))
% 11.41/11.19 [9074]E(f178(x90741,x90742,x90743,x90744,f784(f784(f151(x90742,x90745),x90746),x90747)),f178(x90741,x90742,x90743,x90744,x90745))+~P85(f784(f784(f243(a859),x90746),f784(f188(f860(x90742)),x90745)))+~P85(f784(f784(f242(a859),f784(f188(f860(x90741)),x90744)),x90746))
% 11.41/11.19 [9344]P85(f784(f784(f242(f869(f868(x93441,x93442),a852)),f784(f784(f291(x93441,x93443,x93442),x93444),x93445)),f784(f784(f291(x93441,x93443,x93442),x93446),x93447)))+~P85(f784(f784(f242(f869(f868(x93443,x93442),a852)),x93445),x93447))+~P85(f784(f784(f242(f869(f868(x93441,x93443),a852)),x93444),x93446))
% 11.41/11.19 [9660]~P85(f784(f784(f347(x96601),x96606),x96605))+P85(f784(f76(x96601,x96602,x96603,x96604,x96605),f784(f784(x96603,x96606),x96607)))+~P85(f784(f76(x96601,x96602,x96603,x96604,f784(f784(f3(f869(x96601,a852)),x96605),f784(f784(f312(x96601),x96606),f187(f869(x96601,a852))))),x96607))
% 11.41/11.19 [10048]~P139(x100481)+~P26(f868(x100482,x100483),x100481,f784(f261(x100482,x100483,x100481),f784(f784(f9(x100482,f869(x100483,x100481),f869(x100483,x100481)),f784(f784(f10(f869(x100481,x100481),f869(f869(x100483,x100481),f869(x100483,x100481)),x100482),f10(x100481,x100481,x100483)),f784(f784(f10(x100481,f869(x100481,x100481),x100482),f90(x100481)),x100484))),x100485)),f784(f784(f258(x100482,x100483),x100486),f784(f18(f869(x100483,a852),x100482),x100487)))+E(f784(f784(f8(x100481,x100481),f41(x100481)),f784(f266(x100481),f784(f784(f10(f869(x100482,a852),a852,x100481),f96(x100482)),f784(f784(f10(f869(x100482,f869(x100483,a852)),f869(x100482,a852),x100481),f784(f10(f869(x100483,a852),a852,x100482),f96(x100483))),f784(f784(f9(x100481,f869(x100482,f869(x100483,a852)),f869(x100482,f869(x100483,a852))),f784(f784(f10(f869(x100482,f869(f869(x100483,a852),f869(x100483,a852))),f869(f869(x100482,f869(x100483,a852)),f869(x100482,f869(x100483,a852))),x100481),f20(x100482,f869(x100483,a852),f869(x100483,a852))),f784(f784(f10(f869(x100482,f869(x100483,f869(a852,a852))),f869(x100482,f869(f869(x100483,a852),f869(x100483,a852))),x100481),f784(f10(f869(x100483,f869(a852,a852)),f869(f869(x100483,a852),f869(x100483,a852)),x100482),f20(x100483,a852,a852))),f784(f784(f10(f869(x100482,f869(x100483,a852)),f869(x100482,f869(x100483,f869(a852,a852))),x100481),f784(f10(f869(x100483,a852),f869(x100483,f869(a852,a852)),x100482),f784(f10(a852,f869(a852,a852),x100483),a344))),f784(f784(f9(x100481,f869(x100482,f869(x100483,x100481)),f869(x100482,f869(x100483,a852))),f784(f784(f10(f869(f869(x100483,x100481),f869(x100483,a852)),f869(f869(x100482,f869(x100483,x100481)),f869(x100482,f869(x100483,a852))),x100481),f10(f869(x100483,x100481),f869(x100483,a852),x100482)),f784(f784(f10(f869(x100481,a852),f869(f869(x100483,x100481),f869(x100483,a852)),x100481),f10(x100481,a852,x100483)),a343))),f784(f784(f9(x100482,f869(x100483,x100481),f869(x100483,x100481)),f784(f784(f10(f869(x100481,x100481),f869(f869(x100483,x100481),f869(x100483,x100481)),x100482),f10(x100481,x100481,x100483)),f784(f784(f10(x100481,f869(x100481,x100481),x100482),f90(x100481)),x100484))),x100485)))))),f784(f784(f9(x100482,f869(x100483,a852),f869(x100483,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x100483,a852),f869(x100483,a852)),x100482),f10(a852,a852,x100483)),f784(f784(f10(a852,f869(a852,a852),x100482),a344),f784(f784(f9(x100482,f869(x100482,a852),a852),f347(x100482)),x100486)))),f784(f784(f9(x100483,f869(x100483,a852),a852),f347(x100483)),x100487))))))),f784(f784(f90(x100481),f784(f784(f8(x100482,x100481),x100484),x100486)),f784(f784(f8(x100483,x100481),x100485),x100487)))
% 11.41/11.19 [9736]P50(x97361,x97362,x97363,x97364,x97365,x97366,x97367)+~P85(f784(f784(x97364,x97366),x97368))+~P85(f784(f784(x97365,x97368),x97367))
% 11.41/11.19 [9737]P50(x97371,x97372,x97373,x97374,x97375,x97376,x97377)+~P85(f784(f784(x97374,x97376),x97378))+~P85(f784(f784(x97375,x97378),x97377))
% 11.41/11.19 [9131]~P20(x91318,x91311,x91313,x91315)+~P85(f784(f71(x91318),x91316))+E(f784(f82(x91311,x91311,x91312,f784(x91313,x91314)),f784(f82(x91311,x91311,x91312,f784(x91315,x91316)),x91317)),f784(f82(x91311,x91311,x91312,f784(x91315,x91316)),f784(f82(x91311,x91311,x91312,f784(x91313,x91314)),x91317)))
% 11.41/11.19 [9493]~P23(x94937,x94932,x94935,x94938,x94936,x94931)+~P85(f784(f71(x94932),x94934))+E(f784(x94931,f784(f784(f312(x94932),x94933),x94934)),f784(f784(x94935,f784(x94936,x94933)),f784(x94931,x94934)))
% 11.41/11.19 [9609]~P26(x96092,x96094,x96096,x96098)+~P26(x96091,x96093,x96095,x96097)+P26(f868(x96091,x96092),f868(x96093,x96094),f262(x96091,x96093,x96092,x96094,x96095,x96096),f784(f784(f258(x96091,x96092),x96097),f784(f18(f869(x96092,a852),x96091),x96098)))
% 11.41/11.19 [9286]P85(f784(f784(f347(f868(x92861,x92862)),f784(f784(f251(x92861,x92862),x92863),x92864)),f784(f784(f291(x92861,x92865,x92862),x92866),x92867)))+~P85(f784(f784(f347(f868(x92861,x92865)),f784(f784(f251(x92861,x92865),x92863),x92868)),x92866))+~P85(f784(f784(f347(f868(x92865,x92862)),f784(f784(f251(x92865,x92862),x92868),x92864)),x92867))
% 11.41/11.19 [9476]~P85(f784(f784(f242(f869(f868(x94763,x94762),a852)),x94765),f784(f784(f258(x94763,x94762),x94768),f784(f18(f869(x94762,a852),x94763),x94767))))+~P85(f784(f784(f242(f869(f868(x94761,x94763),a852)),x94764),f784(f784(f258(x94761,x94763),x94766),f784(f18(f869(x94763,a852),x94761),x94768))))+P85(f784(f784(f242(f869(f868(x94761,x94762),a852)),f784(f784(f291(x94761,x94763,x94762),x94764),x94765)),f784(f784(f258(x94761,x94762),x94766),f784(f18(f869(x94762,a852),x94761),x94767))))
% 11.41/11.19 [9522]~E(x95223,x95225)+P85(f784(f784(f347(f868(f868(x95221,x95222),f868(x95221,x95222))),f784(f784(f251(f868(x95221,x95222),f868(x95221,x95222)),f784(f784(f251(x95221,x95222),x95223),x95224)),f784(f784(f251(x95221,x95222),x95225),x95226))),f339(x95221,x95222,x95227,x95228)))+~P85(f784(f784(f347(f868(x95222,x95222)),f784(f784(f251(x95222,x95222),x95224),x95226)),x95228))
% 11.41/11.19 [9628]E(x96281,x96282)+~P85(f784(f784(f347(f868(f868(x96283,x96285),f868(x96283,x96285))),f784(f784(f251(f868(x96283,x96285),f868(x96283,x96285)),f784(f784(f251(x96283,x96285),x96281),x96286)),f784(f784(f251(x96283,x96285),x96282),x96287))),f339(x96283,x96285,x96284,x96288)))+P85(f784(f784(f347(f868(x96283,x96283)),f784(f784(f251(x96283,x96283),x96281),x96282)),x96284))
% 11.41/11.19 [9643]~P85(f784(f784(f347(f868(f868(x96431,x96435),f868(x96431,x96435))),f784(f784(f251(f868(x96431,x96435),f868(x96431,x96435)),f784(f784(f251(x96431,x96435),x96432),x96436)),f784(f784(f251(x96431,x96435),x96433),x96437))),f339(x96431,x96435,x96434,x96438)))+P85(f784(f784(f347(f868(x96431,x96431)),f784(f784(f251(x96431,x96431),x96432),x96433)),x96434))+P85(f784(f784(f347(f868(x96435,x96435)),f784(f784(f251(x96435,x96435),x96436),x96437)),x96438))
% 11.41/11.19 [9552]~P24(x95527,x95525,x95521,x95528,x95522,x95524)+~P85(f784(f71(x95525),x95526))+E(f784(f784(x95521,f784(x95522,x95523)),f784(x95524,f784(f784(f3(f869(x95525,a852)),x95526),f784(f784(f312(x95525),x95523),f187(f869(x95525,a852)))))),f784(x95524,f784(f784(f312(x95525),x95523),x95526)))
% 11.41/11.19 [9090]~P85(f784(f784(f784(x90905,x90908),x90906),x90907))+~P85(f784(f784(f347(x90901),x90908),x90904))+P85(f784(f784(f784(f784(f54(x90901,f869(x90902,f869(x90903,a852))),x90904),x90905),x90906),x90907))
% 11.41/11.19 [9091]~P85(f784(f784(f784(x90915,x90918),x90916),x90917))+~P85(f784(f784(f347(x90911),x90918),x90914))+P85(f784(f784(f784(f784(f54(x90911,f869(x90912,f869(x90913,a852))),x90914),x90915),x90916),x90917))
% 11.41/11.19 [9272]P85(f784(f784(f784(x92721,x92722),x92723),x92724))+~P85(f784(f784(f347(x92725),x92722),x92726))+~P85(f784(f784(f784(f784(f55(x92725,f869(x92727,f869(x92728,a852))),x92726),x92721),x92723),x92724))
% 11.41/11.19 [9273]P85(f784(f784(f784(x92731,x92732),x92733),x92734))+~P85(f784(f784(f347(x92735),x92732),x92736))+~P85(f784(f784(f784(f784(f55(x92735,f869(x92737,f869(x92738,a852))),x92736),x92731),x92733),x92734))
% 11.41/11.19 [9274]P85(f784(f784(f784(x92741,x92742),x92743),x92744))+~P85(f784(f784(f347(x92745),x92742),x92746))+~P85(f784(f784(f784(f784(f55(x92745,f869(x92747,f869(x92748,a852))),x92746),x92741),x92743),x92744))
% 11.41/11.19 [9467]~P22(x94673,x94672,x94674,x94678,x94671)+~P85(f784(f71(x94672),x94677))+E(f784(f784(x94671,f784(f784(f20(x94672,x94673,x94673),f784(f784(f10(x94673,f869(x94673,x94673),x94672),x94674),x94675)),x94676)),x94677),f784(f784(x94674,f784(f784(x94671,x94675),x94677)),f784(f784(x94671,x94676),x94677)))
% 11.41/11.19 [9715]~E(f784(f313(x97152,x97154,x97156),x97158),x971510)+~E(f784(f313(x97151,x97153,x97155),x97157),x97159)+E(f784(f313(f868(x97151,x97152),f868(x97153,x97154),f262(x97151,x97153,x97152,x97154,x97155,x97156)),f784(f784(f258(x97151,x97152),x97157),f784(f18(f869(x97152,a852),x97151),x97158))),f784(f784(f258(x97153,x97154),x97159),f784(f18(f869(x97154,a852),x97153),x971510)))
% 11.41/11.19 [4755]~P101(x47552)+~P15(x47552,x47551)+P15(x47552,f121(x47552,x47551))+E(x47551,f120(x47552))
% 11.41/11.19 [4991]~P6(x49912)+E(f12(x49912,x49911),f53(x49912,x49911))+E(x49911,f187(f869(x49912,a852)))+~P85(f784(f71(x49912),x49911))
% 11.41/11.19 [4992]~P6(x49922)+E(f15(x49922,x49921),f52(x49922,x49921))+E(x49921,f187(f869(x49922,a852)))+~P85(f784(f71(x49922),x49921))
% 11.41/11.19 [5928]~P93(x59282)+E(x59281,f187(f869(x59282,a852)))+P85(f784(f784(f242(x59282),f12(x59282,x59281)),f15(x59282,x59281)))+~P85(f784(f71(x59282),x59281))
% 11.41/11.19 [5942]~P37(x59422)+~P37(x59421)+E(x59421,x59422)+~E(f784(f313(a1,a859,a114),x59421),f784(f313(a1,a859,a114),x59422))
% 11.41/11.19 [8952]~P113(x89521)+~P85(f784(f784(f347(x89521),x89522),f119(x89521)))+P85(f784(f784(f243(x89521),f784(f784(f89(x89521),f784(f784(f89(x89521),f87(x89521)),x89522)),x89522)),f2(x89521)))+~P85(f784(f784(f243(x89521),x89522),f2(x89521)))
% 11.41/11.19 [9172]~P113(x91721)+~P85(f784(f784(f347(x91721),x91722),f119(x91721)))+~P85(f784(f784(f243(x91721),f784(f784(f89(x91721),f784(f784(f89(x91721),f87(x91721)),x91722)),x91722)),f2(x91721)))+P85(f784(f784(f243(x91721),x91722),f2(x91721)))
% 11.41/11.19 [4808]~P106(x48082)+~P139(x48082)+E(x48081,f2(a859))+E(f784(f784(f252(x48082),f2(x48082)),x48081),f2(x48082))
% 11.41/11.19 [4812]~P106(x48121)+~P139(x48121)+~E(x48122,f2(a859))+E(f784(f784(f252(x48121),f2(x48121)),x48122),f87(x48121))
% 11.41/11.19 [4978]~P135(x49782)+E(x49781,f87(x49782))+E(x49781,f784(f88(x49782),f87(x49782)))+~E(f784(f784(f90(x49782),x49781),x49781),f87(x49782))
% 11.41/11.19 [5219]~P82(x52192)+E(x52191,f2(x52192))+E(f91(x52192,x52191),f784(f88(x52192),f87(x52192)))+P85(f784(f784(f243(x52192),f2(x52192)),x52191))
% 11.41/11.19 [5411]~E(x54112,f87(a1))+~E(x54111,f87(a1))+E(f784(f784(f90(a1),x54111),x54112),f87(a1))+~P85(f784(f784(f243(a1),f2(a1)),x54111))
% 11.41/11.19 [5451]~P82(x54512)+E(f91(x54512,x54511),f87(x54512))+E(x54511,f2(x54512))+~P85(f784(f784(f243(x54512),f2(x54512)),x54511))
% 11.41/11.19 [5460]E(x54601,x54602)+~E(f784(f113(a859),x54601),f784(f113(a859),x54602))+P85(f784(a193,f784(f113(a1),x54602)))+P85(f784(a193,f784(f113(a1),x54601)))
% 11.41/11.19 [5506]~P88(x55061)+~E(x55062,f2(x55061))+E(f784(f784(f89(x55061),x55062),x55062),f2(x55061))+~P85(f784(f784(f347(x55061),x55062),f119(x55061)))
% 11.41/11.19 [5543]E(x55431,f2(a1))+~E(f784(f784(f51(a1),x55432),x55431),f2(a1))+P85(f784(f784(f243(a1),x55431),x55432))+P85(f784(f784(f243(a1),x55432),x55431))
% 11.41/11.19 [5572]E(x55721,f2(a1))+~E(f784(f784(f51(a1),x55722),x55721),f2(a1))+P85(f784(f784(f242(a1),x55722),f2(a1)))+P85(f784(f784(f243(a1),x55722),x55721))
% 11.41/11.19 [5604]E(x56041,f2(a1))+~E(f784(f784(f51(a1),x56042),x56041),f2(a1))+P85(f784(f784(f242(a1),f2(a1)),x56042))+P85(f784(f784(f243(a1),x56041),x56042))
% 11.41/11.19 [5640]E(x56401,f2(a1))+~E(f784(f784(f51(a1),x56402),x56401),f2(a1))+P85(f784(f784(f242(a1),x56402),f2(a1)))+P85(f784(f784(f242(a1),f2(a1)),x56402))
% 11.41/11.19 [5641]~P88(x56412)+E(x56411,f2(x56412))+~E(f784(f784(f89(x56412),x56411),x56411),f2(x56412))+~P85(f784(f784(f347(x56412),x56411),f119(x56412)))
% 11.41/11.19 [5708]E(f784(f113(a859),x57081),f784(f113(a859),x57082))+~E(f784(f113(a1),x57082),f2(a1))+P85(f784(a193,f784(f113(a1),x57082)))+~P85(f784(a193,f784(f113(a1),x57081)))
% 11.41/11.19 [5737]~E(f784(f113(a859),x57372),f784(f113(a859),x57371))+E(f784(f113(a1),x57371),f2(a1))+P85(f784(a193,f784(f113(a1),x57371)))+~P85(f784(a193,f784(f113(a1),x57372)))
% 11.41/11.19 [5746]~P101(x57462)+E(x57461,f187(f869(x57462,a852)))+~P85(f784(f71(x57462),x57461))+P85(f784(f784(f347(x57462),f16(x57462,x57461)),x57461))
% 11.41/11.19 [5747]~P101(x57472)+E(x57471,f187(f869(x57472,a852)))+~P85(f784(f71(x57472),x57471))+P85(f784(f784(f347(x57472),f17(x57472,x57471)),x57471))
% 11.41/11.19 [5909]~P113(x59091)+~P89(x59091)+P85(f784(f784(f243(x59091),f2(x59091)),f784(f113(x59091),x59092)))+~P85(f784(f784(f243(a1),a92),x59092))
% 11.41/11.19 [5910]~P113(x59101)+~P89(x59101)+P85(f784(f784(f242(x59101),f2(x59101)),f784(f113(x59101),x59102)))+~P85(f784(f784(f242(a1),a92),x59102))
% 11.41/11.19 [5927]~P113(x59271)+~P89(x59271)+E(f784(f84(x59271),f784(f113(x59271),x59272)),f784(f113(x59271),x59272))+P85(f784(f784(f243(x59271),f784(f113(x59271),x59272)),f2(x59271)))
% 11.41/11.19 [5968]E(x59681,x59682)+~E(f784(a114,x59681),f784(a114,x59682))+~P85(f784(f784(f242(a1),f2(a1)),x59682))+~P85(f784(f784(f242(a1),f2(a1)),x59681))
% 11.41/11.19 [5969]E(x59691,x59692)+~E(f784(a114,x59691),f784(a114,x59692))+~P85(f784(f784(f242(a1),f2(a1)),x59692))+~P85(f784(f784(f242(a1),f2(a1)),x59691))
% 11.41/11.19 [5995]~E(x59951,f2(a1))+E(f61(x59951,x59952),f784(f784(f251(a1,a1),f2(a1)),f2(a1)))+P85(f784(f784(f242(a1),f2(a1)),x59952))+~P85(f784(f784(f242(a1),f2(a1)),x59951))
% 11.41/11.19 [6164]~P89(x61642)+~P113(x61642)+~P85(f784(f784(f243(x61642),f2(x61642)),f784(f113(x61642),x61641)))+P85(f784(f784(f243(a1),a92),x61641))
% 11.41/11.19 [6165]~P89(x61652)+~P113(x61652)+~P85(f784(f784(f242(x61652),f2(x61652)),f784(f113(x61652),x61651)))+P85(f784(f784(f242(a1),a92),x61651))
% 11.41/11.19 [6170]~P113(x61701)+~P89(x61701)+P85(f784(f784(f243(x61701),f784(f113(x61701),x61702)),f2(x61701)))+~P85(f784(f784(f243(a1),x61702),a92))
% 11.41/11.19 [6171]~P113(x61711)+~P89(x61711)+P85(f784(f784(f242(x61711),f784(f113(x61711),x61712)),f2(x61711)))+~P85(f784(f784(f242(a1),x61712),a92))
% 11.41/11.19 [6499]~P89(x64992)+~P113(x64992)+~P85(f784(f784(f243(x64992),f784(f113(x64992),x64991)),f2(x64992)))+P85(f784(f784(f243(a1),x64991),a92))
% 11.41/11.19 [6500]~P89(x65002)+~P113(x65002)+~P85(f784(f784(f242(x65002),f784(f113(x65002),x65001)),f2(x65002)))+P85(f784(f784(f242(a1),x65001),a92))
% 11.41/11.19 [6591]~P113(x65911)+~P89(x65911)+E(f784(f84(x65911),f784(f113(x65911),x65912)),f784(f88(x65911),f784(f113(x65911),x65912)))+~P85(f784(f784(f243(x65911),f784(f113(x65911),x65912)),f2(x65911)))
% 11.41/11.19 [6608]E(f784(f113(a859),x66081),f784(f113(a859),x66082))+~E(f784(f113(a1),x66082),f2(a1))+~P85(f784(f784(f242(a1),f784(f113(a1),x66081)),f2(a1)))+~P85(f784(a193,f784(f113(a1),x66081)))
% 11.41/11.19 [6788]E(x67881,x67882)+~E(f784(a5,x67881),f784(a5,x67882))+~P85(f784(f784(f347(a859),x67882),f249(f869(a859,a852))))+~P85(f784(f784(f347(a859),x67881),f249(f869(a859,a852))))
% 11.41/11.19 [7015]P85(f784(f784(f243(a859),f784(a114,x70151)),f784(a114,x70152)))+~P85(f784(f784(f242(a1),f2(a1)),x70152))+~P85(f784(f784(f242(a1),f2(a1)),x70151))+~P85(f784(f784(f243(a1),x70151),x70152))
% 11.41/11.19 [7016]P85(f784(f784(f242(a859),f784(a114,x70161)),f784(a114,x70162)))+~P85(f784(f784(f242(a1),f2(a1)),x70162))+~P85(f784(f784(f242(a1),f2(a1)),x70161))+~P85(f784(f784(f242(a1),x70161),x70162))
% 11.41/11.19 [7017]P85(f784(f784(f289(a859),f784(a114,x70171)),f784(a114,x70172)))+~P85(f784(f784(f242(a1),f2(a1)),x70172))+~P85(f784(f784(f242(a1),f2(a1)),x70171))+~P85(f784(f784(f289(a1),x70171),x70172))
% 11.41/11.19 [7249]~P7(x72491)+~P37(x72492)+~P85(f784(f784(f347(a1),x72491),x72492))+P85(f784(f784(f347(a859),f784(a114,x72491)),f784(f313(a1,a859,a114),x72492)))
% 11.41/11.19 [7257]~P85(f784(f784(f243(a859),f784(a114,x72571)),f784(a114,x72572)))+~P85(f784(f784(f242(a1),f2(a1)),x72572))+~P85(f784(f784(f242(a1),f2(a1)),x72571))+P85(f784(f784(f243(a1),x72571),x72572))
% 11.41/11.19 [7258]~P85(f784(f784(f242(a859),f784(a114,x72581)),f784(a114,x72582)))+~P85(f784(f784(f242(a1),f2(a1)),x72582))+~P85(f784(f784(f242(a1),f2(a1)),x72581))+P85(f784(f784(f242(a1),x72581),x72582))
% 11.41/11.19 [7259]~P85(f784(f784(f289(a859),f784(a114,x72591)),f784(a114,x72592)))+~P85(f784(f784(f242(a1),f2(a1)),x72592))+~P85(f784(f784(f242(a1),f2(a1)),x72591))+P85(f784(f784(f289(a1),x72591),x72592))
% 11.41/11.19 [7522]~P101(x75222)+E(x75221,f187(f869(x75222,a852)))+~P85(f784(f71(x75222),x75221))+P85(f784(f784(f242(x75222),f14(x75222,f246(x75222),x75221)),f13(x75222,f186(x75222),x75221)))
% 11.41/11.19 [7846]~P7(x78461)+~P37(x78462)+P85(f784(f784(f347(a1),x78461),x78462))+~P85(f784(f784(f347(a859),f784(a114,x78461)),f784(f313(a1,a859,a114),x78462)))
% 11.41/11.19 [5743]~P136(x57432)+E(x57431,f2(a1))+E(f784(f88(x57432),f784(f112(x57432),f784(f88(a1),x57431))),f784(f112(x57432),x57431))+~P85(f784(f784(f243(a1),x57431),f2(a1)))
% 11.41/11.19 [5818]~P88(x58181)+~P89(x58181)+~P30(x58181,f784(f113(x58181),x58182))+P30(x58181,f784(f113(x58181),f784(f784(f89(a1),x58182),x58182)))
% 11.41/11.19 [6154]~P69(x61542)+E(x61541,f187(f869(x61542,a852)))+E(f17(x61542,f784(f313(x61542,x61542,f88(x61542)),x61541)),f784(f88(x61542),f16(x61542,x61541)))+~P85(f784(f71(x61542),x61541))
% 11.41/11.19 [6155]~P69(x61552)+E(x61551,f187(f869(x61552,a852)))+E(f16(x61552,f784(f313(x61552,x61552,f88(x61552)),x61551)),f784(f88(x61552),f17(x61552,x61551)))+~P85(f784(f71(x61552),x61551))
% 11.41/11.19 [6185]~P88(x61851)+~P89(x61851)+P30(x61851,f784(f113(x61851),x61852))+~P30(x61851,f784(f113(x61851),f784(f784(f89(a1),x61852),x61852)))
% 11.41/11.19 [6278]E(x62781,f2(a1))+E(f784(a66,f65(f784(f88(a1),x62781),f784(f88(a1),x62782))),f61(x62781,x62782))+P85(f784(f784(f242(a1),f2(a1)),x62782))+~P85(f784(f784(f242(a1),f2(a1)),x62781))
% 11.41/11.19 [7159]~P85(f784(f784(f243(a1),f2(a1)),x71592))+~P85(f784(f784(f242(a1),f2(a1)),x71591))+~P85(f784(f784(f242(a1),x71592),x71591))+P85(f784(f784(f243(a1),f2(a1)),f784(f784(f51(a1),x71591),x71592)))
% 11.41/11.19 [7599]~E(x75992,f2(a1))+E(f220(x75991,x75992),f784(f784(f251(a1,a1),f2(a1)),f87(a1)))+P85(f784(f784(f243(a1),x75992),f2(a1)))+~P85(f784(f334(f868(a1,a1),a226),f784(f784(f251(a1,a1),x75991),x75992)))
% 11.41/11.19 [7600]~E(x76001,f2(a1))+E(f220(x76001,x76002),f784(f784(f251(a1,a1),f2(a1)),f87(a1)))+P85(f784(f784(f243(a1),x76002),f2(a1)))+~P85(f784(f334(f868(a1,a1),a226),f784(f784(f251(a1,a1),x76001),x76002)))
% 11.41/11.19 [8599]~P37(x85992)+~P37(x85991)+P85(f784(f784(f243(f869(a859,a852)),f784(f313(a1,a859,a114),x85991)),f784(f313(a1,a859,a114),x85992)))+~P85(f784(f784(f243(f869(a1,a852)),x85991),x85992))
% 11.41/11.19 [8600]~P37(x86002)+~P37(x86001)+P85(f784(f784(f242(f869(a859,a852)),f784(f313(a1,a859,a114),x86001)),f784(f313(a1,a859,a114),x86002)))+~P85(f784(f784(f242(f869(a1,a852)),x86001),x86002))
% 11.41/11.19 [8876]~P37(x88762)+~P37(x88761)+~P85(f784(f784(f243(f869(a859,a852)),f784(f313(a1,a859,a114),x88761)),f784(f313(a1,a859,a114),x88762)))+P85(f784(f784(f243(f869(a1,a852)),x88761),x88762))
% 11.41/11.19 [8877]~P37(x88772)+~P37(x88771)+~P85(f784(f784(f242(f869(a859,a852)),f784(f313(a1,a859,a114),x88771)),f784(f313(a1,a859,a114),x88772)))+P85(f784(f784(f242(f869(a1,a852)),x88771),x88772))
% 11.41/11.19 [9315]E(x93151,f2(a1))+E(x93152,f2(a1))+E(f784(f784(f95(a1,f868(a1,a1)),f784(f784(a222,x93152),x93151)),f784(f784(f20(a1,a1,f868(a1,a1)),f784(f784(f10(a1,f869(a1,f868(a1,a1)),a1),f251(a1,a1)),f784(f51(a1),x93152))),f784(f51(a1),x93151))),f220(x93152,x93151))+P85(f784(f784(f243(a1),x93151),f2(a1)))
% 11.41/11.19 [8164]~P89(x81642)+~P113(x81642)+~P85(f784(f784(f243(x81642),f784(f113(x81642),x81641)),f87(x81642)))+P85(f784(f784(f243(a1),x81641),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))
% 11.41/11.19 [8165]~P89(x81652)+~P113(x81652)+~P85(f784(f784(f242(x81652),f784(f113(x81652),x81651)),f87(x81652)))+P85(f784(f784(f242(a1),x81651),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))
% 11.41/11.19 [8439]~P113(x84391)+~P89(x84391)+P85(f784(f784(f243(x84391),f784(f113(x84391),x84392)),f87(x84391)))+~P85(f784(f784(f243(a1),x84392),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))
% 11.41/11.19 [8440]~P113(x84401)+~P89(x84401)+P85(f784(f784(f242(x84401),f784(f113(x84401),x84402)),f87(x84401)))+~P85(f784(f784(f242(a1),x84402),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))
% 11.41/11.19 [8624]~P89(x86242)+~P113(x86242)+~P85(f784(f784(f243(x86242),f87(x86242)),f784(f113(x86242),x86241)))+P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),x86241))
% 11.41/11.19 [8625]~P89(x86252)+~P113(x86252)+~P85(f784(f784(f242(x86252),f87(x86252)),f784(f113(x86252),x86251)))+P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),x86251))
% 11.41/11.19 [8958]~P113(x89581)+~P89(x89581)+P85(f784(f784(f243(x89581),f87(x89581)),f784(f113(x89581),x89582)))+~P85(f784(f784(f243(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),x89582))
% 11.41/11.19 [8959]~P113(x89591)+~P89(x89591)+P85(f784(f784(f242(x89591),f87(x89591)),f784(f113(x89591),x89592)))+~P85(f784(f784(f242(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),x89592))
% 11.41/11.19 [9436]~P135(x94362)+E(x94361,f87(x94362))+E(x94361,f784(f88(x94362),f87(x94362)))+~E(f784(f784(f252(x94362),x94361),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f87(x94362))
% 11.41/11.19 [9690]~P61(x96901)+~P89(x96901)+~P85(f784(f784(f243(x96901),f2(x96901)),x96902))+P85(f784(f784(f243(x96901),f2(x96901)),f784(f784(f293(x96901),x96902),f784(f113(x96901),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.19 [9691]~P61(x96911)+~P89(x96911)+~P85(f784(f784(f243(x96911),f2(x96911)),x96912))+P85(f784(f784(f243(x96911),f2(x96911)),f784(f784(f293(x96911),x96912),f784(f113(x96911),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.19 [9746]~P61(x97461)+~P89(x97461)+P85(f784(f784(f243(x97461),f2(x97461)),x97462))+~P85(f784(f784(f243(x97461),f2(x97461)),f784(f784(f293(x97461),x97462),f784(f113(x97461),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.19 [10022]~P136(x100222)+E(x100221,f2(a1))+P85(f784(f784(f243(a1),x100221),f2(a1)))+E(f784(f784(f261(a1,a1,x100222),f784(f784(f9(a1,f869(a1,f869(x100222,x100222)),f869(a1,x100222)),f784(f784(f10(f869(f869(x100222,x100222),x100222),f869(f869(a1,f869(x100222,x100222)),f869(a1,x100222)),a1),f10(f869(x100222,x100222),x100222,a1)),f784(f784(f10(x100222,f869(f869(x100222,x100222),x100222),a1),f95(x100222,x100222)),f112(x100222)))),f784(f784(f9(a1,f869(x100222,x100222),f869(x100222,x100222)),f784(f784(f10(f869(x100222,f869(x100222,x100222)),f869(f869(x100222,x100222),f869(x100222,x100222)),a1),f20(x100222,x100222,x100222)),f784(f784(f9(a1,f869(x100222,x100222),f869(x100222,f869(x100222,x100222))),f784(f784(f10(f869(x100222,f869(x100222,x100222)),f869(f869(x100222,x100222),f869(x100222,f869(x100222,x100222))),a1),f10(x100222,f869(x100222,x100222),x100222)),f784(f784(f10(a852,f869(x100222,f869(x100222,x100222)),a1),f105(x100222)),f784(f784(f9(a1,a1,a852),a343),f2(a1))))),f784(f784(f20(x100222,x100222,x100222),f89(x100222)),f7(x100222))))),f784(f784(f9(x100222,x100222,x100222),f784(f784(f10(x100222,f869(x100222,x100222),x100222),f89(x100222)),f784(f784(f20(x100222,x100222,x100222),f89(x100222)),f7(x100222)))),f87(x100222))))),f61(x100221,f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f112(x100222),x100221))
% 11.41/11.19 [9793]P85(f784(f784(f242(a1),x97931),f2(a1)))+P85(f784(f784(f243(a1),x97932),x97931))+~P85(f784(f334(f868(a1,a1),a70),f784(f784(f251(a1,a1),x97932),x97931)))+E(f784(f58(x97931),f62(x97932,f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97931))),f62(x97932,x97931))
% 11.41/11.19 [9797]P85(f784(f784(f242(a1),x97971),f2(a1)))+~P85(f784(f334(f868(a1,a1),a67),f784(f784(f251(a1,a1),x97972),x97971)))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),x97972),x97971)))+E(f784(f58(x97971),f65(x97972,f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),x97971))),f65(x97972,x97971))
% 11.41/11.19 [4781]~P88(x47813)+~P89(x47813)+E(x47811,x47812)+~E(f784(f113(x47813),x47811),f784(f113(x47813),x47812))
% 11.41/11.19 [5918]~P85(f784(x59181,x59182))+~P85(f784(x59181,x59183))+~P85(f784(f784(f242(a859),x59183),f801(x59182,x59181)))+P85(f784(x59181,f2(a859)))
% 11.41/11.19 [6345]P142(x63452,x63453,x63451)+E(x63451,f2(a1))+P85(f784(f784(f242(a1),f2(a1)),f790(x63451,x63453,x63452)))+P85(f784(f784(f243(a1),x63451),f2(a1)))
% 11.41/11.19 [6346]P143(x63462,x63463,x63461)+E(x63461,f2(a1))+P85(f784(f784(f242(a1),f2(a1)),f794(x63461,x63463,x63462)))+P85(f784(f784(f243(a1),x63461),f2(a1)))
% 11.41/11.19 [6478]P142(x64781,x64782,x64783)+~P85(f784(x64781,x64782))+P85(f784(f784(f242(a1),f2(a1)),f790(x64783,x64782,x64781)))+P85(f784(f784(f243(a1),x64783),f2(a1)))
% 11.41/11.19 [6502]P143(x65021,x65022,x65023)+P85(f784(f784(f242(a1),f2(a1)),f794(x65023,x65022,x65021)))+~P85(f784(x65021,f2(a1)))+P85(f784(f784(f243(a1),x65023),f2(a1)))
% 11.41/11.19 [6534]P142(x65342,x65343,x65341)+E(x65341,f2(a1))+~P85(f784(x65342,f790(x65341,x65343,x65342)))+P85(f784(f784(f243(a1),x65341),f2(a1)))
% 11.41/11.19 [6535]P143(x65352,x65353,x65351)+E(x65351,f2(a1))+~P85(f784(x65352,f795(x65351,x65353,x65352)))+P85(f784(f784(f243(a1),x65351),f2(a1)))
% 11.41/11.19 [6638]~P101(x66381)+~P6(x66381)+~P85(f784(f784(f243(x66381),x66382),f52(x66381,x66383)))+P85(f784(f784(f243(x66381),x66382),f662(x66383,x66382,x66381)))
% 11.41/11.19 [6648]P142(x66481,x66482,x66483)+~P85(f784(x66481,x66482))+~P85(f784(x66481,f790(x66483,x66482,x66481)))+P85(f784(f784(f243(a1),x66483),f2(a1)))
% 11.41/11.19 [6680]P143(x66801,x66802,x66803)+~P85(f784(x66801,f795(x66803,x66802,x66801)))+~P85(f784(x66801,f2(a1)))+P85(f784(f784(f243(a1),x66803),f2(a1)))
% 11.41/11.19 [6940]P142(x69402,x69403,x69401)+E(x69401,f2(a1))+P85(f784(f784(f242(a1),f2(a1)),f790(x69401,x69403,x69402)))+P85(f784(f784(f243(a1),x69401),f789(x69401,x69403,x69402)))
% 11.41/11.19 [6941]P143(x69412,x69413,x69411)+E(x69411,f2(a1))+P85(f784(f784(f242(a1),f2(a1)),f794(x69411,x69413,x69412)))+P85(f784(f784(f243(a1),x69411),f793(x69411,x69413,x69412)))
% 11.41/11.19 [7058]P142(x70581,x70582,x70583)+~P85(f784(x70581,x70582))+P85(f784(f784(f242(a1),f2(a1)),f790(x70583,x70582,x70581)))+P85(f784(f784(f243(a1),x70583),f789(x70583,x70582,x70581)))
% 11.41/11.19 [7079]P143(x70791,x70792,x70793)+P85(f784(f784(f242(a1),f2(a1)),f794(x70793,x70792,x70791)))+P85(f784(f784(f243(a1),x70793),f793(x70793,x70792,x70791)))+~P85(f784(x70791,f2(a1)))
% 11.41/11.19 [7109]P142(x71092,x71093,x71091)+E(x71091,f2(a1))+~P85(f784(x71092,f790(x71091,x71093,x71092)))+P85(f784(f784(f243(a1),x71091),f789(x71091,x71093,x71092)))
% 11.41/11.19 [7110]P143(x71102,x71103,x71101)+E(x71101,f2(a1))+~P85(f784(x71102,f795(x71101,x71103,x71102)))+P85(f784(f784(f243(a1),x71101),f793(x71101,x71103,x71102)))
% 11.41/11.19 [7150]P142(x71502,x71503,x71501)+E(x71501,f2(a1))+P85(f784(f784(f242(a1),f2(a1)),f790(x71501,x71503,x71502)))+~P85(f784(x71502,f789(x71501,x71503,x71502)))
% 11.41/11.19 [7151]P143(x71512,x71513,x71511)+E(x71511,f2(a1))+P85(f784(f784(f242(a1),f2(a1)),f794(x71511,x71513,x71512)))+~P85(f784(x71512,f797(x71511,x71513,x71512)))
% 11.41/11.19 [7256]P142(x72561,x72562,x72563)+~P85(f784(x72561,x72562))+~P85(f784(x72561,f790(x72563,x72562,x72561)))+P85(f784(f784(f243(a1),x72563),f789(x72563,x72562,x72561)))
% 11.41/11.19 [7272]P143(x72721,x72722,x72723)+~P85(f784(x72721,f795(x72723,x72722,x72721)))+P85(f784(f784(f243(a1),x72723),f793(x72723,x72722,x72721)))+~P85(f784(x72721,f2(a1)))
% 11.41/11.19 [7278]P142(x72781,x72782,x72783)+~P85(f784(x72781,x72782))+P85(f784(f784(f242(a1),f2(a1)),f790(x72783,x72782,x72781)))+~P85(f784(x72781,f789(x72783,x72782,x72781)))
% 11.41/11.19 [7296]P143(x72961,x72962,x72963)+P85(f784(f784(f242(a1),f2(a1)),f794(x72963,x72962,x72961)))+~P85(f784(x72961,f797(x72963,x72962,x72961)))+~P85(f784(x72961,f2(a1)))
% 11.41/11.19 [7320]P142(x73202,x73203,x73201)+E(x73201,f2(a1))+~P85(f784(x73202,f790(x73201,x73203,x73202)))+~P85(f784(x73202,f789(x73201,x73203,x73202)))
% 11.41/11.19 [7321]P143(x73212,x73213,x73211)+E(x73211,f2(a1))+~P85(f784(x73212,f795(x73211,x73213,x73212)))+~P85(f784(x73212,f797(x73211,x73213,x73212)))
% 11.41/11.19 [7417]P142(x74171,x74172,x74173)+~P85(f784(x74171,x74172))+~P85(f784(x74171,f790(x74173,x74172,x74171)))+~P85(f784(x74171,f789(x74173,x74172,x74171)))
% 11.41/11.19 [7432]P143(x74321,x74322,x74323)+~P85(f784(x74321,f795(x74323,x74322,x74321)))+~P85(f784(x74321,f797(x74323,x74322,x74321)))+~P85(f784(x74321,f2(a1)))
% 11.41/11.19 [7482]P142(x74822,x74823,x74821)+E(x74821,f2(a1))+P85(f784(f784(f242(a1),f2(a1)),f790(x74821,x74823,x74822)))+P85(f784(f784(f242(a1),f789(x74821,x74823,x74822)),f2(a1)))
% 11.41/11.19 [7483]P143(x74832,x74833,x74831)+E(x74831,f2(a1))+P85(f784(f784(f242(a1),f2(a1)),f794(x74831,x74833,x74832)))+P85(f784(f784(f242(a1),f793(x74831,x74833,x74832)),f2(a1)))
% 11.41/11.19 [7484]~P81(x74841)+~P85(f784(f784(f243(x74841),x74843),f2(x74841)))+~P85(f784(f784(f243(x74841),x74842),f2(x74841)))+P85(f784(f784(f243(x74841),f784(f784(f89(x74841),x74842),x74843)),f2(x74841)))
% 11.41/11.19 [7485]~P81(x74851)+~P85(f784(f784(f242(x74851),x74852),f2(x74851)))+~P85(f784(f784(f243(x74851),x74853),f2(x74851)))+P85(f784(f784(f243(x74851),f784(f784(f89(x74851),x74852),x74853)),f2(x74851)))
% 11.41/11.19 [7486]~P81(x74861)+~P85(f784(f784(f242(x74861),x74863),f2(x74861)))+~P85(f784(f784(f243(x74861),x74862),f2(x74861)))+P85(f784(f784(f243(x74861),f784(f784(f89(x74861),x74862),x74863)),f2(x74861)))
% 11.41/11.19 [7487]~P81(x74871)+~P85(f784(f784(f242(x74871),x74873),f2(x74871)))+~P85(f784(f784(f242(x74871),x74872),f2(x74871)))+P85(f784(f784(f242(x74871),f784(f784(f89(x74871),x74872),x74873)),f2(x74871)))
% 11.41/11.19 [7488]~P112(x74881)+~P85(f784(f784(f347(x74881),x74883),f183(x74881)))+~P85(f784(f784(f347(x74881),x74882),f183(x74881)))+P85(f784(f784(f347(x74881),f784(f784(f89(x74881),x74882),x74883)),f183(x74881)))
% 11.41/11.19 [7489]~P136(x74891)+~P85(f784(f784(f347(x74891),x74893),f119(x74891)))+~P85(f784(f784(f347(x74891),x74892),f119(x74891)))+P85(f784(f784(f347(x74891),f784(f784(f89(x74891),x74892),x74893)),f119(x74891)))
% 11.41/11.19 [7490]~P112(x74901)+~P85(f784(f784(f347(x74901),x74903),f183(x74901)))+~P85(f784(f784(f347(x74901),x74902),f183(x74901)))+P85(f784(f784(f347(x74901),f784(f784(f90(x74901),x74902),x74903)),f183(x74901)))
% 11.41/11.19 [7491]~P136(x74911)+~P85(f784(f784(f347(x74911),x74913),f119(x74911)))+~P85(f784(f784(f347(x74911),x74912),f119(x74911)))+P85(f784(f784(f347(x74911),f784(f784(f90(x74911),x74912),x74913)),f119(x74911)))
% 11.41/11.19 [7492]~P136(x74921)+~P85(f784(f784(f347(x74921),x74923),f119(x74921)))+~P85(f784(f784(f347(x74921),x74922),f119(x74921)))+P85(f784(f784(f347(x74921),f784(f784(f3(x74921),x74922),x74923)),f119(x74921)))
% 11.41/11.19 [7518]P142(x75183,x75182,x75181)+E(x75181,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x75181),f791(x75181,x75182,x75183))),f790(x75181,x75182,x75183)),x75182)+P85(f784(f784(f243(a1),x75181),f2(a1)))
% 11.41/11.19 [7519]P143(x75193,x75192,x75191)+E(x75191,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x75191),f795(x75191,x75192,x75193))),f794(x75191,x75192,x75193)),x75192)+P85(f784(f784(f243(a1),x75191),f2(a1)))
% 11.41/11.19 [7604]P142(x76041,x76042,x76043)+~P85(f784(x76041,x76042))+P85(f784(f784(f242(a1),f2(a1)),f790(x76043,x76042,x76041)))+P85(f784(f784(f242(a1),f789(x76043,x76042,x76041)),f2(a1)))
% 11.41/11.19 [7635]P143(x76351,x76352,x76353)+P85(f784(f784(f242(a1),f2(a1)),f794(x76353,x76352,x76351)))+~P85(f784(x76351,f2(a1)))+P85(f784(f784(f242(a1),f793(x76353,x76352,x76351)),f2(a1)))
% 11.41/11.19 [7643]P142(x76433,x76432,x76431)+~P85(f784(x76433,x76432))+E(f784(f784(f89(a1),f784(f784(f90(a1),x76431),f791(x76431,x76432,x76433))),f790(x76431,x76432,x76433)),x76432)+P85(f784(f784(f243(a1),x76431),f2(a1)))
% 11.41/11.19 [7648]P142(x76482,x76483,x76481)+E(x76481,f2(a1))+~P85(f784(x76482,f790(x76481,x76483,x76482)))+P85(f784(f784(f242(a1),f789(x76481,x76483,x76482)),f2(a1)))
% 11.41/11.19 [7649]P143(x76492,x76493,x76491)+E(x76491,f2(a1))+~P85(f784(x76492,f795(x76491,x76493,x76492)))+P85(f784(f784(f242(a1),f793(x76491,x76493,x76492)),f2(a1)))
% 11.41/11.19 [7654]P143(x76543,x76542,x76541)+E(f784(f784(f89(a1),f784(f784(f90(a1),x76541),f795(x76541,x76542,x76543))),f794(x76541,x76542,x76543)),x76542)+~P85(f784(x76543,f2(a1)))+P85(f784(f784(f243(a1),x76541),f2(a1)))
% 11.41/11.19 [7706]P142(x77061,x77062,x77063)+~P85(f784(x77061,x77062))+~P85(f784(x77061,f790(x77063,x77062,x77061)))+P85(f784(f784(f242(a1),f789(x77063,x77062,x77061)),f2(a1)))
% 11.41/11.19 [7711]P143(x77111,x77112,x77113)+~P85(f784(x77111,f795(x77113,x77112,x77111)))+~P85(f784(x77111,f2(a1)))+P85(f784(f784(f242(a1),f793(x77113,x77112,x77111)),f2(a1)))
% 11.41/11.19 [7785]~P61(x77851)+~P85(f784(f784(f243(x77851),f784(f784(f293(x77851),x77853),x77852)),f2(x77851)))+P85(f784(f784(f243(x77851),x77852),f2(x77851)))+P85(f784(f784(f243(x77851),x77853),f2(x77851)))
% 11.41/11.19 [7786]~P122(x77861)+~P85(f784(f784(f242(x77861),f784(f784(f90(x77861),x77863),x77862)),f2(x77861)))+P85(f784(f784(f242(x77861),x77862),f2(x77861)))+P85(f784(f784(f242(x77861),x77863),f2(x77861)))
% 11.41/11.19 [7787]~P61(x77871)+~P85(f784(f784(f242(x77871),f784(f784(f293(x77871),x77873),x77872)),f2(x77871)))+P85(f784(f784(f242(x77871),x77872),f2(x77871)))+P85(f784(f784(f242(x77871),x77873),f2(x77871)))
% 11.41/11.19 [7899]P142(x78993,x78992,x78991)+E(x78991,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x78991),f791(x78991,x78992,x78993))),f790(x78991,x78992,x78993)),x78992)+P85(f784(f784(f243(a1),x78991),f789(x78991,x78992,x78993)))
% 11.41/11.19 [7900]P143(x79003,x79002,x79001)+E(x79001,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x79001),f795(x79001,x79002,x79003))),f794(x79001,x79002,x79003)),x79002)+P85(f784(f784(f243(a1),x79001),f793(x79001,x79002,x79003)))
% 11.41/11.19 [7911]P142(x79113,x79112,x79111)+E(x79111,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x79111),f792(x79111,x79112,x79113))),f789(x79111,x79112,x79113)),x79112)+P85(f784(f784(f242(a1),f2(a1)),f790(x79111,x79112,x79113)))
% 11.41/11.19 [7912]P143(x79123,x79122,x79121)+E(x79121,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x79121),f797(x79121,x79122,x79123))),f793(x79121,x79122,x79123)),x79122)+P85(f784(f784(f242(a1),f2(a1)),f794(x79121,x79122,x79123)))
% 11.41/11.19 [7958]P142(x79583,x79582,x79581)+~P85(f784(x79583,x79582))+E(f784(f784(f89(a1),f784(f784(f90(a1),x79581),f791(x79581,x79582,x79583))),f790(x79581,x79582,x79583)),x79582)+P85(f784(f784(f243(a1),x79581),f789(x79581,x79582,x79583)))
% 11.41/11.19 [7969]P143(x79693,x79692,x79691)+E(f784(f784(f89(a1),f784(f784(f90(a1),x79691),f795(x79691,x79692,x79693))),f794(x79691,x79692,x79693)),x79692)+P85(f784(f784(f243(a1),x79691),f793(x79691,x79692,x79693)))+~P85(f784(x79693,f2(a1)))
% 11.41/11.19 [7975]P142(x79753,x79752,x79751)+~P85(f784(x79753,x79752))+E(f784(f784(f89(a1),f784(f784(f90(a1),x79751),f792(x79751,x79752,x79753))),f789(x79751,x79752,x79753)),x79752)+P85(f784(f784(f242(a1),f2(a1)),f790(x79751,x79752,x79753)))
% 11.41/11.19 [7982]P143(x79823,x79822,x79821)+E(f784(f784(f89(a1),f784(f784(f90(a1),x79821),f797(x79821,x79822,x79823))),f793(x79821,x79822,x79823)),x79822)+P85(f784(f784(f242(a1),f2(a1)),f794(x79821,x79822,x79823)))+~P85(f784(x79823,f2(a1)))
% 11.41/11.19 [7992]P142(x79923,x79922,x79921)+E(x79921,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x79921),f791(x79921,x79922,x79923))),f790(x79921,x79922,x79923)),x79922)+~P85(f784(x79923,f789(x79921,x79922,x79923)))
% 11.41/11.19 [7993]P143(x79933,x79932,x79931)+E(x79931,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x79931),f795(x79931,x79932,x79933))),f794(x79931,x79932,x79933)),x79932)+~P85(f784(x79933,f797(x79931,x79932,x79933)))
% 11.41/11.19 [7994]P142(x79943,x79942,x79941)+E(x79941,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x79941),f792(x79941,x79942,x79943))),f789(x79941,x79942,x79943)),x79942)+~P85(f784(x79943,f790(x79941,x79942,x79943)))
% 11.41/11.19 [7995]P143(x79953,x79952,x79951)+E(x79951,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x79951),f797(x79951,x79952,x79953))),f793(x79951,x79952,x79953)),x79952)+~P85(f784(x79953,f795(x79951,x79952,x79953)))
% 11.41/11.19 [8047]P142(x80473,x80472,x80471)+~P85(f784(x80473,x80472))+E(f784(f784(f89(a1),f784(f784(f90(a1),x80471),f791(x80471,x80472,x80473))),f790(x80471,x80472,x80473)),x80472)+~P85(f784(x80473,f789(x80471,x80472,x80473)))
% 11.41/11.19 [8048]P142(x80483,x80482,x80481)+~P85(f784(x80483,x80482))+E(f784(f784(f89(a1),f784(f784(f90(a1),x80481),f792(x80481,x80482,x80483))),f789(x80481,x80482,x80483)),x80482)+~P85(f784(x80483,f790(x80481,x80482,x80483)))
% 11.41/11.19 [8060]P143(x80603,x80602,x80601)+E(f784(f784(f89(a1),f784(f784(f90(a1),x80601),f795(x80601,x80602,x80603))),f794(x80601,x80602,x80603)),x80602)+~P85(f784(x80603,f797(x80601,x80602,x80603)))+~P85(f784(x80603,f2(a1)))
% 11.41/11.19 [8061]P143(x80613,x80612,x80611)+E(f784(f784(f89(a1),f784(f784(f90(a1),x80611),f797(x80611,x80612,x80613))),f793(x80611,x80612,x80613)),x80612)+~P85(f784(x80613,f795(x80611,x80612,x80613)))+~P85(f784(x80613,f2(a1)))
% 11.41/11.19 [8157]P142(x81573,x81572,x81571)+E(x81571,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x81571),f791(x81571,x81572,x81573))),f790(x81571,x81572,x81573)),x81572)+P85(f784(f784(f242(a1),f789(x81571,x81572,x81573)),f2(a1)))
% 11.41/11.19 [8158]P143(x81583,x81582,x81581)+E(x81581,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x81581),f795(x81581,x81582,x81583))),f794(x81581,x81582,x81583)),x81582)+P85(f784(f784(f242(a1),f793(x81581,x81582,x81583)),f2(a1)))
% 11.41/11.19 [8196]P142(x81963,x81962,x81961)+~P85(f784(x81963,x81962))+E(f784(f784(f89(a1),f784(f784(f90(a1),x81961),f791(x81961,x81962,x81963))),f790(x81961,x81962,x81963)),x81962)+P85(f784(f784(f242(a1),f789(x81961,x81962,x81963)),f2(a1)))
% 11.41/11.19 [8201]P143(x82013,x82012,x82011)+E(f784(f784(f89(a1),f784(f784(f90(a1),x82011),f795(x82011,x82012,x82013))),f794(x82011,x82012,x82013)),x82012)+~P85(f784(x82013,f2(a1)))+P85(f784(f784(f242(a1),f793(x82011,x82012,x82013)),f2(a1)))
% 11.41/11.19 [8333]P142(x83333,x83332,x83331)+E(x83331,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x83331),f792(x83331,x83332,x83333))),f789(x83331,x83332,x83333)),x83332)+E(f784(f784(f89(a1),f784(f784(f90(a1),x83331),f791(x83331,x83332,x83333))),f790(x83331,x83332,x83333)),x83332)
% 11.41/11.19 [8334]P143(x83343,x83342,x83341)+E(x83341,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x83341),f797(x83341,x83342,x83343))),f793(x83341,x83342,x83343)),x83342)+E(f784(f784(f89(a1),f784(f784(f90(a1),x83341),f795(x83341,x83342,x83343))),f794(x83341,x83342,x83343)),x83342)
% 11.41/11.19 [8357]P142(x83573,x83572,x83571)+~P85(f784(x83573,x83572))+E(f784(f784(f89(a1),f784(f784(f90(a1),x83571),f792(x83571,x83572,x83573))),f789(x83571,x83572,x83573)),x83572)+E(f784(f784(f89(a1),f784(f784(f90(a1),x83571),f791(x83571,x83572,x83573))),f790(x83571,x83572,x83573)),x83572)
% 11.41/11.19 [8369]P143(x83693,x83692,x83691)+E(f784(f784(f89(a1),f784(f784(f90(a1),x83691),f797(x83691,x83692,x83693))),f793(x83691,x83692,x83693)),x83692)+E(f784(f784(f89(a1),f784(f784(f90(a1),x83691),f795(x83691,x83692,x83693))),f794(x83691,x83692,x83693)),x83692)+~P85(f784(x83693,f2(a1)))
% 11.41/11.19 [8963]~P122(x89631)+~E(x89633,f2(x89631))+~E(x89632,f2(x89631))+P85(f784(f784(f242(x89631),f784(f784(f89(x89631),f784(f784(f90(x89631),x89632),x89632)),f784(f784(f90(x89631),x89633),x89633))),f2(x89631)))
% 11.41/11.19 [9973]~P113(x99731)+~E(x99733,f2(x99731))+~E(x99732,f2(x99731))+P85(f784(f784(f242(x99731),f784(f784(f89(x99731),f784(f784(f252(x99731),x99732),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99731),x99733),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))),f2(x99731)))
% 11.41/11.19 [4731]~E(x47313,x47311)+~P116(x47312)+E(x47311,f2(x47312))+E(f784(f784(f293(x47312),x47313),x47311),f87(x47312))
% 11.41/11.19 [4782]~P95(x47821)+~E(x47823,f187(x47821))+~E(x47822,f187(x47821))+E(f784(f784(f110(x47821),x47822),x47823),f187(x47821))
% 11.41/11.19 [4783]~P94(x47831)+~E(x47833,f249(x47831))+~E(x47832,f249(x47831))+E(f784(f784(f111(x47831),x47832),x47833),f249(x47831))
% 11.41/11.19 [4869]~P116(x48693)+E(x48691,x48692)+E(x48692,f2(x48693))+~E(f784(f784(f293(x48693),x48691),x48692),f87(x48693))
% 11.41/11.19 [4885]~P137(x48852)+E(x48851,f2(x48852))+E(x48853,f2(x48852))+~E(f784(f784(f90(x48852),x48853),x48851),f2(x48852))
% 11.41/11.19 [4886]~P129(x48862)+E(x48861,f2(x48862))+E(x48863,f2(x48862))+~E(f784(f784(f90(x48862),x48863),x48861),f2(x48862))
% 11.41/11.19 [4887]~P129(x48872)+E(x48871,f2(x48872))+E(x48873,f2(x48872))+~E(f784(f784(f90(x48872),x48873),x48871),f2(x48872))
% 11.41/11.19 [5255]~P114(x52553)+E(x52551,x52552)+E(x52551,f784(f88(x52553),x52552))+~E(f784(f784(f90(x52553),x52551),x52551),f784(f784(f90(x52553),x52552),x52552))
% 11.41/11.19 [5291]~P91(x52911)+E(f784(f88(x52911),x52912),x52913)+~E(f784(f784(f110(x52911),x52912),x52913),f249(x52911))+~E(f784(f784(f111(x52911),x52912),x52913),f187(x52911))
% 11.41/11.19 [5367]~P113(x53673)+E(x53671,x53672)+P85(f784(f784(f243(x53673),x53672),x53671))+P85(f784(f784(f243(x53673),x53671),x53672))
% 11.41/11.19 [5368]~P101(x53683)+E(x53681,x53682)+P85(f784(f784(f243(x53683),x53682),x53681))+P85(f784(f784(f243(x53683),x53681),x53682))
% 11.41/11.19 [5369]~P101(x53693)+E(x53691,x53692)+P85(f784(f784(f243(x53693),x53692),x53691))+P85(f784(f784(f243(x53693),x53691),x53692))
% 11.41/11.19 [5370]~P101(x53703)+E(x53701,x53702)+P85(f784(f784(f243(x53703),x53702),x53701))+P85(f784(f784(f243(x53703),x53701),x53702))
% 11.41/11.19 [5371]~P101(x53713)+E(x53711,x53712)+P85(f784(f784(f243(x53713),x53712),x53711))+P85(f784(f784(f243(x53713),x53711),x53712))
% 11.41/11.19 [5372]~P101(x53723)+E(x53721,x53722)+P85(f784(f784(f243(x53723),x53722),x53721))+P85(f784(f784(f243(x53723),x53721),x53722))
% 11.41/11.19 [5373]~P101(x53733)+E(x53731,x53732)+P85(f784(f784(f243(x53733),x53732),x53731))+P85(f784(f784(f243(x53733),x53731),x53732))
% 11.41/11.19 [5374]~E(x53742,x53743)+~P101(x53741)+P85(f784(f784(f242(x53741),x53742),x53743))+P85(f784(f784(f243(x53741),x53742),x53743))
% 11.41/11.19 [5535]P142(x55352,x55353,x55351)+E(x55351,f2(a1))+P85(f784(f784(f243(a1),x55351),f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x55351))
% 11.41/11.19 [5536]P143(x55362,x55363,x55361)+E(x55361,f2(a1))+P85(f784(f784(f243(a1),x55361),f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x55361))
% 11.41/11.19 [5561]E(x55611,x55612)+P85(f784(f784(x55613,x55611),x55612))+P85(f784(f784(f243(a859),x55612),x55611))+P85(f784(f784(f243(a859),x55611),x55612))
% 11.41/11.19 [5620]~P100(x56203)+E(x56201,x56202)+~P85(f784(f784(f242(x56203),x56202),x56201))+P85(f784(f784(f243(x56203),x56202),x56201))
% 11.41/11.19 [5621]~P100(x56213)+E(x56211,x56212)+~P85(f784(f784(f242(x56213),x56211),x56212))+P85(f784(f784(f243(x56213),x56211),x56212))
% 11.41/11.19 [5622]~P100(x56223)+E(x56221,x56222)+~P85(f784(f784(f242(x56223),x56221),x56222))+P85(f784(f784(f243(x56223),x56221),x56222))
% 11.41/11.19 [5623]~P100(x56233)+E(x56231,x56232)+~P85(f784(f784(f242(x56233),x56231),x56232))+P85(f784(f784(f243(x56233),x56231),x56232))
% 11.41/11.19 [5624]~P100(x56243)+E(x56241,x56242)+~P85(f784(f784(f242(x56243),x56241),x56242))+P85(f784(f784(f243(x56243),x56241),x56242))
% 11.41/11.19 [5625]~P100(x56253)+E(x56251,x56252)+~P85(f784(f784(f242(x56253),x56251),x56252))+P85(f784(f784(f243(x56253),x56251),x56252))
% 11.41/11.19 [5626]~P100(x56263)+E(x56261,x56262)+~P85(f784(f784(f242(x56263),x56261),x56262))+P85(f784(f784(f243(x56263),x56261),x56262))
% 11.41/11.19 [5627]~P101(x56273)+E(x56271,x56272)+~P85(f784(f784(f242(x56273),x56271),x56272))+P85(f784(f784(f243(x56273),x56271),x56272))
% 11.41/11.19 [5628]~P101(x56283)+E(x56281,x56282)+~P85(f784(f784(f242(x56283),x56281),x56282))+P85(f784(f784(f243(x56283),x56281),x56282))
% 11.41/11.19 [5740]P142(x57401,x57402,x57403)+~P85(f784(x57401,x57402))+P85(f784(f784(f243(a1),x57403),f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x57403))
% 11.41/11.19 [5791]P143(x57911,x57912,x57913)+~P85(f784(x57911,f2(a1)))+P85(f784(f784(f243(a1),x57913),f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x57913))
% 11.41/11.19 [5795]~P93(x57951)+E(f784(f784(f110(x57951),x57952),f12(x57951,x57953)),x57952)+~P85(f784(f71(x57951),x57953))+~P85(f784(f784(f347(x57951),x57952),x57953))
% 11.41/11.19 [5796]~P93(x57961)+E(f784(f784(f111(x57961),x57962),f15(x57961,x57963)),x57962)+~P85(f784(f71(x57961),x57963))+~P85(f784(f784(f347(x57961),x57962),x57963))
% 11.41/11.19 [5828]~P101(x58281)+E(f784(f784(f246(x58281),x58282),f17(x58281,x58283)),f17(x58281,x58283))+~P85(f784(f71(x58281),x58283))+~P85(f784(f784(f347(x58281),x58282),x58283))
% 11.41/11.19 [5829]~P101(x58291)+E(f784(f784(f186(x58291),x58292),f16(x58291,x58293)),f16(x58291,x58293))+~P85(f784(f71(x58291),x58293))+~P85(f784(f784(f347(x58291),x58292),x58293))
% 11.41/11.19 [5830]~P93(x58301)+E(f784(f784(f110(x58301),x58302),f15(x58301,x58303)),f15(x58301,x58303))+~P85(f784(f71(x58301),x58303))+~P85(f784(f784(f347(x58301),x58302),x58303))
% 11.41/11.19 [5831]~P93(x58311)+E(f784(f784(f111(x58311),x58312),f12(x58311,x58313)),f12(x58311,x58313))+~P85(f784(f71(x58311),x58313))+~P85(f784(f784(f347(x58311),x58312),x58313))
% 11.41/11.19 [5869]E(x58691,x58692)+~P100(x58693)+~P85(f784(f784(f242(x58693),x58692),x58691))+~P85(f784(f784(f242(x58693),x58691),x58692))
% 11.41/11.19 [5870]E(x58701,x58702)+~P100(x58703)+~P85(f784(f784(f242(x58703),x58702),x58701))+~P85(f784(f784(f242(x58703),x58701),x58702))
% 11.41/11.19 [5871]E(x58711,x58712)+~P100(x58713)+~P85(f784(f784(f242(x58713),x58712),x58711))+~P85(f784(f784(f242(x58713),x58711),x58712))
% 11.41/11.19 [5872]E(x58721,x58722)+~P100(x58723)+~P85(f784(f784(f242(x58723),x58722),x58721))+~P85(f784(f784(f242(x58723),x58721),x58722))
% 11.41/11.19 [5874]~E(x58741,x58742)+~P101(x58743)+~P85(f784(f784(f243(x58743),x58741),x58742))+~P85(f784(f784(f242(x58743),x58741),x58742))
% 11.41/11.19 [6012]~P104(x60121)+P85(f784(f784(f242(x60121),x60123),x60122))+~P85(f784(f784(f242(x60121),x60122),x60123))+P85(f784(f784(f243(x60121),x60122),x60123))
% 11.41/11.19 [6036]~P101(x60361)+~P85(f784(f71(x60361),x60363))+P85(f784(f784(f242(x60361),x60362),f16(x60361,x60363)))+~P85(f784(f784(f347(x60361),x60362),x60363))
% 11.41/11.19 [6089]~P101(x60891)+E(f784(f784(f246(x60891),x60892),f13(x60891,f186(x60891),x60893)),x60892)+~P85(f784(f71(x60891),x60893))+~P85(f784(f784(f347(x60891),x60892),x60893))
% 11.41/11.19 [6090]~P101(x60901)+E(f784(f784(f186(x60901),x60902),f14(x60901,f246(x60901),x60903)),x60902)+~P85(f784(f71(x60901),x60903))+~P85(f784(f784(f347(x60901),x60902),x60903))
% 11.41/11.19 [6230]E(x62301,x62302)+~E(f784(f784(f3(a859),x62301),x62303),f784(f784(f3(a859),x62302),x62303))+~P85(f784(f784(f242(a859),x62303),x62301))+~P85(f784(f784(f242(a859),x62303),x62302))
% 11.41/11.19 [6257]~P101(x62571)+~P85(f784(f71(x62571),x62572))+~P85(f784(f784(f347(x62571),x62573),x62572))+P85(f784(f784(f242(x62571),f17(x62571,x62572)),x62573))
% 11.41/11.19 [6301]E(x63011,f2(a859))+~P85(f784(f63(x63013,x63011),x63012))+P85(f784(f784(f243(a859),f2(a859)),x63011))+P85(f784(f784(f243(a859),x63011),f784(f260(a859,a859),x63012)))
% 11.41/11.19 [6324]P142(x63242,x63243,x63241)+E(x63241,f2(a1))+P85(f784(f784(f243(a1),x63241),f789(x63241,x63243,x63242)))+P85(f784(f784(f243(a1),f2(a1)),x63241))
% 11.41/11.19 [6325]P143(x63252,x63253,x63251)+E(x63251,f2(a1))+P85(f784(f784(f243(a1),x63251),f793(x63251,x63253,x63252)))+P85(f784(f784(f243(a1),f2(a1)),x63251))
% 11.41/11.19 [6326]~P101(x63261)+E(f784(f784(f246(x63261),x63262),f14(x63261,f246(x63261),x63263)),f14(x63261,f246(x63261),x63263))+~P85(f784(f71(x63261),x63263))+~P85(f784(f784(f347(x63261),x63262),x63263))
% 11.41/11.19 [6327]~P101(x63271)+E(f784(f784(f186(x63271),x63272),f13(x63271,f186(x63271),x63273)),f13(x63271,f186(x63271),x63273))+~P85(f784(f71(x63271),x63273))+~P85(f784(f784(f347(x63271),x63272),x63273))
% 11.41/11.19 [6334]~P85(f784(x63341,x63342))+P85(f784(x63341,f818(x63342,x63341,x63343)))+P85(f784(x63341,f2(a859)))+~P85(f784(f784(f243(a859),x63342),x63343))
% 11.41/11.19 [6372]~P85(f784(f784(f289(a859),x63722),x63721))+~P85(f784(f784(f289(a859),x63721),x63723))+P85(f784(f784(f289(a859),x63721),x63722))+P85(f784(f784(f289(a859),x63722),x63723))
% 11.41/11.19 [6373]~P85(f784(f784(f289(a859),x63733),x63732))+~P85(f784(f784(f289(a859),x63732),x63731))+P85(f784(f784(f289(a859),x63731),x63732))+P85(f784(f784(f289(a859),x63733),x63731))
% 11.41/11.19 [6393]~P85(f784(x63931,x63932))+~P85(f784(f71(x63933),x63932))+P85(f784(x63931,f495(x63931,x63932,x63933)))+P85(f784(x63931,f187(f869(x63933,a852))))
% 11.41/11.19 [6408]~P113(x64081)+~P89(x64081)+P85(f784(f784(f243(x64081),f784(f113(x64081),x64082)),f784(f113(x64081),x64083)))+~P85(f784(f784(f243(a1),x64082),x64083))
% 11.41/11.19 [6409]~P113(x64091)+~P89(x64091)+P85(f784(f784(f242(x64091),f784(f113(x64091),x64092)),f784(f113(x64091),x64093)))+~P85(f784(f784(f242(a1),x64092),x64093))
% 11.41/11.19 [6412]~P85(f784(x64121,x64123))+~P85(f784(f71(x64122),x64123))+P85(f784(f71(x64122),f495(x64121,x64123,x64122)))+P85(f784(x64121,f187(f869(x64122,a852))))
% 11.41/11.19 [6446]P142(x64461,x64462,x64463)+~P85(f784(x64461,x64462))+P85(f784(f784(f243(a1),x64463),f789(x64463,x64462,x64461)))+P85(f784(f784(f243(a1),f2(a1)),x64463))
% 11.41/11.19 [6486]P143(x64861,x64862,x64863)+P85(f784(f784(f243(a1),x64863),f793(x64863,x64862,x64861)))+~P85(f784(x64861,f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x64863))
% 11.41/11.19 [6513]~P103(x65131)+~P90(x65131)+E(f784(f784(f246(x65131),f784(f113(x65131),x65132)),f784(f113(x65131),x65133)),f784(f113(x65131),x65133))+P85(f784(f784(f242(x65131),f784(f113(x65131),x65132)),f784(f113(x65131),x65133)))
% 11.41/11.19 [6514]~P103(x65141)+~P90(x65141)+E(f784(f784(f186(x65141),f784(f113(x65141),x65142)),f784(f113(x65141),x65143)),f784(f113(x65141),x65142))+P85(f784(f784(f242(x65141),f784(f113(x65141),x65142)),f784(f113(x65141),x65143)))
% 11.41/11.19 [6521]E(x65211,f2(a859))+~P85(f784(f63(x65213,x65211),x65212))+~P85(f784(f784(f243(a859),f2(a859)),x65211))+P85(f784(f784(f242(a859),f2(a859)),f784(f260(a859,a859),x65212)))
% 11.41/11.19 [6527]~P85(f784(f784(f289(a859),x65271),x65273))+~P85(f784(f784(f289(a859),x65272),x65271))+~P85(f784(f784(f289(a859),x65273),x65272))+P85(f784(f784(f289(a859),x65271),x65272))
% 11.41/11.19 [6528]~P85(f784(f784(f289(a859),x65281),x65283))+~P85(f784(f784(f289(a859),x65282),x65281))+P85(f784(f784(f289(a859),x65281),x65282))+~P85(f784(f784(f289(a859),x65283),x65282))
% 11.41/11.19 [6576]P142(x65762,x65763,x65761)+E(x65761,f2(a1))+~P85(f784(x65762,f789(x65761,x65763,x65762)))+P85(f784(f784(f243(a1),f2(a1)),x65761))
% 11.41/11.19 [6577]P143(x65772,x65773,x65771)+E(x65771,f2(a1))+~P85(f784(x65772,f797(x65771,x65773,x65772)))+P85(f784(f784(f243(a1),f2(a1)),x65771))
% 11.41/11.19 [6597]~P4(x65971)+~P90(x65971)+~E(f60(x65971,f784(f113(x65971),x65973),f784(f113(x65971),x65972)),f2(x65971))+P85(f784(f784(f289(x65971),f784(f113(x65971),x65972)),f784(f113(x65971),x65973)))
% 11.41/11.19 [6670]P142(x66701,x66702,x66703)+~P85(f784(x66701,x66702))+~P85(f784(x66701,f789(x66703,x66702,x66701)))+P85(f784(f784(f243(a1),f2(a1)),x66703))
% 11.41/11.19 [6700]P143(x67001,x67002,x67003)+~P85(f784(x67001,f797(x67003,x67002,x67001)))+~P85(f784(x67001,f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x67003))
% 11.41/11.19 [6711]E(x67111,f2(a859))+~P85(f784(f63(x67113,x67111),x67112))+P85(f784(f784(f242(a859),f784(f260(a859,a859),x67112)),f2(a859)))+P85(f784(f784(f243(a859),f2(a859)),x67111))
% 11.41/11.19 [6816]~P89(x68163)+~P113(x68163)+~P85(f784(f784(f243(x68163),f784(f113(x68163),x68161)),f784(f113(x68163),x68162)))+P85(f784(f784(f243(a1),x68161),x68162))
% 11.41/11.19 [6817]~P89(x68173)+~P113(x68173)+~P85(f784(f784(f242(x68173),f784(f113(x68173),x68171)),f784(f113(x68173),x68172)))+P85(f784(f784(f242(a1),x68171),x68172))
% 11.41/11.19 [6846]~P101(x68461)+~P15(x68461,x68463)+P15(x68461,f784(f784(f144(x68461),x68462),x68463))+~P85(f784(f784(f242(x68461),x68462),f774(x68463,x68462,x68461)))
% 11.41/11.19 [6847]~P101(x68471)+~P15(x68471,x68473)+P15(x68471,f784(f784(f144(x68471),x68472),x68473))+~P85(f784(f784(f242(x68471),x68472),f775(x68473,x68472,x68471)))
% 11.41/11.19 [6919]~P4(x69191)+~P90(x69191)+E(f60(x69191,f784(f113(x69191),x69192),f784(f113(x69191),x69193)),f2(x69191))+~P85(f784(f784(f289(x69191),f784(f113(x69191),x69193)),f784(f113(x69191),x69192)))
% 11.41/11.19 [6933]P142(x69332,x69333,x69331)+E(x69331,f2(a1))+P85(f784(f784(f243(a1),x69331),f2(a1)))+P85(f784(f784(f243(a1),f790(x69331,x69333,x69332)),x69331))
% 11.41/11.19 [6934]P143(x69342,x69343,x69341)+E(x69341,f2(a1))+P85(f784(f784(f243(a1),x69341),f2(a1)))+P85(f784(f784(f243(a1),f794(x69341,x69343,x69342)),x69341))
% 11.41/11.19 [6938]~P101(x69381)+~P90(x69381)+P85(f784(f784(f243(x69381),f784(f113(x69381),x69382)),f784(f113(x69381),x69383)))+P85(f784(f784(f242(x69381),f784(f113(x69381),x69383)),f784(f113(x69381),x69382)))
% 11.41/11.19 [6972]P142(x69722,x69723,x69721)+E(x69721,f2(a1))+P85(f784(f784(f242(a1),f789(x69721,x69723,x69722)),f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x69721))
% 11.41/11.19 [6973]P143(x69732,x69733,x69731)+E(x69731,f2(a1))+P85(f784(f784(f242(a1),f793(x69731,x69733,x69732)),f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x69731))
% 11.41/11.19 [6991]~P101(x69911)+~P15(x69911,x69913)+E(f784(f784(f142(x69911,x69911,f7(x69911)),x69912),f154(x69911,x69912,x69913)),x69913)+~P85(f784(f784(f347(x69911),x69912),f784(f164(x69911),x69913)))
% 11.41/11.19 [7041]P142(x70411,x70412,x70413)+~P85(f784(x70411,x70412))+P85(f784(f784(f243(a1),x70413),f2(a1)))+P85(f784(f784(f243(a1),f790(x70413,x70412,x70411)),x70413))
% 11.41/11.19 [7047]~P103(x70471)+~P90(x70471)+E(f784(f784(f246(x70471),f784(f113(x70471),x70472)),f784(f113(x70471),x70473)),f784(f113(x70471),x70472))+~P85(f784(f784(f242(x70471),f784(f113(x70471),x70472)),f784(f113(x70471),x70473)))
% 11.41/11.19 [7048]~P103(x70481)+~P90(x70481)+E(f784(f784(f186(x70481),f784(f113(x70481),x70482)),f784(f113(x70481),x70483)),f784(f113(x70481),x70483))+~P85(f784(f784(f242(x70481),f784(f113(x70481),x70482)),f784(f113(x70481),x70483)))
% 11.41/11.19 [7061]P143(x70611,x70612,x70613)+~P85(f784(x70611,f2(a1)))+P85(f784(f784(f243(a1),x70613),f2(a1)))+P85(f784(f784(f243(a1),f794(x70613,x70612,x70611)),x70613))
% 11.41/11.19 [7071]P142(x70711,x70712,x70713)+~P85(f784(x70711,x70712))+P85(f784(f784(f242(a1),f789(x70713,x70712,x70711)),f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x70713))
% 11.41/11.19 [7095]P143(x70951,x70952,x70953)+~P85(f784(x70951,f2(a1)))+P85(f784(f784(f242(a1),f793(x70953,x70952,x70951)),f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x70953))
% 11.41/11.19 [7121]~P85(f784(x71211,x71212))+P85(f784(x71211,f2(a859)))+~P85(f784(f784(f243(a859),x71212),x71213))+P85(f784(f784(f243(a859),f818(x71212,x71211,x71213)),x71213))
% 11.41/11.19 [7138]~P101(x71381)+~P15(x71381,x71383)+P15(x71381,f784(f784(f144(x71381),x71382),x71383))+P85(f784(f784(f347(x71381),f774(x71383,x71382,x71381)),f784(f164(x71381),x71383)))
% 11.41/11.19 [7139]~P101(x71391)+~P15(x71391,x71393)+P15(x71391,f784(f784(f144(x71391),x71392),x71393))+P85(f784(f784(f347(x71391),f775(x71393,x71392,x71391)),f784(f164(x71391),x71393)))
% 11.41/11.19 [7261]~P101(x72611)+~P6(x72611)+~P85(f784(f784(f243(x72611),x72613),f52(x72611,x72612)))+P85(f784(f784(f347(x72611),f662(x72612,x72613,x72611)),x72612))
% 11.41/11.19 [7430]~P101(x74301)+~P6(x74301)+~P85(f784(f784(f243(x74301),f53(x74301,x74303)),x74302))+P85(f784(f784(f243(x74301),f663(x74302,x74303,x74301)),x74302))
% 11.41/11.19 [7431]~P101(x74311)+~P6(x74311)+~P85(f784(f784(f243(x74311),f53(x74311,x74313)),x74312))+P85(f784(f784(f347(x74311),f663(x74312,x74313,x74311)),x74313))
% 11.41/11.19 [7444]P142(x74442,x74443,x74441)+E(x74441,f2(a1))+P85(f784(f784(f243(a1),x74441),f789(x74441,x74443,x74442)))+P85(f784(f784(f243(a1),f790(x74441,x74443,x74442)),x74441))
% 11.41/11.19 [7445]P143(x74452,x74453,x74451)+E(x74451,f2(a1))+P85(f784(f784(f243(a1),x74451),f793(x74451,x74453,x74452)))+P85(f784(f784(f243(a1),f794(x74451,x74453,x74452)),x74451))
% 11.41/11.19 [7541]P142(x75413,x75412,x75411)+E(x75411,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x75411),f792(x75411,x75412,x75413))),f789(x75411,x75412,x75413)),x75412)+P85(f784(f784(f243(a1),f2(a1)),x75411))
% 11.41/11.19 [7542]P143(x75423,x75422,x75421)+E(x75421,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x75421),f797(x75421,x75422,x75423))),f793(x75421,x75422,x75423)),x75422)+P85(f784(f784(f243(a1),f2(a1)),x75421))
% 11.41/11.19 [7543]~P125(x75431)+~P85(f784(f784(f243(x75431),x75432),f2(x75431)))+P85(f784(f784(f243(x75431),f784(f784(f90(x75431),x75432),x75433)),f2(x75431)))+~P85(f784(f784(f243(x75431),f2(x75431)),x75433))
% 11.41/11.19 [7544]~P125(x75441)+~P85(f784(f784(f243(x75441),x75443),f2(x75441)))+P85(f784(f784(f243(x75441),f784(f784(f90(x75441),x75442),x75443)),f2(x75441)))+~P85(f784(f784(f243(x75441),f2(x75441)),x75442))
% 11.41/11.19 [7545]~P125(x75451)+~P85(f784(f784(f243(x75451),x75452),f2(x75451)))+P85(f784(f784(f243(x75451),f784(f784(f90(x75451),x75452),x75453)),f2(x75451)))+~P85(f784(f784(f243(x75451),f2(x75451)),x75453))
% 11.41/11.19 [7546]~P61(x75461)+~P85(f784(f784(f243(x75461),x75463),f2(x75461)))+P85(f784(f784(f243(x75461),f784(f784(f293(x75461),x75462),x75463)),f2(x75461)))+~P85(f784(f784(f243(x75461),f2(x75461)),x75462))
% 11.41/11.19 [7547]~P61(x75471)+~P85(f784(f784(f243(x75471),x75472),f2(x75471)))+P85(f784(f784(f243(x75471),f784(f784(f293(x75471),x75472),x75473)),f2(x75471)))+~P85(f784(f784(f243(x75471),f2(x75471)),x75473))
% 11.41/11.19 [7548]~P62(x75481)+~P85(f784(f784(f243(x75481),x75483),f2(x75481)))+P85(f784(f784(f243(x75481),f784(f784(f293(x75481),x75482),x75483)),f2(x75481)))+~P85(f784(f784(f243(x75481),f2(x75481)),x75482))
% 11.41/11.19 [7549]~P62(x75491)+~P85(f784(f784(f243(x75491),x75492),f2(x75491)))+P85(f784(f784(f243(x75491),f784(f784(f293(x75491),x75492),x75493)),f2(x75491)))+~P85(f784(f784(f243(x75491),f2(x75491)),x75493))
% 11.41/11.19 [7550]~P130(x75501)+~P85(f784(f784(f242(x75501),x75502),f2(x75501)))+P85(f784(f784(f242(x75501),f784(f784(f90(x75501),x75502),x75503)),f2(x75501)))+~P85(f784(f784(f242(x75501),f2(x75501)),x75503))
% 11.41/11.19 [7551]~P122(x75511)+~P85(f784(f784(f242(x75511),x75513),f2(x75511)))+P85(f784(f784(f242(x75511),f784(f784(f90(x75511),x75512),x75513)),f2(x75511)))+~P85(f784(f784(f242(x75511),f2(x75511)),x75512))
% 11.41/11.19 [7552]~P122(x75521)+~P85(f784(f784(f242(x75521),x75522),f2(x75521)))+P85(f784(f784(f242(x75521),f784(f784(f90(x75521),x75522),x75523)),f2(x75521)))+~P85(f784(f784(f242(x75521),f2(x75521)),x75523))
% 11.41/11.19 [7553]~P130(x75531)+~P85(f784(f784(f242(x75531),x75533),f2(x75531)))+P85(f784(f784(f242(x75531),f784(f784(f90(x75531),x75532),x75533)),f2(x75531)))+~P85(f784(f784(f242(x75531),f2(x75531)),x75532))
% 11.41/11.19 [7554]~P130(x75541)+~P85(f784(f784(f242(x75541),x75543),f2(x75541)))+P85(f784(f784(f242(x75541),f784(f784(f90(x75541),x75542),x75543)),f2(x75541)))+~P85(f784(f784(f242(x75541),f2(x75541)),x75542))
% 11.41/11.19 [7555]~P130(x75551)+~P85(f784(f784(f242(x75551),x75552),f2(x75551)))+P85(f784(f784(f242(x75551),f784(f784(f90(x75551),x75552),x75553)),f2(x75551)))+~P85(f784(f784(f242(x75551),f2(x75551)),x75553))
% 11.41/11.19 [7556]~P130(x75561)+~P85(f784(f784(f242(x75561),x75562),f2(x75561)))+P85(f784(f784(f242(x75561),f784(f784(f90(x75561),x75562),x75563)),f2(x75561)))+~P85(f784(f784(f242(x75561),f2(x75561)),x75563))
% 11.41/11.19 [7557]~P61(x75571)+~P85(f784(f784(f242(x75571),x75573),f2(x75571)))+P85(f784(f784(f242(x75571),f784(f784(f293(x75571),x75572),x75573)),f2(x75571)))+~P85(f784(f784(f242(x75571),f2(x75571)),x75572))
% 11.41/11.19 [7558]~P61(x75581)+~P85(f784(f784(f242(x75581),x75582),f2(x75581)))+P85(f784(f784(f242(x75581),f784(f784(f293(x75581),x75582),x75583)),f2(x75581)))+~P85(f784(f784(f242(x75581),f2(x75581)),x75583))
% 11.41/11.19 [7559]~P62(x75591)+~P85(f784(f784(f243(x75591),x75593),f2(x75591)))+P85(f784(f784(f242(x75591),f784(f784(f293(x75591),x75592),x75593)),f2(x75591)))+~P85(f784(f784(f242(x75591),f2(x75591)),x75592))
% 11.41/11.19 [7560]~P62(x75601)+~P85(f784(f784(f242(x75601),x75602),f2(x75601)))+P85(f784(f784(f242(x75601),f784(f784(f293(x75601),x75602),x75603)),f2(x75601)))+~P85(f784(f784(f243(x75601),f2(x75601)),x75603))
% 11.41/11.19 [7576]P142(x75761,x75762,x75763)+~P85(f784(x75761,x75762))+P85(f784(f784(f243(a1),x75763),f789(x75763,x75762,x75761)))+P85(f784(f784(f243(a1),f790(x75763,x75762,x75761)),x75763))
% 11.41/11.19 [7589]P143(x75891,x75892,x75893)+P85(f784(f784(f243(a1),x75893),f793(x75893,x75892,x75891)))+~P85(f784(x75891,f2(a1)))+P85(f784(f784(f243(a1),f794(x75893,x75892,x75891)),x75893))
% 11.41/11.19 [7641]P142(x76412,x76413,x76411)+E(x76411,f2(a1))+~P85(f784(x76412,f789(x76411,x76413,x76412)))+P85(f784(f784(f243(a1),f790(x76411,x76413,x76412)),x76411))
% 11.41/11.19 [7642]P143(x76422,x76423,x76421)+E(x76421,f2(a1))+~P85(f784(x76422,f797(x76421,x76423,x76422)))+P85(f784(f784(f243(a1),f794(x76421,x76423,x76422)),x76421))
% 11.41/11.19 [7651]P142(x76513,x76512,x76511)+~P85(f784(x76513,x76512))+E(f784(f784(f89(a1),f784(f784(f90(a1),x76511),f792(x76511,x76512,x76513))),f789(x76511,x76512,x76513)),x76512)+P85(f784(f784(f243(a1),f2(a1)),x76511))
% 11.41/11.19 [7669]P143(x76693,x76692,x76691)+E(f784(f784(f89(a1),f784(f784(f90(a1),x76691),f797(x76691,x76692,x76693))),f793(x76691,x76692,x76693)),x76692)+~P85(f784(x76693,f2(a1)))+P85(f784(f784(f243(a1),f2(a1)),x76691))
% 11.41/11.19 [7692]~P85(f784(x76921,x76923))+~P85(f784(f71(x76922),x76923))+P85(f784(f784(f347(x76922),f496(x76921,x76923,x76922)),f495(x76921,x76923,x76922)))+P85(f784(x76921,f187(f869(x76922,a852))))
% 11.41/11.19 [7702]P142(x77021,x77022,x77023)+~P85(f784(x77021,x77022))+~P85(f784(x77021,f789(x77023,x77022,x77021)))+P85(f784(f784(f243(a1),f790(x77023,x77022,x77021)),x77023))
% 11.41/11.19 [7708]P143(x77081,x77082,x77083)+~P85(f784(x77081,f797(x77083,x77082,x77081)))+~P85(f784(x77081,f2(a1)))+P85(f784(f784(f243(a1),f794(x77083,x77082,x77081)),x77083))
% 11.41/11.19 [7780]~P90(x77801)+~P101(x77801)+~P85(f784(f784(f243(x77801),f784(f113(x77801),x77802)),f784(f113(x77801),x77803)))+~P85(f784(f784(f242(x77801),f784(f113(x77801),x77803)),f784(f113(x77801),x77802)))
% 11.41/11.19 [7816]~P61(x78161)+~P85(f784(f784(f243(x78161),f784(f784(f293(x78161),x78163),x78162)),f2(x78161)))+P85(f784(f784(f243(x78161),x78162),f2(x78161)))+P85(f784(f784(f243(x78161),f2(x78161)),x78162))
% 11.41/11.19 [7817]~P61(x78171)+~P85(f784(f784(f243(x78171),f784(f784(f293(x78171),x78172),x78173)),f2(x78171)))+P85(f784(f784(f243(x78171),x78172),f2(x78171)))+P85(f784(f784(f243(x78171),f2(x78171)),x78172))
% 11.41/11.19 [7818]~P122(x78181)+~P85(f784(f784(f242(x78181),f784(f784(f90(x78181),x78183),x78182)),f2(x78181)))+P85(f784(f784(f242(x78181),x78182),f2(x78181)))+P85(f784(f784(f242(x78181),f2(x78181)),x78182))
% 11.41/11.19 [7819]~P122(x78191)+~P85(f784(f784(f242(x78191),f784(f784(f90(x78191),x78192),x78193)),f2(x78191)))+P85(f784(f784(f242(x78191),x78192),f2(x78191)))+P85(f784(f784(f242(x78191),f2(x78191)),x78192))
% 11.41/11.19 [7820]~P61(x78201)+~P85(f784(f784(f242(x78201),f784(f784(f293(x78201),x78203),x78202)),f2(x78201)))+P85(f784(f784(f242(x78201),x78202),f2(x78201)))+P85(f784(f784(f242(x78201),f2(x78201)),x78202))
% 11.41/11.19 [7821]~P61(x78211)+~P85(f784(f784(f242(x78211),f784(f784(f293(x78211),x78212),x78213)),f2(x78211)))+P85(f784(f784(f242(x78211),x78212),f2(x78211)))+P85(f784(f784(f242(x78211),f2(x78211)),x78212))
% 11.41/11.19 [7847]~P61(x78471)+~P85(f784(f784(f243(x78471),f784(f784(f293(x78471),x78472),x78473)),f2(x78471)))+P85(f784(f784(f243(x78471),f2(x78471)),x78472))+P85(f784(f784(f243(x78471),f2(x78471)),x78473))
% 11.41/11.19 [7848]~P122(x78481)+~P85(f784(f784(f242(x78481),f784(f784(f90(x78481),x78482),x78483)),f2(x78481)))+P85(f784(f784(f242(x78481),f2(x78481)),x78482))+P85(f784(f784(f242(x78481),f2(x78481)),x78483))
% 11.41/11.19 [7849]~P61(x78491)+~P85(f784(f784(f242(x78491),f784(f784(f293(x78491),x78492),x78493)),f2(x78491)))+P85(f784(f784(f242(x78491),f2(x78491)),x78492))+P85(f784(f784(f242(x78491),f2(x78491)),x78493))
% 11.41/11.19 [7868]P142(x78682,x78683,x78681)+E(x78681,f2(a1))+P85(f784(f784(f242(a1),f789(x78681,x78683,x78682)),f2(a1)))+P85(f784(f784(f243(a1),f790(x78681,x78683,x78682)),x78681))
% 11.41/11.19 [7869]P143(x78692,x78693,x78691)+E(x78691,f2(a1))+P85(f784(f784(f242(a1),f793(x78691,x78693,x78692)),f2(a1)))+P85(f784(f784(f243(a1),f794(x78691,x78693,x78692)),x78691))
% 11.41/11.19 [7875]~P120(x78751)+~P85(f784(f784(f243(x78751),x78752),f87(x78751)))+P85(f784(f784(f243(x78751),f784(f784(f252(x78751),x78752),f784(a160,x78753))),f87(x78751)))+~P85(f784(f784(f243(x78751),f2(x78751)),x78752))
% 11.41/11.19 [7928]~P101(x79281)+~E(x79283,f120(x79281))+~P15(x79281,f784(f162(x79281),x79283))+E(f784(f136(x79281,x79281,f784(f9(x79281,x79281,x79281),f186(x79281)),x79282),f784(f162(x79281),x79283)),x79282)
% 11.41/11.19 [7930]P142(x79301,x79302,x79303)+~P85(f784(x79301,x79302))+P85(f784(f784(f242(a1),f789(x79303,x79302,x79301)),f2(a1)))+P85(f784(f784(f243(a1),f790(x79303,x79302,x79301)),x79303))
% 11.41/11.19 [7942]P143(x79421,x79422,x79423)+~P85(f784(x79421,f2(a1)))+P85(f784(f784(f242(a1),f793(x79423,x79422,x79421)),f2(a1)))+P85(f784(f784(f243(a1),f794(x79423,x79422,x79421)),x79423))
% 11.41/11.19 [8152]P142(x81523,x81522,x81521)+E(x81521,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x81521),f792(x81521,x81522,x81523))),f789(x81521,x81522,x81523)),x81522)+P85(f784(f784(f243(a1),f790(x81521,x81522,x81523)),x81521))
% 11.41/11.19 [8153]P143(x81533,x81532,x81531)+E(x81531,f2(a1))+E(f784(f784(f89(a1),f784(f784(f90(a1),x81531),f797(x81531,x81532,x81533))),f793(x81531,x81532,x81533)),x81532)+P85(f784(f784(f243(a1),f794(x81531,x81532,x81533)),x81531))
% 11.41/11.19 [8188]P142(x81883,x81882,x81881)+~P85(f784(x81883,x81882))+E(f784(f784(f89(a1),f784(f784(f90(a1),x81881),f792(x81881,x81882,x81883))),f789(x81881,x81882,x81883)),x81882)+P85(f784(f784(f243(a1),f790(x81881,x81882,x81883)),x81881))
% 11.41/11.19 [8189]~P68(x81891)+~P71(x81891)+~P37(x81893)+E(f784(f784(f8(a859,x81891),f784(f784(f10(a1,x81891,a859),x81892),f109(a1))),f784(f313(a1,a859,a114),x81893)),f784(f784(f8(a1,x81891),x81892),x81893))
% 11.41/11.19 [8190]~P68(x81901)+~P71(x81901)+~P37(x81903)+E(f784(f784(f11(a859,x81901),f784(f784(f10(a1,x81901,a859),x81902),f109(a1))),f784(f313(a1,a859,a114),x81903)),f784(f784(f11(a1,x81901),x81902),x81903))
% 11.41/11.19 [8198]P143(x81983,x81982,x81981)+E(f784(f784(f89(a1),f784(f784(f90(a1),x81981),f797(x81981,x81982,x81983))),f793(x81981,x81982,x81983)),x81982)+~P85(f784(x81983,f2(a1)))+P85(f784(f784(f243(a1),f794(x81981,x81982,x81983)),x81981))
% 11.41/11.19 [8216]~E(x82162,f2(a859))+~E(f784(f250(a859,a859),x82163),f2(a859))+~E(x82161,f784(f784(f89(a859),f784(f784(f90(a859),f784(f250(a859,a859),x82163)),x82162)),f784(f260(a859,a859),x82163)))+P85(f784(f63(x82161,x82162),x82163))
% 11.41/11.19 [9067]P85(f784(f784(f242(a1),x90671),f2(a1)))+~P85(f784(f784(f243(a1),f784(f784(f89(a1),f784(f784(f90(a1),x90672),x90671)),x90673)),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x90672))+~P85(f784(f784(f242(a1),f2(a1)),x90673))
% 11.41/11.19 [5689]~P93(x56892)+E(x56891,f187(f869(x56892,a852)))+~P85(f784(f71(x56892),x56891))+E(f15(x56892,f784(f784(f312(x56892),x56893),x56891)),f784(f784(f110(x56892),x56893),f15(x56892,x56891)))
% 11.41/11.19 [5690]~P101(x56902)+E(x56901,f187(f869(x56902,a852)))+~P85(f784(f71(x56902),x56901))+E(f16(x56902,f784(f784(f312(x56902),x56903),x56901)),f784(f784(f186(x56902),x56903),f16(x56902,x56901)))
% 11.41/11.19 [5691]~P101(x56912)+E(x56911,f187(f869(x56912,a852)))+~P85(f784(f71(x56912),x56911))+E(f17(x56912,f784(f784(f312(x56912),x56913),x56911)),f784(f784(f246(x56912),x56913),f17(x56912,x56911)))
% 11.41/11.19 [5692]~P93(x56922)+E(x56921,f187(f869(x56922,a852)))+~P85(f784(f71(x56922),x56921))+E(f12(x56922,f784(f784(f312(x56922),x56923),x56921)),f784(f784(f111(x56922),x56923),f12(x56922,x56921)))
% 11.41/11.19 [6009]~P122(x60091)+~E(x60093,f2(x60091))+~E(x60092,f2(x60091))+E(f784(f784(f89(x60091),f784(f784(f90(x60091),x60092),x60092)),f784(f784(f90(x60091),x60093),x60093)),f2(x60091))
% 11.41/11.19 [6083]~P92(x60832)+E(x60831,f187(f869(x60832,a852)))+~P85(f784(f71(x60832),x60831))+E(f784(f73(x60832,f90(x60832)),f784(f784(f312(x60832),x60833),x60831)),f784(f784(f90(x60832),x60833),f784(f73(x60832,f90(x60832)),x60831)))
% 11.41/11.19 [6209]~P101(x62092)+E(x62091,f187(f869(x62092,a852)))+~P85(f784(f71(x62092),x62091))+E(f13(x62092,f186(x62092),f784(f784(f312(x62092),x62093),x62091)),f784(f784(f186(x62092),x62093),f13(x62092,f186(x62092),x62091)))
% 11.41/11.19 [6210]~P101(x62102)+E(x62101,f187(f869(x62102,a852)))+~P85(f784(f71(x62102),x62101))+E(f14(x62102,f246(x62102),f784(f784(f312(x62102),x62103),x62101)),f784(f784(f246(x62102),x62103),f14(x62102,f246(x62102),x62101)))
% 11.41/11.19 [6618]~P93(x66181)+~P85(f784(f71(x66181),x66183))+E(f784(f784(f74(x66181,x66181,f110(x66181)),x66182),x66183),f15(x66181,f784(f784(f312(x66181),x66182),x66183)))+P85(f784(f784(f347(x66181),x66182),x66183))
% 11.41/11.19 [6619]~P101(x66191)+~P85(f784(f71(x66191),x66193))+E(f784(f784(f74(x66191,x66191,f186(x66191)),x66192),x66193),f16(x66191,f784(f784(f312(x66191),x66192),x66193)))+P85(f784(f784(f347(x66191),x66192),x66193))
% 11.41/11.19 [6620]~P101(x66201)+~P85(f784(f71(x66201),x66203))+E(f784(f784(f74(x66201,x66201,f246(x66201)),x66202),x66203),f17(x66201,f784(f784(f312(x66201),x66202),x66203)))+P85(f784(f784(f347(x66201),x66202),x66203))
% 11.41/11.19 [6621]~P93(x66211)+~P85(f784(f71(x66211),x66213))+E(f784(f784(f74(x66211,x66211,f111(x66211)),x66212),x66213),f12(x66211,f784(f784(f312(x66211),x66212),x66213)))+P85(f784(f784(f347(x66211),x66212),x66213))
% 11.41/11.19 [6735]~P65(x67351)+~P85(f784(f71(x67351),x67353))+E(f784(f73(x67351,f90(x67351)),f784(f784(f312(x67351),x67352),x67353)),f784(f784(f74(x67351,x67351,f90(x67351)),x67352),x67353))+P85(f784(f784(f347(x67351),x67352),x67353))
% 11.41/11.19 [6753]~P101(x67531)+~P85(f784(f71(x67531),x67533))+E(f13(x67531,f186(x67531),f784(f784(f312(x67531),x67532),x67533)),f784(f784(f74(x67531,x67531,f186(x67531)),x67532),x67533))+P85(f784(f784(f347(x67531),x67532),x67533))
% 11.41/11.19 [6754]~P101(x67541)+~P85(f784(f71(x67541),x67543))+E(f14(x67541,f246(x67541),f784(f784(f312(x67541),x67542),x67543)),f784(f784(f74(x67541,x67541,f246(x67541)),x67542),x67543))+P85(f784(f784(f347(x67541),x67542),x67543))
% 11.41/11.19 [6821]~E(f784(f784(f89(a1),x68212),f784(f784(f90(a1),x68213),x68211)),x68213)+~P85(f784(f784(f243(a1),f2(a1)),x68213))+P85(f784(f784(f242(a1),f87(a1)),x68211))+~P85(f784(f784(f243(a1),x68212),x68213))
% 11.41/11.19 [6852]~E(f784(f784(f89(a1),x68522),f784(f784(f90(a1),x68523),x68521)),x68523)+P85(f784(f784(f242(a1),x68521),f87(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x68523))+~P85(f784(f784(f242(a1),f2(a1)),x68522))
% 11.41/11.19 [6870]E(x68701,f2(a859))+~P85(f784(f63(x68703,x68701),x68702))+~P85(f784(f784(f243(a859),f2(a859)),x68701))+P85(f784(f784(f243(a859),f784(f260(a859,a859),x68702)),x68701))
% 11.41/11.19 [6898]~P134(x68981)+~P85(f784(f784(f242(x68981),x68982),f2(x68981)))+~P85(f784(f784(f242(x68981),x68983),f2(x68981)))+E(f784(f784(f90(x68981),f784(f84(x68981),x68982)),f784(f84(x68981),x68983)),f784(f84(x68981),f784(f784(f90(x68981),x68982),x68983)))
% 11.41/11.19 [6949]~P134(x69491)+~P85(f784(f784(f242(x69491),x69492),f2(x69491)))+E(f784(f784(f90(x69491),f784(f84(x69491),x69492)),f784(f84(x69491),x69493)),f784(f84(x69491),f784(f784(f90(x69491),x69492),x69493)))+~P85(f784(f784(f242(x69491),f2(x69491)),x69493))
% 11.41/11.19 [6950]~P134(x69501)+~P85(f784(f784(f242(x69501),x69503),f2(x69501)))+E(f784(f784(f90(x69501),f784(f84(x69501),x69502)),f784(f84(x69501),x69503)),f784(f84(x69501),f784(f784(f90(x69501),x69502),x69503)))+~P85(f784(f784(f242(x69501),f2(x69501)),x69502))
% 11.41/11.19 [7000]~P134(x70001)+E(f784(f784(f90(x70001),f784(f84(x70001),x70002)),f784(f84(x70001),x70003)),f784(f84(x70001),f784(f784(f90(x70001),x70002),x70003)))+~P85(f784(f784(f242(x70001),f2(x70001)),x70002))+~P85(f784(f784(f242(x70001),f2(x70001)),x70003))
% 11.41/11.19 [7018]~P122(x70181)+~P85(f784(f784(f243(x70181),x70183),f2(x70181)))+~P85(f784(f784(f243(x70181),x70182),f2(x70181)))+P85(f784(f784(f243(x70181),f2(x70181)),f784(f784(f90(x70181),x70182),x70183)))
% 11.41/11.19 [7019]~P61(x70191)+~P85(f784(f784(f243(x70191),x70193),f2(x70191)))+~P85(f784(f784(f243(x70191),x70192),f2(x70191)))+P85(f784(f784(f243(x70191),f2(x70191)),f784(f784(f293(x70191),x70192),x70193)))
% 11.41/11.19 [7020]~P62(x70201)+~P85(f784(f784(f243(x70201),x70203),f2(x70201)))+~P85(f784(f784(f243(x70201),x70202),f2(x70201)))+P85(f784(f784(f243(x70201),f2(x70201)),f784(f784(f293(x70201),x70202),x70203)))
% 11.41/11.19 [7021]~P122(x70211)+~P85(f784(f784(f242(x70211),x70213),f2(x70211)))+~P85(f784(f784(f242(x70211),x70212),f2(x70211)))+P85(f784(f784(f242(x70211),f2(x70211)),f784(f784(f90(x70211),x70212),x70213)))
% 11.41/11.19 [7022]~P131(x70221)+~P85(f784(f784(f242(x70221),x70223),f2(x70221)))+~P85(f784(f784(f242(x70221),x70222),f2(x70221)))+P85(f784(f784(f242(x70221),f2(x70221)),f784(f784(f90(x70221),x70222),x70223)))
% 11.41/11.19 [7023]~P131(x70231)+~P85(f784(f784(f242(x70231),x70233),f2(x70231)))+~P85(f784(f784(f242(x70231),x70232),f2(x70231)))+P85(f784(f784(f242(x70231),f2(x70231)),f784(f784(f90(x70231),x70232),x70233)))
% 11.41/11.19 [7024]~P61(x70241)+~P85(f784(f784(f242(x70241),x70243),f2(x70241)))+~P85(f784(f784(f242(x70241),x70242),f2(x70241)))+P85(f784(f784(f242(x70241),f2(x70241)),f784(f784(f293(x70241),x70242),x70243)))
% 11.41/11.19 [7025]~P62(x70251)+~P85(f784(f784(f243(x70251),x70253),f2(x70251)))+~P85(f784(f784(f242(x70251),x70252),f2(x70251)))+P85(f784(f784(f242(x70251),f2(x70251)),f784(f784(f293(x70251),x70252),x70253)))
% 11.41/11.19 [7026]~P120(x70261)+~P85(f784(f784(f243(a859),f2(a859)),x70263))+~P85(f784(f784(f243(x70261),f87(x70261)),x70262))+P85(f784(f784(f243(x70261),f87(x70261)),f784(f784(f252(x70261),x70262),x70263)))
% 11.41/11.19 [7122]~P81(x71221)+~P85(f784(f784(f243(x71221),f2(x71221)),x71223))+~P85(f784(f784(f243(x71221),f2(x71221)),x71222))+P85(f784(f784(f243(x71221),f2(x71221)),f784(f784(f89(x71221),x71222),x71223)))
% 11.41/11.19 [7123]~P81(x71231)+~P85(f784(f784(f242(x71231),f2(x71231)),x71232))+~P85(f784(f784(f243(x71231),f2(x71231)),x71233))+P85(f784(f784(f243(x71231),f2(x71231)),f784(f784(f89(x71231),x71232),x71233)))
% 11.41/11.19 [7124]~P81(x71241)+~P85(f784(f784(f242(x71241),f2(x71241)),x71243))+~P85(f784(f784(f243(x71241),f2(x71241)),x71242))+P85(f784(f784(f243(x71241),f2(x71241)),f784(f784(f89(x71241),x71242),x71243)))
% 11.41/11.19 [7125]~P125(x71251)+~P85(f784(f784(f243(x71251),f2(x71251)),x71253))+~P85(f784(f784(f243(x71251),f2(x71251)),x71252))+P85(f784(f784(f243(x71251),f2(x71251)),f784(f784(f90(x71251),x71252),x71253)))
% 11.41/11.19 [7126]~P61(x71261)+~P85(f784(f784(f243(x71261),f2(x71261)),x71263))+~P85(f784(f784(f243(x71261),f2(x71261)),x71262))+P85(f784(f784(f243(x71261),f2(x71261)),f784(f784(f293(x71261),x71262),x71263)))
% 11.41/11.19 [7127]~P62(x71271)+~P85(f784(f784(f243(x71271),f2(x71271)),x71273))+~P85(f784(f784(f243(x71271),f2(x71271)),x71272))+P85(f784(f784(f243(x71271),f2(x71271)),f784(f784(f293(x71271),x71272),x71273)))
% 11.41/11.19 [7128]~P120(x71281)+~P85(f784(f784(f243(x71281),f87(x71281)),x71283))+~P85(f784(f784(f243(x71281),f87(x71281)),x71282))+P85(f784(f784(f243(x71281),f87(x71281)),f784(f784(f90(x71281),x71282),x71283)))
% 11.41/11.19 [7129]~P81(x71291)+~P85(f784(f784(f242(x71291),f2(x71291)),x71293))+~P85(f784(f784(f242(x71291),f2(x71291)),x71292))+P85(f784(f784(f242(x71291),f2(x71291)),f784(f784(f89(x71291),x71292),x71293)))
% 11.41/11.19 [7130]~P122(x71301)+~P85(f784(f784(f242(x71301),f2(x71301)),x71303))+~P85(f784(f784(f242(x71301),f2(x71301)),x71302))+P85(f784(f784(f242(x71301),f2(x71301)),f784(f784(f90(x71301),x71302),x71303)))
% 11.41/11.19 [7131]~P130(x71311)+~P85(f784(f784(f242(x71311),f2(x71311)),x71313))+~P85(f784(f784(f242(x71311),f2(x71311)),x71312))+P85(f784(f784(f242(x71311),f2(x71311)),f784(f784(f90(x71311),x71312),x71313)))
% 11.41/11.19 [7132]~P131(x71321)+~P85(f784(f784(f242(x71321),f2(x71321)),x71323))+~P85(f784(f784(f242(x71321),f2(x71321)),x71322))+P85(f784(f784(f242(x71321),f2(x71321)),f784(f784(f90(x71321),x71322),x71323)))
% 11.41/11.19 [7133]~P61(x71331)+~P85(f784(f784(f242(x71331),f2(x71331)),x71333))+~P85(f784(f784(f242(x71331),f2(x71331)),x71332))+P85(f784(f784(f242(x71331),f2(x71331)),f784(f784(f293(x71331),x71332),x71333)))
% 11.41/11.19 [7134]~P62(x71341)+~P85(f784(f784(f243(x71341),f2(x71341)),x71343))+~P85(f784(f784(f242(x71341),f2(x71341)),x71342))+P85(f784(f784(f242(x71341),f2(x71341)),f784(f784(f293(x71341),x71342),x71343)))
% 11.41/11.19 [7212]~P93(x72121)+~P85(f784(f71(x72121),x72123))+E(f15(x72121,f784(f784(f312(x72121),x72122),x72123)),x72122)+~E(f784(f784(f3(f869(x72121,a852)),x72123),f784(f784(f312(x72121),x72122),f187(f869(x72121,a852)))),f187(f869(x72121,a852)))
% 11.41/11.19 [7213]~P101(x72131)+~P85(f784(f71(x72131),x72133))+E(f16(x72131,f784(f784(f312(x72131),x72132),x72133)),x72132)+~E(f784(f784(f3(f869(x72131,a852)),x72133),f784(f784(f312(x72131),x72132),f187(f869(x72131,a852)))),f187(f869(x72131,a852)))
% 11.41/11.19 [7214]~P101(x72141)+~P85(f784(f71(x72141),x72143))+E(f17(x72141,f784(f784(f312(x72141),x72142),x72143)),x72142)+~E(f784(f784(f3(f869(x72141,a852)),x72143),f784(f784(f312(x72141),x72142),f187(f869(x72141,a852)))),f187(f869(x72141,a852)))
% 11.41/11.19 [7215]~P93(x72151)+~P85(f784(f71(x72151),x72153))+E(f12(x72151,f784(f784(f312(x72151),x72152),x72153)),x72152)+~E(f784(f784(f3(f869(x72151,a852)),x72153),f784(f784(f312(x72151),x72152),f187(f869(x72151,a852)))),f187(f869(x72151,a852)))
% 11.41/11.19 [7216]~P61(x72161)+P85(f784(f784(f243(x72161),x72162),f2(x72161)))+P85(f784(f784(f243(x72161),f2(x72161)),x72163))+~P85(f784(f784(f243(x72161),f2(x72161)),f784(f784(f293(x72161),x72163),x72162)))
% 11.41/11.19 [7217]~P61(x72171)+P85(f784(f784(f243(x72171),x72172),f2(x72171)))+P85(f784(f784(f243(x72171),f2(x72171)),x72173))+~P85(f784(f784(f243(x72171),f2(x72171)),f784(f784(f293(x72171),x72172),x72173)))
% 11.41/11.19 [7218]~P61(x72181)+P85(f784(f784(f243(x72181),x72182),f2(x72181)))+P85(f784(f784(f243(x72181),f2(x72181)),x72182))+~P85(f784(f784(f243(x72181),f2(x72181)),f784(f784(f293(x72181),x72183),x72182)))
% 11.41/11.19 [7219]~P61(x72191)+P85(f784(f784(f243(x72191),x72192),f2(x72191)))+P85(f784(f784(f243(x72191),f2(x72191)),x72192))+~P85(f784(f784(f243(x72191),f2(x72191)),f784(f784(f293(x72191),x72192),x72193)))
% 11.41/11.19 [7220]~P122(x72201)+P85(f784(f784(f242(x72201),x72202),f2(x72201)))+P85(f784(f784(f242(x72201),f2(x72201)),x72203))+~P85(f784(f784(f242(x72201),f2(x72201)),f784(f784(f90(x72201),x72203),x72202)))
% 11.41/11.19 [7221]~P122(x72211)+P85(f784(f784(f242(x72211),x72212),f2(x72211)))+P85(f784(f784(f242(x72211),f2(x72211)),x72213))+~P85(f784(f784(f242(x72211),f2(x72211)),f784(f784(f90(x72211),x72212),x72213)))
% 11.41/11.19 [7222]~P61(x72221)+P85(f784(f784(f242(x72221),x72222),f2(x72221)))+P85(f784(f784(f242(x72221),f2(x72221)),x72223))+~P85(f784(f784(f242(x72221),f2(x72221)),f784(f784(f293(x72221),x72223),x72222)))
% 11.41/11.19 [7223]~P61(x72231)+P85(f784(f784(f242(x72231),x72232),f2(x72231)))+P85(f784(f784(f242(x72231),f2(x72231)),x72233))+~P85(f784(f784(f242(x72231),f2(x72231)),f784(f784(f293(x72231),x72232),x72233)))
% 11.41/11.19 [7224]~P122(x72241)+P85(f784(f784(f242(x72241),x72242),f2(x72241)))+P85(f784(f784(f242(x72241),f2(x72241)),x72242))+~P85(f784(f784(f242(x72241),f2(x72241)),f784(f784(f90(x72241),x72243),x72242)))
% 11.41/11.19 [7225]~P122(x72251)+P85(f784(f784(f242(x72251),x72252),f2(x72251)))+P85(f784(f784(f242(x72251),f2(x72251)),x72252))+~P85(f784(f784(f242(x72251),f2(x72251)),f784(f784(f90(x72251),x72252),x72253)))
% 11.41/11.19 [7226]~P61(x72261)+P85(f784(f784(f242(x72261),x72262),f2(x72261)))+P85(f784(f784(f242(x72261),f2(x72261)),x72262))+~P85(f784(f784(f242(x72261),f2(x72261)),f784(f784(f293(x72261),x72263),x72262)))
% 11.41/11.19 [7227]~P61(x72271)+P85(f784(f784(f242(x72271),x72272),f2(x72271)))+P85(f784(f784(f242(x72271),f2(x72271)),x72272))+~P85(f784(f784(f242(x72271),f2(x72271)),f784(f784(f293(x72271),x72272),x72273)))
% 11.41/11.19 [7312]~P85(f784(f784(f289(a859),x73121),x73123))+P85(f784(f784(f289(a859),x73121),x73122))+~P85(f784(f784(f242(a859),x73122),x73123))+~P85(f784(f784(f289(a859),x73121),f784(f784(f3(a859),x73123),x73122)))
% 11.41/11.19 [7313]~P85(f784(f784(f289(a859),x73131),x73133))+P85(f784(f784(f289(a859),x73131),x73132))+~P85(f784(f784(f242(a859),x73133),x73132))+~P85(f784(f784(f289(a859),x73131),f784(f784(f3(a859),x73132),x73133)))
% 11.41/11.19 [7328]~E(f784(f784(f111(f869(x73281,a852)),f784(f164(x73281),x73282)),f784(f164(x73281),x73283)),f187(f869(x73281,a852)))+~P85(f784(f132(x73281),x73283))+~P85(f784(f132(x73281),x73282))+P85(f784(f132(x73281),f784(f784(f130(x73281),x73282),x73283)))
% 11.41/11.19 [7329]~P101(x73291)+~P85(f784(f71(x73291),x73293))+E(f13(x73291,f186(x73291),f784(f784(f312(x73291),x73292),x73293)),x73292)+~E(f784(f784(f3(f869(x73291,a852)),x73293),f784(f784(f312(x73291),x73292),f187(f869(x73291,a852)))),f187(f869(x73291,a852)))
% 11.41/11.19 [7330]~P101(x73301)+~P85(f784(f71(x73301),x73303))+E(f14(x73301,f246(x73301),f784(f784(f312(x73301),x73302),x73303)),x73302)+~E(f784(f784(f3(f869(x73301,a852)),x73303),f784(f784(f312(x73301),x73302),f187(f869(x73301,a852)))),f187(f869(x73301,a852)))
% 11.41/11.19 [7348]~P113(x73481)+~P85(f784(f784(f243(x73481),x73482),x73483))+~P85(f784(f784(f243(x73481),f784(f88(x73481),x73482)),x73483))+P85(f784(f784(f243(x73481),f784(f84(x73481),x73482)),x73483))
% 11.41/11.19 [7349]~P79(x73491)+~P85(f784(f784(f242(x73491),x73492),x73493))+~P85(f784(f784(f242(x73491),f784(f88(x73491),x73492)),x73493))+P85(f784(f784(f242(x73491),f784(f84(x73491),x73492)),x73493))
% 11.41/11.19 [7350]~P79(x73501)+~P85(f784(f784(f242(x73501),x73502),x73503))+~P85(f784(f784(f242(x73501),f784(f88(x73501),x73502)),x73503))+P85(f784(f784(f242(x73501),f784(f84(x73501),x73502)),x73503))
% 11.41/11.19 [7419]~P125(x74191)+P85(f784(f784(f243(x74191),f2(x74191)),x74192))+~P85(f784(f784(f243(x74191),f2(x74191)),x74193))+~P85(f784(f784(f243(x74191),f2(x74191)),f784(f784(f90(x74191),x74193),x74192)))
% 11.41/11.19 [7420]~P125(x74201)+P85(f784(f784(f243(x74201),f2(x74201)),x74202))+~P85(f784(f784(f243(x74201),f2(x74201)),x74203))+~P85(f784(f784(f243(x74201),f2(x74201)),f784(f784(f90(x74201),x74202),x74203)))
% 11.41/11.19 [7725]E(x77251,x77252)+~P85(f784(f71(x77253),x77251))+~P85(f784(f784(f242(a859),f784(f50(x77253),x77251)),f784(f50(x77253),x77252)))+~P85(f784(f784(f242(f869(x77253,a852)),x77252),x77251))
% 11.41/11.19 [7796]~P85(f784(f784(f242(a859),x77962),x77961))+~P85(f784(f784(f243(a859),x77961),x77963))+~P85(f784(f784(f242(a859),x77962),x77963))+P85(f784(f784(f243(a859),f784(f784(f3(a859),x77961),x77962)),f784(f784(f3(a859),x77963),x77962)))
% 11.41/11.19 [7797]~P85(f784(f784(f242(a859),x77972),x77971))+~P85(f784(f784(f242(a859),x77972),x77973))+~P85(f784(f784(f242(a859),x77971),x77973))+P85(f784(f784(f242(a859),f784(f784(f3(a859),x77971),x77972)),f784(f784(f3(a859),x77973),x77972)))
% 11.41/11.19 [7872]~P85(f784(f784(f243(a1),x78721),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x78722))+~P85(f784(f784(f242(a1),x78722),x78723))+P85(f784(f784(f242(a1),f784(f784(f51(a1),x78721),x78722)),f784(f784(f51(a1),x78721),x78723)))
% 11.41/11.19 [7883]~P85(f784(f784(f243(a1),f2(a1)),x78833))+~P85(f784(f784(f242(a1),f2(a1)),x78831))+~P85(f784(f784(f242(a1),x78833),x78832))+P85(f784(f784(f242(a1),f784(f784(f51(a1),x78831),x78832)),f784(f784(f51(a1),x78831),x78833)))
% 11.41/11.19 [8017]E(f784(x80171,f822(x80172,x80171,x80173)),x80172)+~P85(f784(f784(f242(a1),x80172),f784(x80171,x80173)))+P85(f784(f784(f243(a859),f823(x80172,x80171,x80173)),x80173))+~P85(f784(f784(f242(a1),f784(x80171,f2(a859))),x80172))
% 11.41/11.19 [8018]E(f784(x80181,f824(x80182,x80181,x80183)),x80182)+~P85(f784(f784(f242(a1),x80182),f784(x80181,x80183)))+P85(f784(f784(f243(a859),f825(x80182,x80181,x80183)),x80183))+~P85(f784(f784(f242(a1),f784(x80181,f2(a859))),x80182))
% 11.41/11.19 [8114]~P85(f784(f71(x81141),x81143))+~P85(f784(f784(f243(a859),f784(f50(x81141),x81142)),f784(f50(x81141),x81143)))+~P85(f784(f784(f242(f869(x81141,a852)),x81142),x81143))+P85(f784(f784(f243(f869(x81141,a852)),x81142),x81143))
% 11.41/11.19 [8142]E(f784(f784(f3(a1),f431(x81423,x81421,x81422)),f432(x81423,x81421,x81422)),x81421)+E(f784(f784(f89(a1),x81421),x81422),x81421)+~P85(f784(f784(f243(a1),f2(a1)),x81422))+~P85(f784(f784(f347(a1),f784(f784(f89(a1),x81421),f87(a1))),x81423))
% 11.41/11.19 [8143]E(f784(f784(f89(a1),f433(x81433,x81431,x81432)),f434(x81433,x81431,x81432)),x81431)+E(f784(f784(f3(a1),x81431),x81432),x81431)+~P85(f784(f784(f243(a1),f2(a1)),x81432))+~P85(f784(f784(f347(a1),f784(f784(f3(a1),x81431),f87(a1))),x81433))
% 11.41/11.19 [8194]~P85(f784(f784(f242(a859),x81943),x81941))+P85(f784(f784(f243(a859),x81941),x81942))+~P85(f784(f784(f242(a859),x81943),x81942))+~P85(f784(f784(f243(a859),f784(f784(f3(a859),x81941),x81943)),f784(f784(f3(a859),x81942),x81943)))
% 11.41/11.19 [8195]~P85(f784(f784(f242(a859),x81953),x81951))+P85(f784(f784(f242(a859),x81951),x81952))+~P85(f784(f784(f242(a859),x81953),x81952))+~P85(f784(f784(f242(a859),f784(f784(f3(a859),x81951),x81953)),f784(f784(f3(a859),x81952),x81953)))
% 11.41/11.19 [8209]~P101(x82092)+E(x82091,f120(x82092))+~P15(x82092,f784(f162(x82092),x82091))+E(f784(f136(x82092,x82092,f784(f9(x82092,x82092,x82092),f186(x82092)),x82093),f784(f162(x82092),x82091)),f784(f784(f186(x82092),f784(f784(f155(x82092),x82091),f2(a859))),x82093))
% 11.41/11.19 [8275]E(f784(f784(f89(a1),x82751),x82752),x82751)+~P85(f784(f784(f243(a1),f2(a1)),x82752))+P85(f784(f784(f347(a1),f431(x82753,x82751,x82752)),x82753))+~P85(f784(f784(f347(a1),f784(f784(f89(a1),x82751),f87(a1))),x82753))
% 11.41/11.19 [8276]E(f784(f784(f3(a1),x82761),x82762),x82761)+~P85(f784(f784(f243(a1),f2(a1)),x82762))+P85(f784(f784(f347(a1),f433(x82763,x82761,x82762)),x82763))+~P85(f784(f784(f347(a1),f784(f784(f3(a1),x82761),f87(a1))),x82763))
% 11.41/11.19 [8355]~P85(f784(f784(f242(a1),x83551),f784(x83552,x83553)))+P85(f784(f784(f242(a859),f822(x83551,x83552,x83553)),x83553))+P85(f784(f784(f243(a859),f823(x83551,x83552,x83553)),x83553))+~P85(f784(f784(f242(a1),f784(x83552,f2(a859))),x83551))
% 11.41/11.19 [8356]~P85(f784(f784(f242(a1),x83561),f784(x83562,x83563)))+P85(f784(f784(f242(a859),f824(x83561,x83562,x83563)),x83563))+P85(f784(f784(f243(a859),f825(x83561,x83562,x83563)),x83563))+~P85(f784(f784(f242(a1),f784(x83562,f2(a859))),x83561))
% 11.41/11.19 [8430]E(f784(f784(f89(a1),x84301),x84302),x84301)+~P85(f784(f784(f243(a1),f2(a1)),x84302))+P85(f784(f784(f347(a1),f432(x84303,x84301,x84302)),f305(a1,f87(a1),x84302)))+~P85(f784(f784(f347(a1),f784(f784(f89(a1),x84301),f87(a1))),x84303))
% 11.41/11.19 [8431]E(f784(f784(f3(a1),x84311),x84312),x84311)+~P85(f784(f784(f243(a1),f2(a1)),x84312))+P85(f784(f784(f347(a1),f434(x84313,x84311,x84312)),f305(a1,f87(a1),x84312)))+~P85(f784(f784(f347(a1),f784(f784(f3(a1),x84311),f87(a1))),x84313))
% 11.41/11.19 [8555]~P120(x85551)+~P85(f784(f784(f243(x85551),x85552),f87(x85551)))+~P85(f784(f784(f243(x85551),f2(x85551)),x85552))+P85(f784(f784(f243(x85551),f784(f784(f90(x85551),x85552),f784(f784(f252(x85551),x85552),x85553))),f784(f784(f252(x85551),x85552),x85553)))
% 11.41/11.19 [8631]~P85(f784(x86311,x86312))+P85(f784(x86311,f2(a859)))+~P85(f784(f784(f243(a859),x86312),x86313))+~P85(f784(x86311,f60(a859,f784(a160,f818(x86312,x86311,x86313)),x86313)))
% 11.41/11.19 [8761]E(f843(x87611,x87612,x87613),f2(a859))+P85(f784(f784(x87611,x87613),x87612))+P85(f784(f784(x87611,f843(x87611,x87612,x87613)),f60(a859,f841(x87611,x87612,x87613),f843(x87611,x87612,x87613))))+~P85(f784(f334(f868(a859,a859),a224),f784(f784(f251(a859,a859),x87613),x87612)))
% 11.41/11.19 [8793]~P26(x87931,x87931,x87932,x87933)+E(f784(f313(x87931,x87931,x87932),x87933),x87933)+~P85(f784(f71(x87931),x87933))+~P85(f784(f784(f242(f869(x87931,a852)),f784(f313(x87931,x87931,x87932),x87933)),x87933))
% 11.41/11.19 [9014]P85(f784(f784(x90141,x90142),x90143))+~P85(f784(f784(f243(a1),f840(x90141,x90143,x90142)),f2(a1)))+P85(f784(f784(x90141,f784(f88(a1),f837(x90141,x90143,x90142))),f784(f88(a1),f840(x90141,x90143,x90142))))+~P85(f784(f334(f868(a1,a1),a226),f784(f784(f251(a1,a1),x90142),x90143)))
% 11.41/11.19 [9174]P85(f784(f784(x91741,x91742),x91743))+P85(f784(f784(x91741,f784(f784(f89(a1),f407(x91741,x91743,x91742)),f87(a1))),f408(x91741,x91743,x91742)))+~P85(f784(f784(f242(a1),f407(x91741,x91743,x91742)),f408(x91741,x91743,x91742)))+~P85(f784(f334(f868(a1,a1),a174),f784(f784(f251(a1,a1),x91742),x91743)))
% 11.41/11.19 [9858]E(f784(x98581,f822(x98582,x98581,x98583)),x98582)+~P85(f784(f784(f242(a1),x98582),f784(x98581,x98583)))+~P85(f784(f784(f242(a1),f784(f84(a1),f784(f784(f3(a1),f784(x98581,f784(f784(f89(a859),f823(x98582,x98581,x98583)),f87(a859)))),f784(x98581,f823(x98582,x98581,x98583))))),f87(a1)))+~P85(f784(f784(f242(a1),f784(x98581,f2(a859))),x98582))
% 11.41/11.19 [9859]E(f784(x98591,f824(x98592,x98591,x98593)),x98592)+~P85(f784(f784(f242(a1),x98592),f784(x98591,x98593)))+~P85(f784(f784(f242(a1),f784(f84(a1),f784(f784(f3(a1),f784(x98591,f784(f784(f89(a859),f825(x98592,x98591,x98593)),f87(a859)))),f784(x98591,f825(x98592,x98591,x98593))))),f87(a1)))+~P85(f784(f784(f242(a1),f784(x98591,f2(a859))),x98592))
% 11.41/11.19 [9863]~P85(f784(f784(f242(a1),x98631),f784(x98632,x98633)))+~P85(f784(f784(f242(a1),f784(f84(a1),f784(f784(f3(a1),f784(x98632,f784(f784(f89(a859),f823(x98631,x98632,x98633)),f87(a859)))),f784(x98632,f823(x98631,x98632,x98633))))),f87(a1)))+P85(f784(f784(f242(a859),f822(x98631,x98632,x98633)),x98633))+~P85(f784(f784(f242(a1),f784(x98632,f2(a859))),x98631))
% 11.41/11.19 [9864]~P85(f784(f784(f242(a1),x98641),f784(x98642,x98643)))+~P85(f784(f784(f242(a1),f784(f84(a1),f784(f784(f3(a1),f784(x98642,f784(f784(f89(a859),f825(x98641,x98642,x98643)),f87(a859)))),f784(x98642,f825(x98641,x98642,x98643))))),f87(a1)))+P85(f784(f784(f242(a859),f824(x98641,x98642,x98643)),x98643))+~P85(f784(f784(f242(a1),f784(x98642,f2(a859))),x98641))
% 11.41/11.19 [9916]E(x99161,x99162)+~E(f784(f136(f860(x99163),f860(x99163),f130(x99163),f120(x99163)),x99161),f784(f136(f860(x99163),f860(x99163),f130(x99163),f120(x99163)),x99162))+~E(f784(f188(f860(f860(x99163))),x99161),f784(f188(f860(f860(x99163))),x99162))+~P85(f784(f784(f261(f860(x99163),f860(x99163),a852),f784(f784(f9(f860(x99163),f869(f860(x99163),a859),f869(f860(x99163),a852)),f784(f784(f10(f869(a859,a852),f869(f869(f860(x99163),a859),f869(f860(x99163),a852)),f860(x99163)),f10(a859,a852,f860(x99163))),f784(f784(f10(a859,f869(a859,a852),f860(x99163)),a343),f188(f860(x99163))))),f188(f860(x99163)))),f781(x99162,x99161,x99163)))
% 11.41/11.19 [9917]E(x99171,x99172)+~E(f784(f136(f860(x99173),f860(x99173),f130(x99173),f120(x99173)),x99171),f784(f136(f860(x99173),f860(x99173),f130(x99173),f120(x99173)),x99172))+~E(f784(f188(f860(f860(x99173))),x99171),f784(f188(f860(f860(x99173))),x99172))+~P85(f784(f784(f261(f860(x99173),f860(x99173),a852),f784(f784(f9(f860(x99173),f869(f860(x99173),a859),f869(f860(x99173),a852)),f784(f784(f10(f869(a859,a852),f869(f869(f860(x99173),a859),f869(f860(x99173),a852)),f860(x99173)),f10(a859,a852,f860(x99173))),f784(f784(f10(a859,f869(a859,a852),f860(x99173)),a343),f188(f860(x99173))))),f188(f860(x99173)))),f782(x99171,x99172,x99173)))
% 11.41/11.19 [6724]~E(f87(a859),f2(a859))+~P85(f784(f71(x67241),x67243))+~P85(f784(f71(x67241),x67242))+E(f784(f784(f89(a859),f784(f50(x67241),x67242)),f784(f50(x67241),x67243)),f784(f50(x67241),f784(f784(f110(f869(x67241,a852)),x67242),x67243)))
% 11.41/11.19 [7140]~P101(x71401)+~P85(f784(f71(x71401),x71402))+~P85(f784(f784(f347(x71401),x71403),x71402))+P85(f784(f784(f242(x71401),f784(f73(x71401,f246(x71401)),x71402)),x71403))
% 11.41/11.19 [7141]~P99(x71411)+~P85(f784(f71(x71411),x71412))+~P85(f784(f784(f347(x71411),x71413),x71412))+P85(f784(f784(f242(x71411),f784(f73(x71411,f111(x71411)),x71412)),x71413))
% 11.41/11.19 [7416]~P85(f784(f71(x74161),x74163))+~P85(f784(f71(x74161),x74162))+~E(f784(f784(f111(f869(x74161,a852)),x74162),x74163),f187(f869(x74161,a852)))+E(f784(f784(f89(a859),f784(f50(x74161),x74162)),f784(f50(x74161),x74163)),f784(f50(x74161),f784(f784(f110(f869(x74161,a852)),x74162),x74163)))
% 11.41/11.19 [8199]~P35(x81991,x81993)+~P35(x81991,x81992)+~E(f784(f784(f111(f869(x81991,a852)),f784(f271(x81991,x81991),x81992)),f784(f269(x81991,x81991),x81993)),f187(f869(x81991,a852)))+P35(x81991,f784(f784(f110(f869(f868(x81991,x81991),a852)),x81992),x81993))
% 11.41/11.19 [8288]E(x82881,f784(f784(f51(a859),x82882),x82883))+~P85(f784(f784(f243(a859),f2(a859)),x82883))+~P85(f784(f784(f243(a859),x82882),f784(f784(f90(a859),x82883),f784(a160,x82881))))+~P85(f784(f784(f242(a859),f784(f784(f90(a859),x82883),x82881)),x82882))
% 11.41/11.19 [8428]~P85(f784(f71(x84281),x84282))+~P85(f784(f71(x84281),x84283))+E(f784(f784(f89(a859),f784(f50(x84281),x84282)),f784(f50(x84281),x84283)),f784(f50(x84281),f784(f784(f110(f869(x84281,a852)),x84282),x84283)))+P85(f784(f784(f347(x84281),f518(x84283,x84282,x84281)),f784(f784(f111(f869(x84281,a852)),x84282),x84283)))
% 11.41/11.19 [8772]~P122(x87722)+~E(x87721,f2(x87722))+~E(x87723,f2(x87722))+~P85(f784(f784(f243(x87722),f2(x87722)),f784(f784(f89(x87722),f784(f784(f90(x87722),x87723),x87723)),f784(f784(f90(x87722),x87721),x87721))))
% 11.41/11.19 [9245]~P35(x92451,x92453)+~P35(x92451,x92452)+P35(x92451,f784(f784(f110(f869(f868(x92451,x92451),a852)),x92452),x92453))+~P85(f784(f784(f242(f869(f868(x92451,x92451),a852)),f784(f784(f291(x92451,x92451,x92451),x92452),x92453)),x92452))
% 11.41/11.19 [9370]~P85(f784(x93701,x93703))+~P85(f784(f71(x93702),x93703))+P85(f784(x93701,f187(f869(x93702,a852))))+~P85(f784(x93701,f784(f784(f3(f869(x93702,a852)),f495(x93701,x93703,x93702)),f784(f784(f312(x93702),f496(x93701,x93703,x93702)),f187(f869(x93702,a852))))))
% 11.41/11.19 [8585]~P85(f784(f784(f243(a1),f2(a1)),x85853))+P85(f784(f784(f242(a1),f2(a1)),x85851))+~P85(f784(f784(f243(a1),x85852),x85853))+~P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),f784(f784(f90(a1),x85853),x85851)),x85852)))
% 11.41/11.19 [8605]~P93(x86051)+~P85(f784(f71(x86051),x86052))+E(f784(f784(f3(f869(x86051,a852)),x86052),f784(f784(f312(x86051),x86053),f187(f869(x86051,a852)))),f187(f869(x86051,a852)))+E(f784(f784(f110(x86051),x86053),f15(x86051,f784(f784(f3(f869(x86051,a852)),x86052),f784(f784(f312(x86051),x86053),f187(f869(x86051,a852)))))),f15(x86051,f784(f784(f312(x86051),x86053),x86052)))
% 11.41/11.19 [8606]~P101(x86061)+~P85(f784(f71(x86061),x86062))+E(f784(f784(f3(f869(x86061,a852)),x86062),f784(f784(f312(x86061),x86063),f187(f869(x86061,a852)))),f187(f869(x86061,a852)))+E(f784(f784(f186(x86061),x86063),f16(x86061,f784(f784(f3(f869(x86061,a852)),x86062),f784(f784(f312(x86061),x86063),f187(f869(x86061,a852)))))),f16(x86061,f784(f784(f312(x86061),x86063),x86062)))
% 11.41/11.19 [8607]~P101(x86071)+~P85(f784(f71(x86071),x86072))+E(f784(f784(f3(f869(x86071,a852)),x86072),f784(f784(f312(x86071),x86073),f187(f869(x86071,a852)))),f187(f869(x86071,a852)))+E(f784(f784(f246(x86071),x86073),f17(x86071,f784(f784(f3(f869(x86071,a852)),x86072),f784(f784(f312(x86071),x86073),f187(f869(x86071,a852)))))),f17(x86071,f784(f784(f312(x86071),x86073),x86072)))
% 11.41/11.19 [8608]~P93(x86081)+~P85(f784(f71(x86081),x86082))+E(f784(f784(f3(f869(x86081,a852)),x86082),f784(f784(f312(x86081),x86083),f187(f869(x86081,a852)))),f187(f869(x86081,a852)))+E(f784(f784(f111(x86081),x86083),f12(x86081,f784(f784(f3(f869(x86081,a852)),x86082),f784(f784(f312(x86081),x86083),f187(f869(x86081,a852)))))),f12(x86081,f784(f784(f312(x86081),x86083),x86082)))
% 11.41/11.19 [8670]~P101(x86701)+~P85(f784(f71(x86701),x86702))+E(f784(f784(f3(f869(x86701,a852)),x86702),f784(f784(f312(x86701),x86703),f187(f869(x86701,a852)))),f187(f869(x86701,a852)))+E(f784(f784(f186(x86701),x86703),f13(x86701,f186(x86701),f784(f784(f3(f869(x86701,a852)),x86702),f784(f784(f312(x86701),x86703),f187(f869(x86701,a852)))))),f13(x86701,f186(x86701),f784(f784(f312(x86701),x86703),x86702)))
% 11.41/11.19 [8671]~P101(x86711)+~P85(f784(f71(x86711),x86712))+E(f784(f784(f3(f869(x86711,a852)),x86712),f784(f784(f312(x86711),x86713),f187(f869(x86711,a852)))),f187(f869(x86711,a852)))+E(f784(f784(f246(x86711),x86713),f14(x86711,f246(x86711),f784(f784(f3(f869(x86711,a852)),x86712),f784(f784(f312(x86711),x86713),f187(f869(x86711,a852)))))),f14(x86711,f246(x86711),f784(f784(f312(x86711),x86713),x86712)))
% 11.41/11.19 [9188]E(x91881,x91882)+~E(f784(f136(f860(x91883),f860(x91883),f130(x91883),f120(x91883)),x91881),f784(f136(f860(x91883),f860(x91883),f130(x91883),f120(x91883)),x91882))+~E(f784(f188(f860(f860(x91883))),x91881),f784(f188(f860(f860(x91883))),x91882))+P85(f784(f784(f347(f868(f860(x91883),f860(x91883))),f781(x91882,x91881,x91883)),f784(f164(f868(f860(x91883),f860(x91883))),f784(f784(f173(f860(x91883),f860(x91883)),x91881),x91882))))
% 11.41/11.19 [9189]E(x91891,x91892)+~E(f784(f136(f860(x91893),f860(x91893),f130(x91893),f120(x91893)),x91891),f784(f136(f860(x91893),f860(x91893),f130(x91893),f120(x91893)),x91892))+~E(f784(f188(f860(f860(x91893))),x91891),f784(f188(f860(f860(x91893))),x91892))+P85(f784(f784(f347(f868(f860(x91893),f860(x91893))),f782(x91891,x91892,x91893)),f784(f164(f868(f860(x91893),f860(x91893))),f784(f784(f173(f860(x91893),f860(x91893)),x91892),x91891))))
% 11.41/11.19 [10006]~P73(x100062)+E(x100061,f187(f869(x100062,a852)))+~P85(f784(f71(x100062),x100061))+E(f16(x100062,f784(f266(x100062),f784(f784(f10(f869(x100062,a852),a852,x100062),f96(x100062)),f784(f784(f9(x100062,f869(x100062,a852),f869(x100062,a852)),f784(f784(f10(f869(x100062,f869(a852,a852)),f869(f869(x100062,a852),f869(x100062,a852)),x100062),f20(x100062,a852,a852)),f784(f784(f10(f869(x100062,a852),f869(x100062,f869(a852,a852)),x100062),f784(f10(a852,f869(a852,a852),x100062),a344)),f784(f784(f9(x100062,f869(x100062,x100062),f869(x100062,a852)),f784(f784(f10(f869(x100062,a852),f869(f869(x100062,x100062),f869(x100062,a852)),x100062),f10(x100062,a852,x100062)),a343)),f784(f89(x100062),x100063))))),f784(f784(f9(x100062,f869(x100062,a852),a852),f347(x100062)),x100061))))),f784(f784(f89(x100062),x100063),f16(x100062,x100061)))
% 11.41/11.19 [10007]~P73(x100072)+E(x100071,f187(f869(x100072,a852)))+~P85(f784(f71(x100072),x100071))+E(f17(x100072,f784(f266(x100072),f784(f784(f10(f869(x100072,a852),a852,x100072),f96(x100072)),f784(f784(f9(x100072,f869(x100072,a852),f869(x100072,a852)),f784(f784(f10(f869(x100072,f869(a852,a852)),f869(f869(x100072,a852),f869(x100072,a852)),x100072),f20(x100072,a852,a852)),f784(f784(f10(f869(x100072,a852),f869(x100072,f869(a852,a852)),x100072),f784(f10(a852,f869(a852,a852),x100072),a344)),f784(f784(f9(x100072,f869(x100072,x100072),f869(x100072,a852)),f784(f784(f10(f869(x100072,a852),f869(f869(x100072,x100072),f869(x100072,a852)),x100072),f10(x100072,a852,x100072)),a343)),f784(f89(x100072),x100073))))),f784(f784(f9(x100072,f869(x100072,a852),a852),f347(x100072)),x100071))))),f784(f784(f89(x100072),x100073),f17(x100072,x100071)))
% 11.41/11.19 [10008]~P97(x100082)+E(x100081,f187(f869(x100082,a852)))+~P85(f784(f71(x100082),x100081))+E(f12(x100082,f784(f266(x100082),f784(f784(f10(f869(x100082,a852),a852,x100082),f96(x100082)),f784(f784(f9(x100082,f869(x100082,a852),f869(x100082,a852)),f784(f784(f10(f869(x100082,f869(a852,a852)),f869(f869(x100082,a852),f869(x100082,a852)),x100082),f20(x100082,a852,a852)),f784(f784(f10(f869(x100082,a852),f869(x100082,f869(a852,a852)),x100082),f784(f10(a852,f869(a852,a852),x100082),a344)),f784(f784(f9(x100082,f869(x100082,x100082),f869(x100082,a852)),f784(f784(f10(f869(x100082,a852),f869(f869(x100082,x100082),f869(x100082,a852)),x100082),f10(x100082,a852,x100082)),a343)),f784(f110(x100082),x100083))))),f784(f784(f9(x100082,f869(x100082,a852),a852),f347(x100082)),x100081))))),f784(f784(f110(x100082),x100083),f12(x100082,x100081)))
% 11.41/11.19 [10009]~P97(x100092)+E(x100091,f187(f869(x100092,a852)))+~P85(f784(f71(x100092),x100091))+E(f15(x100092,f784(f266(x100092),f784(f784(f10(f869(x100092,a852),a852,x100092),f96(x100092)),f784(f784(f9(x100092,f869(x100092,a852),f869(x100092,a852)),f784(f784(f10(f869(x100092,f869(a852,a852)),f869(f869(x100092,a852),f869(x100092,a852)),x100092),f20(x100092,a852,a852)),f784(f784(f10(f869(x100092,a852),f869(x100092,f869(a852,a852)),x100092),f784(f10(a852,f869(a852,a852),x100092),a344)),f784(f784(f9(x100092,f869(x100092,x100092),f869(x100092,a852)),f784(f784(f10(f869(x100092,a852),f869(f869(x100092,x100092),f869(x100092,a852)),x100092),f10(x100092,a852,x100092)),a343)),f784(f111(x100092),x100093))))),f784(f784(f9(x100092,f869(x100092,a852),a852),f347(x100092)),x100091))))),f784(f784(f111(x100092),x100093),f15(x100092,x100091)))
% 11.41/11.19 [10010]~P101(x100102)+E(x100101,f187(f869(x100102,a852)))+~P85(f784(f71(x100102),x100101))+E(f13(x100102,f186(x100102),f784(f266(x100102),f784(f784(f10(f869(x100102,a852),a852,x100102),f96(x100102)),f784(f784(f9(x100102,f869(x100102,a852),f869(x100102,a852)),f784(f784(f10(f869(x100102,f869(a852,a852)),f869(f869(x100102,a852),f869(x100102,a852)),x100102),f20(x100102,a852,a852)),f784(f784(f10(f869(x100102,a852),f869(x100102,f869(a852,a852)),x100102),f784(f10(a852,f869(a852,a852),x100102),a344)),f784(f784(f9(x100102,f869(x100102,x100102),f869(x100102,a852)),f784(f784(f10(f869(x100102,a852),f869(f869(x100102,x100102),f869(x100102,a852)),x100102),f10(x100102,a852,x100102)),a343)),f784(f246(x100102),x100103))))),f784(f784(f9(x100102,f869(x100102,a852),a852),f347(x100102)),x100101))))),f784(f784(f246(x100102),x100103),f13(x100102,f186(x100102),x100101)))
% 11.41/11.19 [10011]~P101(x100112)+E(x100111,f187(f869(x100112,a852)))+~P85(f784(f71(x100112),x100111))+E(f14(x100112,f246(x100112),f784(f266(x100112),f784(f784(f10(f869(x100112,a852),a852,x100112),f96(x100112)),f784(f784(f9(x100112,f869(x100112,a852),f869(x100112,a852)),f784(f784(f10(f869(x100112,f869(a852,a852)),f869(f869(x100112,a852),f869(x100112,a852)),x100112),f20(x100112,a852,a852)),f784(f784(f10(f869(x100112,a852),f869(x100112,f869(a852,a852)),x100112),f784(f10(a852,f869(a852,a852),x100112),a344)),f784(f784(f9(x100112,f869(x100112,x100112),f869(x100112,a852)),f784(f784(f10(f869(x100112,a852),f869(f869(x100112,x100112),f869(x100112,a852)),x100112),f10(x100112,a852,x100112)),a343)),f784(f186(x100112),x100113))))),f784(f784(f9(x100112,f869(x100112,a852),a852),f347(x100112)),x100111))))),f784(f784(f186(x100112),x100113),f14(x100112,f246(x100112),x100111)))
% 11.41/11.19 [9739]~P113(x97391)+~E(x97393,f2(x97391))+~E(x97392,f2(x97391))+E(f784(f784(f89(x97391),f784(f784(f252(x97391),x97392),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x97391),x97393),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f2(x97391))
% 11.41/11.19 [9900]~P120(x99001)+~P85(f784(f784(f242(x99001),f2(x99001)),x99003))+P85(f784(f784(f243(x99001),x99002),x99003))+~P85(f784(f784(f243(x99001),f784(f784(f252(x99001),x99002),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99001),x99003),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.19 [9901]~P120(x99011)+~P85(f784(f784(f242(x99011),f2(x99011)),x99013))+P85(f784(f784(f242(x99011),x99012),x99013))+~P85(f784(f784(f242(x99011),f784(f784(f252(x99011),x99012),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99011),x99013),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))))
% 11.41/11.19 [9945]~P113(x99452)+~E(x99451,f2(x99452))+~E(x99453,f2(x99452))+~P85(f784(f784(f243(x99452),f2(x99452)),f784(f784(f89(x99452),f784(f784(f252(x99452),x99453),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106))))),f784(f784(f252(x99452),x99451),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))))
% 11.41/11.19 [9163]E(x91631,x91632)+~E(f764(x91631,x91632,x91634,x91633),f766(x91631,x91632,x91634,x91633))+P85(f784(f784(f347(f868(f860(x91633),f860(x91633))),f784(f784(f251(f860(x91633),f860(x91633)),x91632),x91631)),f141(x91633,x91634)))+P85(f784(f784(f347(f868(f860(x91633),f860(x91633))),f784(f784(f251(f860(x91633),f860(x91633)),x91631),x91632)),f141(x91633,x91634)))
% 11.41/11.19 [4768]~P59(x47682)+~E(x47684,f2(x47682))+~E(x47681,f2(x47682))+E(x47681,f784(f784(f293(x47682),x47683),x47684))
% 11.41/11.19 [4769]~P59(x47691)+~E(x47693,f2(x47691))+~E(x47694,f2(x47691))+E(f784(f784(f293(x47691),x47692),x47693),x47694)
% 11.41/11.19 [4876]~P59(x48762)+E(x48761,f2(x48762))+~E(x48763,f2(x48762))+~E(x48761,f784(f784(f293(x48762),x48764),x48763))
% 11.41/11.19 [4877]~P59(x48772)+E(x48771,f2(x48772))+~E(x48773,f2(x48772))+~E(f784(f784(f293(x48772),x48774),x48773),x48771)
% 11.41/11.19 [5059]~P116(x50592)+E(x50591,f2(x50592))+~E(f784(f784(f293(x50592),x50593),x50591),x50594)+E(x50593,f784(f784(f90(x50592),x50594),x50591))
% 11.41/11.19 [5060]~P116(x50602)+E(x50601,f2(x50602))+~E(f784(f784(f90(x50602),x50603),x50601),x50604)+E(x50603,f784(f784(f293(x50602),x50604),x50601))
% 11.41/11.19 [5061]~P116(x50612)+E(x50611,f2(x50612))+~E(f784(f784(f90(x50612),x50613),x50611),x50614)+E(x50613,f784(f784(f293(x50612),x50614),x50611))
% 11.41/11.19 [5062]~P59(x50622)+E(x50621,f2(x50622))+~E(f784(f784(f293(x50622),x50623),x50621),x50624)+E(x50623,f784(f784(f90(x50622),x50624),x50621))
% 11.41/11.19 [5063]~P59(x50632)+E(x50631,f2(x50632))+~E(f784(f784(f90(x50632),x50633),x50631),x50634)+E(x50633,f784(f784(f293(x50632),x50634),x50631))
% 11.41/11.19 [5064]~P116(x50642)+E(x50641,f2(x50642))+~E(x50643,f784(f784(f293(x50642),x50644),x50641))+E(f784(f784(f90(x50642),x50643),x50641),x50644)
% 11.41/11.19 [5065]~P116(x50652)+E(x50651,f2(x50652))+~E(x50653,f784(f784(f90(x50652),x50654),x50651))+E(f784(f784(f293(x50652),x50653),x50651),x50654)
% 11.41/11.19 [5066]~P116(x50662)+E(x50661,f2(x50662))+~E(x50663,f784(f784(f90(x50662),x50664),x50661))+E(f784(f784(f293(x50662),x50663),x50661),x50664)
% 11.41/11.19 [5067]~P59(x50672)+E(x50671,f2(x50672))+~E(x50673,f784(f784(f293(x50672),x50674),x50671))+E(f784(f784(f90(x50672),x50673),x50671),x50674)
% 11.41/11.19 [5068]~P59(x50682)+E(x50681,f2(x50682))+~E(x50683,f784(f784(f90(x50682),x50684),x50681))+E(f784(f784(f293(x50682),x50683),x50681),x50684)
% 11.41/11.19 [5100]~P59(x51002)+~E(x51001,f2(x51002))+~E(f784(f784(f90(x51002),x51001),x51004),x51003)+E(x51001,f784(f784(f293(x51002),x51003),x51004))
% 11.41/11.19 [5101]~P59(x51011)+~E(x51014,f2(x51011))+~E(x51012,f784(f784(f90(x51011),x51014),x51013))+E(f784(f784(f293(x51011),x51012),x51013),x51014)
% 11.41/11.19 [5167]~E(x51673,x51674)+~E(x51672,x51673)+~P100(x51671)+E(f305(x51671,x51672,x51673),f784(f784(f312(x51671),x51674),f187(f869(x51671,a852))))
% 11.41/11.19 [5361]~E(f138(x53612,x53611),x53614)+~E(f121(x53612,x53611),x53613)+E(x53611,f120(x53612))+E(f784(f784(f130(x53612),x53613),f784(f784(f144(x53612),x53614),f120(x53612))),x53611)
% 11.41/11.19 [5977]~P120(x59773)+E(x59771,x59772)+~E(f784(f784(f252(x59773),x59774),x59771),f784(f784(f252(x59773),x59774),x59772))+~P85(f784(f784(f243(x59773),f87(x59773)),x59774))
% 11.41/11.19 [5978]E(x59781,x59782)+~E(f784(f784(f312(x59783),x59784),x59781),f784(f784(f312(x59783),x59784),x59782))+P85(f784(f784(f347(x59783),x59784),x59782))+P85(f784(f784(f347(x59783),x59784),x59781))
% 11.41/11.19 [6016]E(f784(x60161,x60162),f2(a859))+~E(f784(f784(f8(x60163,a859),x60161),x60164),f2(a859))+~P85(f784(f71(x60163),x60164))+~P85(f784(f784(f347(x60163),x60162),x60164))
% 11.41/11.19 [6017]E(f784(x60171,x60172),f87(a859))+~E(f784(f784(f11(x60173,a859),x60171),x60174),f87(a859))+~P85(f784(f71(x60173),x60174))+~P85(f784(f784(f347(x60173),x60172),x60174))
% 11.41/11.19 [6239]~P100(x62391)+~P85(f784(f784(f243(x62391),x62394),x62393))+P85(f784(f784(f243(x62391),x62392),x62393))+~P85(f784(f784(f243(x62391),x62392),x62394))
% 11.41/11.19 [6240]~P100(x62401)+~P85(f784(f784(f242(x62401),x62404),x62403))+P85(f784(f784(f243(x62401),x62402),x62403))+~P85(f784(f784(f243(x62401),x62402),x62404))
% 11.41/11.19 [6241]~P100(x62411)+~P85(f784(f784(f242(x62411),x62412),x62414))+P85(f784(f784(f243(x62411),x62412),x62413))+~P85(f784(f784(f243(x62411),x62414),x62413))
% 11.41/11.19 [6242]~P104(x62421)+~P85(f784(f784(f243(x62421),x62422),x62424))+P85(f784(f784(f243(x62421),x62422),x62423))+~P85(f784(f784(f243(x62421),x62424),x62423))
% 11.41/11.19 [6243]~P104(x62431)+~P85(f784(f784(f242(x62431),x62432),x62434))+P85(f784(f784(f243(x62431),x62432),x62433))+~P85(f784(f784(f243(x62431),x62434),x62433))
% 11.41/11.19 [6244]~P104(x62441)+~P85(f784(f784(f242(x62441),x62444),x62443))+P85(f784(f784(f243(x62441),x62442),x62443))+~P85(f784(f784(f243(x62441),x62442),x62444))
% 11.41/11.19 [6245]~P100(x62451)+~P85(f784(f784(f242(x62451),x62454),x62453))+P85(f784(f784(f242(x62451),x62452),x62453))+~P85(f784(f784(f242(x62451),x62452),x62454))
% 11.41/11.19 [6246]~P104(x62461)+~P85(f784(f784(f242(x62461),x62462),x62464))+P85(f784(f784(f242(x62461),x62462),x62463))+~P85(f784(f784(f242(x62461),x62464),x62463))
% 11.41/11.19 [6247]~P86(x62471)+~P85(f784(f784(f289(x62471),x62472),x62474))+P85(f784(f784(f289(x62471),x62472),x62473))+~P85(f784(f784(f289(x62471),x62474),x62473))
% 11.41/11.19 [6491]~P6(x64911)+~P85(f784(f784(f242(x64911),x64912),f53(x64911,x64914)))+P85(f784(f784(f242(x64911),x64912),x64913))+~P85(f784(f784(f347(x64911),x64913),x64914))
% 11.41/11.19 [6640]~P101(x66401)+~P15(x66401,f784(f784(f144(x66401),x66402),x66404))+~P85(f784(f784(f347(x66401),x66403),f784(f164(x66401),x66404)))+P85(f784(f784(f242(x66401),x66402),x66403))
% 11.41/11.19 [6641]~P101(x66411)+~P15(x66411,f784(f784(f144(x66411),x66412),x66414))+~P85(f784(f784(f347(x66411),x66413),f784(f164(x66411),x66414)))+P85(f784(f784(f242(x66411),x66412),x66413))
% 11.41/11.19 [6733]~P6(x67331)+~P85(f784(f784(f242(x67331),f52(x67331,x67334)),x67333))+P85(f784(f784(f242(x67331),x67332),x67333))+~P85(f784(f784(f347(x67331),x67332),x67334))
% 11.41/11.19 [6884]~P4(x68841)+P85(f784(f784(f289(x68841),x68842),f60(x68841,x68843,x68844)))+~P85(f784(f784(f289(x68841),x68842),x68844))+~P85(f784(f784(f289(x68841),x68842),x68843))
% 11.41/11.19 [6885]~P4(x68851)+P85(f784(f784(f289(x68851),x68852),f60(x68851,x68853,x68854)))+~P85(f784(f784(f289(x68851),x68852),x68854))+~P85(f784(f784(f289(x68851),x68852),x68853))
% 11.41/11.19 [7143]~P101(x71431)+E(f784(f784(f110(f869(x71431,a852)),f784(f304(x71431,x71432),x71433)),f784(f304(x71431,x71433),x71434)),f784(f304(x71431,x71432),x71434))+~P85(f784(f784(f242(x71431),x71433),x71434))+~P85(f784(f784(f242(x71431),x71432),x71433))
% 11.41/11.19 [7229]~P4(x72291)+~P85(f784(f784(f289(x72291),x72292),f60(x72291,x72293,x72294)))+P85(f784(f784(f289(x72291),x72292),x72293))+~P85(f784(f784(f289(x72291),x72292),x72294))
% 11.41/11.19 [7230]~P4(x72301)+~P85(f784(f784(f289(x72301),x72302),f60(x72301,x72303,x72304)))+P85(f784(f784(f289(x72301),x72302),x72303))+~P85(f784(f784(f289(x72301),x72302),x72304))
% 11.41/11.19 [7271]~P101(x72711)+E(f784(f784(f110(f869(x72711,a852)),f784(f304(x72711,x72712),x72713)),f305(x72711,x72713,x72714)),f305(x72711,x72712,x72714))+~P85(f784(f784(f242(x72711),x72713),x72714))+~P85(f784(f784(f242(x72711),x72712),x72713))
% 11.41/11.19 [7285]~P100(x72851)+~P49(a859,x72851,f289(a859),x72852)+P85(f784(f784(f242(x72851),f784(x72852,x72853)),f784(x72852,x72854)))+~P85(f784(f784(f289(a859),x72853),x72854))
% 11.41/11.19 [7339]~P101(x73391)+E(f784(f784(f110(f869(x73391,a852)),f308(x73391,x73392,x73393)),f784(f304(x73391,x73393),x73394)),f308(x73391,x73392,x73394))+~P85(f784(f784(f243(x73391),x73392),x73393))+~P85(f784(f784(f242(x73391),x73393),x73394))
% 11.41/11.19 [7362]~P101(x73621)+E(f784(f784(f110(f869(x73621,a852)),f305(x73621,x73622,x73623)),f308(x73621,x73623,x73624)),f784(f304(x73621,x73622),x73624))+~P85(f784(f784(f243(x73621),x73623),x73624))+~P85(f784(f784(f242(x73621),x73622),x73623))
% 11.41/11.19 [7397]~P101(x73971)+E(f784(f784(f110(f869(x73971,a852)),f305(x73971,x73972,x73973)),f307(x73971,x73973,x73974)),f305(x73971,x73972,x73974))+~P85(f784(f784(f242(x73971),x73973),x73974))+~P85(f784(f784(f242(x73971),x73972),x73973))
% 11.41/11.19 [7398]~P101(x73981)+E(f784(f784(f110(f869(x73981,a852)),f307(x73981,x73982,x73983)),f307(x73981,x73983,x73984)),f307(x73981,x73982,x73984))+~P85(f784(f784(f242(x73981),x73983),x73984))+~P85(f784(f784(f242(x73981),x73982),x73983))
% 11.41/11.19 [7399]~P101(x73991)+E(f784(f784(f110(f869(x73991,a852)),f307(x73991,x73992,x73993)),f308(x73991,x73993,x73994)),f308(x73991,x73992,x73994))+~P85(f784(f784(f243(x73991),x73993),x73994))+~P85(f784(f784(f242(x73991),x73992),x73993))
% 11.41/11.19 [7400]~P101(x74001)+E(f784(f784(f110(f869(x74001,a852)),f308(x74001,x74002,x74003)),f305(x74001,x74003,x74004)),f307(x74001,x74002,x74004))+~P85(f784(f784(f243(x74001),x74002),x74003))+~P85(f784(f784(f242(x74001),x74003),x74004))
% 11.41/11.19 [8184]P26(x81841,x81842,f538(x81843,x81842,x81844,x81841),x81844)+~P85(f784(f71(x81842),x81843))+~P85(f784(f71(x81841),x81844))+~P85(f784(f784(f242(a859),f784(f50(x81841),x81844)),f784(f50(x81842),x81843)))
% 11.41/11.19 [8254]~P71(x82541)+~E(f784(x82543,f634(x82543,x82544,x82542,x82541)),f87(x82541))+E(f784(f784(f784(f75(x82541,x82542,f90(x82541)),x82543),f87(x82541)),x82544),f87(x82541))+~P85(f784(f71(x82542),x82544))
% 11.41/11.19 [8527]~P120(x85271)+~P85(f784(f784(f242(x85271),f2(x85271)),x85273))+P85(f784(f784(f242(x85271),x85272),x85273))+~P85(f784(f784(f242(x85271),f784(f784(f252(x85271),x85272),f784(a160,x85274))),f784(f784(f252(x85271),x85273),f784(a160,x85274))))
% 11.41/11.19 [8860]~P71(x88601)+E(f784(f784(f784(f75(x88601,x88602,f90(x88601)),x88603),f87(x88601)),x88604),f87(x88601))+~P85(f784(f71(x88602),x88604))+P85(f784(f784(f347(x88602),f634(x88603,x88604,x88602,x88601)),x88604))
% 11.41/11.19 [9113]~P9(x91132,x91133,x91134)+~P85(f784(f71(x91132),x91133))+~P85(f784(f784(f289(a859),x91131),f784(f50(x91132),f519(x91131,x91134,x91133,x91132))))+P85(f784(f784(f289(a859),x91131),f784(f50(x91132),x91133)))
% 11.41/11.19 [9298]~P85(f784(f784(f289(a859),x92982),x92983))+P85(f784(f784(f289(a859),x92981),x92982))+P85(f784(f784(f289(a859),x92983),x92984))+~P85(f784(f784(f243(f869(a859,a852)),f292(a859,f289(a859),x92982,x92983)),f292(a859,f289(a859),x92981,x92984)))
% 11.41/11.19 [9303]P85(f784(f784(f289(a859),x93031),x93032))+~P85(f784(f784(f289(a859),x93032),x93033))+~P85(f784(f784(f289(a859),x93034),x93033))+~P85(f784(f784(f243(f869(a859,a852)),f292(a859,f289(a859),x93032,x93033)),f292(a859,f289(a859),x93031,x93034)))
% 11.41/11.19 [9304]~P85(f784(f784(f289(a859),x93043),x93041))+P85(f784(f784(f289(a859),x93041),x93042))+~P85(f784(f784(f289(a859),x93043),x93044))+~P85(f784(f784(f243(f869(a859,a852)),f292(a859,f289(a859),x93043,x93041)),f292(a859,f289(a859),x93044,x93042)))
% 11.41/11.19 [9311]~P85(f784(f784(f289(a859),x93111),x93113))+~P85(f784(f784(f289(a859),x93111),x93112))+~P85(f784(f784(f289(a859),x93114),x93113))+~P85(f784(f784(f243(f869(a859,a852)),f292(a859,f289(a859),x93111,x93113)),f292(a859,f289(a859),x93112,x93114)))
% 11.41/11.19 [9316]~P85(f784(f784(f242(a1),x93164),f2(a1)))+P85(f784(f784(f242(a1),f784(f784(f89(a1),f784(f784(f90(a1),x93161),f60(a1,x93162,x93163))),x93164)),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x93163))+~P85(f784(f784(f243(a1),x93161),x93164))
% 11.41/11.19 [9730]~P85(f784(f71(x97301),x97302))+~P85(f784(f784(f347(x97301),x97304),x97302))+~P85(f784(f784(f347(x97301),x97303),x97302))+P85(f784(f784(f243(a859),f784(f50(x97301),f784(f784(f3(f869(x97301,a852)),f784(f784(f3(f869(x97301,a852)),x97302),f784(f784(f312(x97301),x97303),f187(f869(x97301,a852))))),f784(f784(f312(x97301),x97304),f187(f869(x97301,a852)))))),f784(f50(x97301),x97302)))
% 11.41/11.19 [6795]~P139(x67953)+~P115(x67953)+P85(f784(x67951,f831(x67952,x67951,x67953)))+~P85(f784(x67951,f784(f784(f90(x67953),x67952),x67954)))
% 11.41/11.19 [6855]~P101(x68551)+~P85(f784(f784(f243(x68551),x68552),x68554))+~P85(f784(f784(f243(x68551),x68552),x68553))+P85(f784(f784(f243(x68551),x68552),f784(f784(f246(x68551),x68553),x68554)))
% 11.41/11.19 [6856]~P101(x68561)+~P85(f784(f784(f242(x68561),x68562),x68564))+~P85(f784(f784(f242(x68561),x68562),x68563))+P85(f784(f784(f242(x68561),x68562),f784(f784(f246(x68561),x68563),x68564)))
% 11.41/11.19 [6857]~P101(x68571)+~P85(f784(f784(f242(x68571),x68572),x68574))+~P85(f784(f784(f242(x68571),x68572),x68573))+P85(f784(f784(f242(x68571),x68572),f784(f784(f246(x68571),x68573),x68574)))
% 11.41/11.19 [6858]~P101(x68581)+~P85(f784(f784(f242(x68581),x68582),x68584))+~P85(f784(f784(f242(x68581),x68582),x68583))+P85(f784(f784(f242(x68581),x68582),f784(f784(f246(x68581),x68583),x68584)))
% 11.41/11.19 [6859]~P99(x68591)+~P85(f784(f784(f242(x68591),x68592),x68594))+~P85(f784(f784(f242(x68591),x68592),x68593))+P85(f784(f784(f242(x68591),x68592),f784(f784(f111(x68591),x68593),x68594)))
% 11.41/11.19 [6860]~P99(x68601)+~P85(f784(f784(f242(x68601),x68602),x68604))+~P85(f784(f784(f242(x68601),x68602),x68603))+P85(f784(f784(f242(x68601),x68602),f784(f784(f111(x68601),x68603),x68604)))
% 11.41/11.19 [6861]~P99(x68611)+~P85(f784(f784(f242(x68611),x68612),x68614))+~P85(f784(f784(f242(x68611),x68612),x68613))+P85(f784(f784(f242(x68611),x68612),f784(f784(f111(x68611),x68613),x68614)))
% 11.41/11.19 [6862]~P86(x68621)+~P85(f784(f784(f289(x68621),x68622),x68624))+~P85(f784(f784(f289(x68621),x68622),x68623))+P85(f784(f784(f289(x68621),x68622),f784(f784(f89(x68621),x68623),x68624)))
% 11.41/11.19 [6863]~P105(x68631)+~P85(f784(f784(f289(x68631),x68632),x68634))+~P85(f784(f784(f289(x68631),x68632),x68633))+P85(f784(f784(f289(x68631),x68632),f784(f784(f3(x68631),x68633),x68634)))
% 11.41/11.19 [6883]~P60(x68832)+E(x68831,f2(x68832))+E(f784(f784(f293(x68832),f784(f784(f252(x68832),x68831),x68833)),f784(f784(f252(x68832),x68831),x68834)),f784(f784(f252(x68832),x68831),f784(f784(f3(a859),x68833),x68834)))+~P85(f784(f784(f242(a859),x68834),x68833))
% 11.41/11.19 [6926]~P101(x69261)+~P15(x69261,f784(f784(f144(x69261),x69263),x69264))+P15(x69261,f784(f784(f144(x69261),x69262),f784(f784(f144(x69261),x69263),x69264)))+~P85(f784(f784(f242(x69261),x69262),x69263))
% 11.41/11.19 [6927]~P101(x69271)+~P15(x69271,f784(f784(f144(x69271),x69273),x69274))+P15(x69271,f784(f784(f144(x69271),x69272),f784(f784(f144(x69271),x69273),x69274)))+~P85(f784(f784(f242(x69271),x69272),x69273))
% 11.41/11.19 [6966]~P81(x69661)+~P85(f784(f784(f242(x69661),f2(x69661)),x69663))+~P85(f784(f784(f243(x69661),x69662),x69664))+P85(f784(f784(f243(x69661),x69662),f784(f784(f89(x69661),x69663),x69664)))
% 11.41/11.19 [6967]~P81(x69671)+~P85(f784(f784(f242(x69671),x69672),x69674))+~P85(f784(f784(f243(x69671),f2(x69671)),x69673))+P85(f784(f784(f243(x69671),x69672),f784(f784(f89(x69671),x69673),x69674)))
% 11.41/11.19 [6968]~P120(x69681)+~P85(f784(f784(f243(x69681),f2(x69681)),x69683))+~P85(f784(f784(f243(x69681),x69682),x69684))+P85(f784(f784(f243(x69681),x69682),f784(f784(f89(x69681),x69683),x69684)))
% 11.41/11.19 [6969]~P81(x69691)+~P85(f784(f784(f242(x69691),f2(x69691)),x69694))+~P85(f784(f784(f242(x69691),x69692),x69693))+P85(f784(f784(f242(x69691),x69692),f784(f784(f89(x69691),x69693),x69694)))
% 11.41/11.19 [6970]~P81(x69701)+~P85(f784(f784(f242(x69701),f2(x69701)),x69703))+~P85(f784(f784(f242(x69701),x69702),x69704))+P85(f784(f784(f242(x69701),x69702),f784(f784(f89(x69701),x69703),x69704)))
% 11.41/11.19 [7004]~P101(x70041)+P85(f784(f784(f243(x70041),x70042),x70043))+P85(f784(f784(f243(x70041),x70042),x70044))+~P85(f784(f784(f243(x70041),x70042),f784(f784(f186(x70041),x70044),x70043)))
% 11.41/11.19 [7005]~P101(x70051)+P85(f784(f784(f242(x70051),x70052),x70053))+P85(f784(f784(f242(x70051),x70052),x70054))+~P85(f784(f784(f242(x70051),x70052),f784(f784(f186(x70051),x70054),x70053)))
% 11.41/11.19 [7686]~P62(x76861)+~P85(f784(f784(f243(x76861),x76864),f2(x76861)))+~P85(f784(f784(f243(x76861),x76863),f784(f784(f293(x76861),x76862),x76864)))+P85(f784(f784(f243(x76861),x76862),f784(f784(f90(x76861),x76863),x76864)))
% 11.41/11.19 [7687]~P62(x76871)+~P85(f784(f784(f243(x76871),x76874),f2(x76871)))+~P85(f784(f784(f243(x76871),x76873),f784(f784(f90(x76871),x76872),x76874)))+P85(f784(f784(f243(x76871),x76872),f784(f784(f293(x76871),x76873),x76874)))
% 11.41/11.19 [7688]~P62(x76881)+~P85(f784(f784(f243(x76881),x76884),f2(x76881)))+~P85(f784(f784(f242(x76881),x76883),f784(f784(f293(x76881),x76882),x76884)))+P85(f784(f784(f242(x76881),x76882),f784(f784(f90(x76881),x76883),x76884)))
% 11.41/11.19 [7689]~P62(x76891)+~P85(f784(f784(f243(x76891),x76894),f2(x76891)))+~P85(f784(f784(f242(x76891),x76893),f784(f784(f90(x76891),x76892),x76894)))+P85(f784(f784(f242(x76891),x76892),f784(f784(f293(x76891),x76893),x76894)))
% 11.41/11.19 [7799]~P122(x77991)+~P85(f784(f784(f243(x77991),x77992),f2(x77991)))+~P85(f784(f784(f243(x77991),x77994),x77993))+P85(f784(f784(f243(x77991),f784(f784(f90(x77991),x77992),x77993)),f784(f784(f90(x77991),x77992),x77994)))
% 11.41/11.19 [7800]~P122(x78001)+~P85(f784(f784(f243(x78001),x78002),f2(x78001)))+~P85(f784(f784(f243(x78001),x78004),x78003))+P85(f784(f784(f243(x78001),f784(f784(f90(x78001),x78002),x78003)),f784(f784(f90(x78001),x78002),x78004)))
% 11.41/11.19 [7801]~P122(x78011)+~P85(f784(f784(f243(x78011),x78013),f2(x78011)))+~P85(f784(f784(f243(x78011),x78014),x78012))+P85(f784(f784(f243(x78011),f784(f784(f90(x78011),x78012),x78013)),f784(f784(f90(x78011),x78014),x78013)))
% 11.41/11.19 [7802]~P122(x78021)+~P85(f784(f784(f243(x78021),x78023),f2(x78021)))+~P85(f784(f784(f243(x78021),x78024),x78022))+P85(f784(f784(f243(x78021),f784(f784(f90(x78021),x78022),x78023)),f784(f784(f90(x78021),x78024),x78023)))
% 11.41/11.19 [7803]~P122(x78031)+~P85(f784(f784(f243(x78031),x78032),f2(x78031)))+~P85(f784(f784(f243(x78031),x78034),x78033))+P85(f784(f784(f243(x78031),f784(f784(f90(x78031),x78032),x78033)),f784(f784(f90(x78031),x78032),x78034)))
% 11.41/11.19 [7804]~P62(x78041)+~P85(f784(f784(f243(x78041),x78043),f2(x78041)))+~P85(f784(f784(f243(x78041),x78044),x78042))+P85(f784(f784(f243(x78041),f784(f784(f293(x78041),x78042),x78043)),f784(f784(f293(x78041),x78044),x78043)))
% 11.41/11.19 [7805]~P122(x78051)+~P85(f784(f784(f243(x78051),x78052),f2(x78051)))+~P85(f784(f784(f242(x78051),x78054),x78053))+P85(f784(f784(f242(x78051),f784(f784(f90(x78051),x78052),x78053)),f784(f784(f90(x78051),x78052),x78054)))
% 11.41/11.19 [7806]~P131(x78061)+~P85(f784(f784(f242(x78061),x78062),f2(x78061)))+~P85(f784(f784(f242(x78061),x78064),x78063))+P85(f784(f784(f242(x78061),f784(f784(f90(x78061),x78062),x78063)),f784(f784(f90(x78061),x78062),x78064)))
% 11.41/11.19 [7807]~P131(x78071)+~P85(f784(f784(f242(x78071),x78073),f2(x78071)))+~P85(f784(f784(f242(x78071),x78074),x78072))+P85(f784(f784(f242(x78071),f784(f784(f90(x78071),x78072),x78073)),f784(f784(f90(x78071),x78074),x78073)))
% 11.41/11.19 [7808]~P61(x78081)+~P85(f784(f784(f242(x78081),x78083),f2(x78081)))+~P85(f784(f784(f242(x78081),x78084),x78082))+P85(f784(f784(f242(x78081),f784(f784(f293(x78081),x78082),x78083)),f784(f784(f293(x78081),x78084),x78083)))
% 11.41/11.19 [7809]~P120(x78091)+~P85(f784(f784(f243(x78091),f87(x78091)),x78092))+~P85(f784(f784(f243(a859),x78093),x78094))+P85(f784(f784(f243(x78091),f784(f784(f252(x78091),x78092),x78093)),f784(f784(f252(x78091),x78092),x78094)))
% 11.41/11.19 [7810]~P120(x78101)+~P85(f784(f784(f243(x78101),f87(x78101)),x78102))+~P85(f784(f784(f243(a859),x78103),x78104))+P85(f784(f784(f243(x78101),f784(f784(f252(x78101),x78102),x78103)),f784(f784(f252(x78101),x78102),x78104)))
% 11.41/11.19 [7811]~P120(x78111)+~P85(f784(f784(f243(x78111),f87(x78111)),x78112))+~P85(f784(f784(f242(a859),x78113),x78114))+P85(f784(f784(f242(x78111),f784(f784(f252(x78111),x78112),x78113)),f784(f784(f252(x78111),x78112),x78114)))
% 11.41/11.19 [7812]~P120(x78121)+~P85(f784(f784(f242(x78121),f87(x78121)),x78122))+~P85(f784(f784(f242(a859),x78123),x78124))+P85(f784(f784(f242(x78121),f784(f784(f252(x78121),x78122),x78123)),f784(f784(f252(x78121),x78122),x78124)))
% 11.41/11.19 [7839]P85(f784(f784(f243(a859),f2(a859)),f784(x78391,x78392)))+~P85(f784(f71(x78393),x78394))+~P85(f784(f784(f347(x78393),x78392),x78394))+~P85(f784(f784(f243(a859),f2(a859)),f784(f784(f11(x78393,a859),x78391),x78394)))
% 11.41/11.19 [7850]~P122(x78501)+~P85(f784(f784(f243(x78501),x78503),x78504))+~P85(f784(f784(f243(x78501),f2(x78501)),x78502))+P85(f784(f784(f243(x78501),f784(f784(f90(x78501),x78502),x78503)),f784(f784(f90(x78501),x78502),x78504)))
% 11.41/11.19 [7851]~P125(x78511)+~P85(f784(f784(f243(x78511),x78513),x78514))+~P85(f784(f784(f243(x78511),f2(x78511)),x78512))+P85(f784(f784(f243(x78511),f784(f784(f90(x78511),x78512),x78513)),f784(f784(f90(x78511),x78512),x78514)))
% 11.41/11.19 [7852]~P118(x78521)+~P85(f784(f784(f243(x78521),x78523),x78524))+~P85(f784(f784(f243(x78521),f2(x78521)),x78522))+P85(f784(f784(f243(x78521),f784(f784(f90(x78521),x78522),x78523)),f784(f784(f90(x78521),x78522),x78524)))
% 11.41/11.19 [7853]~P122(x78531)+~P85(f784(f784(f243(x78531),x78532),x78534))+~P85(f784(f784(f243(x78531),f2(x78531)),x78533))+P85(f784(f784(f243(x78531),f784(f784(f90(x78531),x78532),x78533)),f784(f784(f90(x78531),x78534),x78533)))
% 11.41/11.19 [7854]~P125(x78541)+~P85(f784(f784(f243(x78541),x78542),x78544))+~P85(f784(f784(f243(x78541),f2(x78541)),x78543))+P85(f784(f784(f243(x78541),f784(f784(f90(x78541),x78542),x78543)),f784(f784(f90(x78541),x78544),x78543)))
% 11.41/11.19 [7855]~P122(x78551)+~P85(f784(f784(f243(x78551),x78553),x78554))+~P85(f784(f784(f243(x78551),f2(x78551)),x78552))+P85(f784(f784(f243(x78551),f784(f784(f90(x78551),x78552),x78553)),f784(f784(f90(x78551),x78552),x78554)))
% 11.41/11.19 [7856]~P62(x78561)+~P85(f784(f784(f243(x78561),x78562),x78564))+~P85(f784(f784(f243(x78561),f2(x78561)),x78563))+P85(f784(f784(f243(x78561),f784(f784(f293(x78561),x78562),x78563)),f784(f784(f293(x78561),x78564),x78563)))
% 11.41/11.19 [7857]~P122(x78571)+~P85(f784(f784(f243(x78571),f2(x78571)),x78572))+~P85(f784(f784(f242(x78571),x78573),x78574))+P85(f784(f784(f242(x78571),f784(f784(f90(x78571),x78572),x78573)),f784(f784(f90(x78571),x78572),x78574)))
% 11.41/11.19 [7858]~P133(x78581)+~P85(f784(f784(f242(x78581),x78583),x78584))+~P85(f784(f784(f242(x78581),f2(x78581)),x78582))+P85(f784(f784(f242(x78581),f784(f784(f90(x78581),x78582),x78583)),f784(f784(f90(x78581),x78582),x78584)))
% 11.41/11.19 [7859]~P132(x78591)+~P85(f784(f784(f242(x78591),x78593),x78594))+~P85(f784(f784(f242(x78591),f2(x78591)),x78592))+P85(f784(f784(f242(x78591),f784(f784(f90(x78591),x78592),x78593)),f784(f784(f90(x78591),x78592),x78594)))
% 11.41/11.19 [7860]~P133(x78601)+~P85(f784(f784(f242(x78601),x78602),x78604))+~P85(f784(f784(f242(x78601),f2(x78601)),x78603))+P85(f784(f784(f242(x78601),f784(f784(f90(x78601),x78602),x78603)),f784(f784(f90(x78601),x78604),x78603)))
% 11.41/11.19 [7861]~P120(x78611)+~P85(f784(f784(f242(x78611),x78612),x78614))+~P85(f784(f784(f242(x78611),f2(x78611)),x78612))+P85(f784(f784(f242(x78611),f784(f784(f252(x78611),x78612),x78613)),f784(f784(f252(x78611),x78614),x78613)))
% 11.41/11.19 [7862]~P61(x78621)+~P85(f784(f784(f242(x78621),x78622),x78624))+~P85(f784(f784(f242(x78621),f2(x78621)),x78623))+P85(f784(f784(f242(x78621),f784(f784(f293(x78621),x78622),x78623)),f784(f784(f293(x78621),x78624),x78623)))
% 11.41/11.19 [7901]~P103(x79012)+P85(f784(f784(f242(f869(x79011,x79012)),x79014),x79013))+~P85(f784(f784(f242(f869(x79011,x79012)),x79013),x79014))+P85(f784(f784(f243(f869(x79011,x79012)),x79013),x79014))
% 11.41/11.19 [7944]P85(f784(f784(f347(x79441),x79442),x79443))+P85(f784(f784(f347(x79441),x79442),x79444))+~P85(f784(f784(f242(f869(x79441,a852)),x79444),x79443))+P85(f784(f784(f243(f869(x79441,a852)),x79444),f784(f784(f312(x79441),x79442),x79443)))
% 11.41/11.19 [8050]~P114(x80502)+E(x80501,f2(x80502))+P85(f784(f784(f289(x80502),x80503),x80504))+~P85(f784(f784(f289(x80502),f784(f784(f90(x80502),x80503),x80501)),f784(f784(f90(x80502),x80504),x80501)))
% 11.41/11.19 [8051]~P114(x80512)+E(x80511,f2(x80512))+P85(f784(f784(f289(x80512),x80513),x80514))+~P85(f784(f784(f289(x80512),f784(f784(f90(x80512),x80511),x80513)),f784(f784(f90(x80512),x80511),x80514)))
% 11.41/11.19 [8095]P85(f784(f784(f347(x80951),x80952),x80953))+P85(f784(f784(f347(x80951),x80952),x80954))+~P85(f784(f784(f243(f869(x80951,a852)),x80954),f784(f784(f312(x80951),x80952),x80953)))+P85(f784(f784(f242(f869(x80951,a852)),x80954),x80953))
% 11.41/11.19 [8162]~P122(x81621)+P85(f784(f784(f243(x81621),x81623),x81622))+P85(f784(f784(f243(x81621),x81622),x81623))+~P85(f784(f784(f243(x81621),f784(f784(f90(x81621),x81624),x81622)),f784(f784(f90(x81621),x81624),x81623)))
% 11.41/11.19 [8163]~P122(x81631)+P85(f784(f784(f243(x81631),x81633),x81632))+P85(f784(f784(f243(x81631),x81632),x81633))+~P85(f784(f784(f243(x81631),f784(f784(f90(x81631),x81632),x81634)),f784(f784(f90(x81631),x81633),x81634)))
% 11.41/11.19 [8174]~P122(x81741)+P85(f784(f784(f243(x81741),x81744),f2(x81741)))+P85(f784(f784(f243(x81741),x81742),x81743))+~P85(f784(f784(f243(x81741),f784(f784(f90(x81741),x81742),x81744)),f784(f784(f90(x81741),x81743),x81744)))
% 11.41/11.19 [8175]~P122(x81751)+P85(f784(f784(f243(x81751),x81754),f2(x81751)))+P85(f784(f784(f243(x81751),x81752),x81753))+~P85(f784(f784(f243(x81751),f784(f784(f90(x81751),x81754),x81752)),f784(f784(f90(x81751),x81754),x81753)))
% 11.41/11.19 [8178]~P122(x81781)+P85(f784(f784(f243(x81781),x81782),x81783))+P85(f784(f784(f243(x81781),f2(x81781)),x81784))+~P85(f784(f784(f243(x81781),f784(f784(f90(x81781),x81784),x81783)),f784(f784(f90(x81781),x81784),x81782)))
% 11.41/11.19 [8179]~P122(x81791)+P85(f784(f784(f243(x81791),x81792),x81793))+P85(f784(f784(f243(x81791),f2(x81791)),x81794))+~P85(f784(f784(f243(x81791),f784(f784(f90(x81791),x81793),x81794)),f784(f784(f90(x81791),x81792),x81794)))
% 11.41/11.19 [8192]~P122(x81921)+P85(f784(f784(f243(x81921),x81922),f2(x81921)))+P85(f784(f784(f243(x81921),f2(x81921)),x81922))+~P85(f784(f784(f243(x81921),f784(f784(f90(x81921),x81923),x81922)),f784(f784(f90(x81921),x81924),x81922)))
% 11.41/11.19 [8193]~P122(x81931)+P85(f784(f784(f243(x81931),x81932),f2(x81931)))+P85(f784(f784(f243(x81931),f2(x81931)),x81932))+~P85(f784(f784(f243(x81931),f784(f784(f90(x81931),x81932),x81933)),f784(f784(f90(x81931),x81932),x81934)))
% 11.41/11.19 [8217]~P122(x82171)+~P85(f784(f784(f243(x82171),x82174),f2(x82171)))+P85(f784(f784(f243(x82171),x82172),x82173))+~P85(f784(f784(f243(x82171),f784(f784(f90(x82171),x82174),x82173)),f784(f784(f90(x82171),x82174),x82172)))
% 11.41/11.19 [8218]~P122(x82181)+~P85(f784(f784(f243(x82181),x82184),f2(x82181)))+P85(f784(f784(f242(x82181),x82182),x82183))+~P85(f784(f784(f242(x82181),f784(f784(f90(x82181),x82184),x82183)),f784(f784(f90(x82181),x82184),x82182)))
% 11.41/11.19 [8229]~P120(x82293)+~P85(f784(f784(f243(x82293),f87(x82293)),x82294))+P85(f784(f784(f243(a859),x82291),x82292))+~P85(f784(f784(f243(x82293),f784(f784(f252(x82293),x82294),x82291)),f784(f784(f252(x82293),x82294),x82292)))
% 11.41/11.19 [8230]~P120(x82303)+~P85(f784(f784(f243(x82303),f87(x82303)),x82304))+P85(f784(f784(f243(a859),x82301),x82302))+~P85(f784(f784(f243(x82303),f784(f784(f252(x82303),x82304),x82301)),f784(f784(f252(x82303),x82304),x82302)))
% 11.41/11.19 [8231]~P120(x82313)+~P85(f784(f784(f243(x82313),f87(x82313)),x82314))+P85(f784(f784(f242(a859),x82311),x82312))+~P85(f784(f784(f242(x82313),f784(f784(f252(x82313),x82314),x82311)),f784(f784(f252(x82313),x82314),x82312)))
% 11.41/11.19 [8232]~P120(x82323)+~P85(f784(f784(f243(x82323),f87(x82323)),x82324))+P85(f784(f784(f242(a859),x82321),x82322))+~P85(f784(f784(f242(x82323),f784(f784(f252(x82323),x82324),x82321)),f784(f784(f252(x82323),x82324),x82322)))
% 11.41/11.19 [8242]~P122(x82421)+P85(f784(f784(f243(x82421),x82422),x82423))+~P85(f784(f784(f243(x82421),f2(x82421)),x82424))+~P85(f784(f784(f243(x82421),f784(f784(f90(x82421),x82424),x82422)),f784(f784(f90(x82421),x82424),x82423)))
% 11.41/11.19 [8243]~P125(x82431)+P85(f784(f784(f243(x82431),x82432),x82433))+~P85(f784(f784(f242(x82431),f2(x82431)),x82434))+~P85(f784(f784(f243(x82431),f784(f784(f90(x82431),x82434),x82432)),f784(f784(f90(x82431),x82434),x82433)))
% 11.41/11.19 [8244]~P127(x82441)+P85(f784(f784(f243(x82441),x82442),x82443))+~P85(f784(f784(f242(x82441),f2(x82441)),x82444))+~P85(f784(f784(f243(x82441),f784(f784(f90(x82441),x82444),x82442)),f784(f784(f90(x82441),x82444),x82443)))
% 11.41/11.19 [8245]~P120(x82451)+~P85(f784(f784(f242(x82451),f2(x82451)),x82453))+P85(f784(f784(f243(x82451),x82452),x82453))+~P85(f784(f784(f243(x82451),f784(f784(f252(x82451),x82452),x82454)),f784(f784(f252(x82451),x82453),x82454)))
% 11.41/11.19 [8246]~P125(x82461)+P85(f784(f784(f243(x82461),x82462),x82463))+~P85(f784(f784(f242(x82461),f2(x82461)),x82464))+~P85(f784(f784(f243(x82461),f784(f784(f90(x82461),x82462),x82464)),f784(f784(f90(x82461),x82463),x82464)))
% 11.41/11.19 [8247]~P127(x82471)+P85(f784(f784(f243(x82471),x82472),x82473))+~P85(f784(f784(f242(x82471),f2(x82471)),x82474))+~P85(f784(f784(f243(x82471),f784(f784(f90(x82471),x82472),x82474)),f784(f784(f90(x82471),x82473),x82474)))
% 11.41/11.19 [8248]~P122(x82481)+P85(f784(f784(f242(x82481),x82482),x82483))+~P85(f784(f784(f243(x82481),f2(x82481)),x82484))+~P85(f784(f784(f242(x82481),f784(f784(f90(x82481),x82484),x82482)),f784(f784(f90(x82481),x82484),x82483)))
% 11.41/11.19 [8249]~P125(x82491)+P85(f784(f784(f242(x82491),x82492),x82493))+~P85(f784(f784(f243(x82491),f2(x82491)),x82494))+~P85(f784(f784(f242(x82491),f784(f784(f90(x82491),x82494),x82492)),f784(f784(f90(x82491),x82494),x82493)))
% 11.41/11.19 [8250]~P125(x82501)+P85(f784(f784(f242(x82501),x82502),x82503))+~P85(f784(f784(f243(x82501),f2(x82501)),x82504))+~P85(f784(f784(f242(x82501),f784(f784(f90(x82501),x82502),x82504)),f784(f784(f90(x82501),x82503),x82504)))
% 11.41/11.19 [8291]P85(f784(f784(f347(x82911),x82912),x82913))+~P85(f784(f784(f242(f869(x82911,a852)),x82913),x82914))+~P85(f784(f784(f243(f869(x82911,a852)),x82913),x82914))+P85(f784(f784(f243(f869(x82911,a852)),x82913),f784(f784(f312(x82911),x82912),x82914)))
% 11.41/11.19 [8326]~P139(x83261)+~P115(x83261)+P85(f784(f784(f289(x83261),x83262),f784(f784(f89(x83261),f831(x83262,x83263,x83261)),f2(x83261))))+~P85(f784(x83263,f784(f784(f90(x83261),x83262),x83264)))
% 11.41/11.19 [8651]E(f784(f784(f3(a1),f359(x86511,x86512,x86513,x86514)),f360(x86511,x86512,x86513,x86514)),x86514)+~P85(f784(f784(f243(a1),f2(a1)),x86513))+~P85(f784(f784(f242(a1),x86511),x86514))+P85(f784(f784(f242(a1),x86511),f784(f784(f89(a1),x86514),x86513)))
% 11.41/11.19 [8652]E(f784(f784(f3(a1),f367(x86521,x86522,x86523,x86524)),f368(x86521,x86522,x86523,x86524)),x86524)+~P85(f784(f784(f243(a1),f2(a1)),x86523))+~P85(f784(f784(f243(a1),x86521),x86524))+P85(f784(f784(f243(a1),x86521),f784(f784(f89(a1),x86524),x86523)))
% 11.41/11.19 [8778]~E(f784(f784(f155(x87781),x87783),f769(x87784,x87783,x87781,x87782)),f784(f784(f155(x87781),x87784),f769(x87784,x87783,x87781,x87782)))+E(f784(f784(f165(x87781),x87782),x87783),f784(f784(f165(x87781),x87782),x87784))+~P85(f784(f784(f242(a859),x87782),f784(f188(f860(x87781)),x87783)))+~P85(f784(f784(f242(a859),x87782),f784(f188(f860(x87781)),x87784)))
% 11.41/11.19 [8832]~P85(f784(f784(f243(a1),f2(a1)),x88323))+~P85(f784(f784(f242(a1),x88321),x88324))+P85(f784(f784(f347(a1),f359(x88321,x88322,x88323,x88324)),x88322))+P85(f784(f784(f242(a1),x88321),f784(f784(f89(a1),x88324),x88323)))
% 11.41/11.19 [8833]~P85(f784(f784(f243(a1),f2(a1)),x88333))+~P85(f784(f784(f243(a1),x88331),x88334))+P85(f784(f784(f347(a1),f367(x88331,x88332,x88333,x88334)),x88332))+P85(f784(f784(f243(a1),x88331),f784(f784(f89(a1),x88334),x88333)))
% 11.41/11.19 [8869]~P101(x88691)+~P85(f784(f71(x88691),x88693))+~P85(f784(f784(f347(x88691),x88694),x88693))+P85(f784(f784(f242(x88691),f784(f784(f74(x88691,x88691,f246(x88691)),x88692),x88693)),f784(f784(f246(x88691),x88694),x88692)))
% 11.41/11.19 [8870]~P99(x88701)+~P85(f784(f71(x88701),x88703))+~P85(f784(f784(f347(x88701),x88704),x88703))+P85(f784(f784(f242(x88701),f784(f784(f74(x88701,x88701,f111(x88701)),x88702),x88703)),f784(f784(f111(x88701),x88704),x88702)))
% 11.41/11.19 [8879]~P9(x88792,x88793,x88794)+~P85(f784(f71(x88792),x88793))+P85(f784(f784(f289(a859),x88791),f784(f50(x88792),x88793)))+P85(f784(f784(f347(f869(x88792,a852)),f519(x88791,x88794,x88793,x88792)),f784(f784(f69(x88792),x88793),x88794)))
% 11.41/11.19 [8918]E(f784(f784(f165(x89181),x89182),x89183),f784(f784(f165(x89181),x89182),x89184))+P85(f784(f784(f243(a859),f769(x89183,x89184,x89181,x89182)),x89182))+~P85(f784(f784(f242(a859),x89182),f784(f188(f860(x89181)),x89183)))+~P85(f784(f784(f242(a859),x89182),f784(f188(f860(x89181)),x89184)))
% 11.41/11.19 [8923]~P85(f784(f784(f243(a1),f2(a1)),x89233))+~P85(f784(f784(f243(a1),x89231),x89232))+P85(f784(f784(f347(a1),f368(x89231,x89234,x89233,x89232)),f305(a1,f87(a1),x89233)))+P85(f784(f784(f243(a1),x89231),f784(f784(f89(a1),x89232),x89233)))
% 11.41/11.19 [8924]~P85(f784(f784(f243(a1),f2(a1)),x89243))+~P85(f784(f784(f242(a1),x89241),x89242))+P85(f784(f784(f347(a1),f360(x89241,x89244,x89243,x89242)),f305(a1,f87(a1),x89243)))+P85(f784(f784(f242(a1),x89241),f784(f784(f89(a1),x89242),x89243)))
% 11.41/11.19 [9089]~E(f172(x90891,x90892,x90893),f172(x90891,x90892,x90894))+E(f784(f164(f868(x90891,x90892)),x90893),f784(f164(f868(x90891,x90892)),x90894))+~P85(f784(f132(x90891),f784(f784(f146(f868(x90891,x90892),x90891),f250(x90891,x90892)),x90894)))+~P85(f784(f132(x90891),f784(f784(f146(f868(x90891,x90892),x90891),f250(x90891,x90892)),x90893)))
% 11.41/11.19 [9092]E(f172(x90921,x90922,x90923),f172(x90921,x90922,x90924))+~E(f784(f164(f868(x90921,x90922)),x90923),f784(f164(f868(x90921,x90922)),x90924))+~P85(f784(f132(x90921),f784(f784(f146(f868(x90921,x90922),x90921),f250(x90921,x90922)),x90924)))+~P85(f784(f132(x90921),f784(f784(f146(f868(x90921,x90922),x90921),f250(x90921,x90922)),x90923)))
% 11.41/11.19 [9207]~P101(x92071)+~P85(f784(f71(x92071),x92074))+P85(f784(f784(f347(x92071),f702(x92072,x92073,x92074,x92071)),x92074))+P85(f784(f784(f242(x92071),f784(f784(f74(x92071,x92071,f186(x92071)),x92072),x92074)),f784(f784(f186(x92071),x92073),x92072)))
% 11.41/11.19 [9208]~P98(x92081)+~P85(f784(f71(x92081),x92084))+P85(f784(f784(f347(x92081),f706(x92082,x92083,x92084,x92081)),x92084))+P85(f784(f784(f242(x92081),f784(f784(f74(x92081,x92081,f110(x92081)),x92082),x92084)),f784(f784(f110(x92081),x92083),x92082)))
% 11.41/11.19 [9333]~P101(x93331)+~P85(f784(f71(x93331),x93333))+~P85(f784(f784(f242(x93331),f702(x93332,x93334,x93333,x93331)),x93334))+P85(f784(f784(f242(x93331),f784(f784(f74(x93331,x93331,f186(x93331)),x93332),x93333)),f784(f784(f186(x93331),x93334),x93332)))
% 11.41/11.19 [9334]~P98(x93341)+~P85(f784(f71(x93341),x93343))+~P85(f784(f784(f242(x93341),f706(x93342,x93344,x93343,x93341)),x93344))+P85(f784(f784(f242(x93341),f784(f784(f74(x93341,x93341,f110(x93341)),x93342),x93343)),f784(f784(f110(x93341),x93344),x93342)))
% 11.41/11.19 [9337]~P85(f784(f784(f243(a1),f2(a1)),x93373))+~P85(f784(f784(f242(a1),f2(a1)),x93374))+~P85(f784(f784(f243(a1),x93374),x93371))+P85(f784(f784(f243(a1),f784(f784(f89(a1),f784(f784(f90(a1),x93371),f60(a1,x93372,x93373))),x93374)),f784(f784(f90(a1),x93371),x93373)))
% 11.41/11.19 [9604]~P100(x96041)+P85(f784(f784(f243(x96041),f784(x96042,x96043)),f784(x96042,x96044)))+~P85(f784(f784(f243(a859),x96043),x96044))+~P85(f784(f784(f243(x96041),f784(x96042,f675(x96044,x96043,x96042,x96041))),f784(x96042,f784(a160,f675(x96044,x96043,x96042,x96041)))))
% 11.41/11.19 [9605]~P100(x96051)+P85(f784(f784(f243(x96051),f784(x96052,x96053)),f784(x96052,x96054)))+~P85(f784(f784(f243(a859),x96053),x96054))+~P85(f784(f784(f243(x96051),f784(x96052,f661(x96054,x96053,x96052,x96051))),f784(x96052,f784(a160,f661(x96054,x96053,x96052,x96051)))))
% 11.41/11.19 [9606]~P100(x96063)+~P85(f784(f784(f243(x96063),f784(x96064,x96061)),f784(x96064,x96062)))+P85(f784(f784(f243(a859),x96061),x96062))+~P85(f784(f784(f243(x96063),f784(x96064,f675(x96062,x96061,x96064,x96063))),f784(x96064,f784(a160,f675(x96062,x96061,x96064,x96063)))))
% 11.41/11.19 [9700]E(x97001,x97002)+P85(f784(f784(f347(f868(f860(x97003),f860(x97003))),f784(f784(f251(f860(x97003),f860(x97003)),x97002),x97001)),f141(x97003,x97004)))+P85(f784(f784(f347(f868(f860(x97003),f860(x97003))),f784(f784(f251(f860(x97003),f860(x97003)),x97001),x97002)),f141(x97003,x97004)))+~P85(f784(f784(f347(f868(x97003,x97003)),f784(f784(f251(x97003,x97003),f764(x97001,x97002,x97004,x97003)),f766(x97001,x97002,x97004,x97003))),x97004))
% 11.41/11.19 [9701]E(x97011,x97012)+P85(f784(f784(f347(f868(f860(x97013),f860(x97013))),f784(f784(f251(f860(x97013),f860(x97013)),x97012),x97011)),f141(x97013,x97014)))+P85(f784(f784(f347(f868(f860(x97013),f860(x97013))),f784(f784(f251(f860(x97013),f860(x97013)),x97011),x97012)),f141(x97013,x97014)))+~P85(f784(f784(f347(f868(x97013,x97013)),f784(f784(f251(x97013,x97013),f766(x97011,x97012,x97014,x97013)),f764(x97011,x97012,x97014,x97013))),x97014))
% 11.41/11.19 [7386]~P101(x73861)+~P85(f784(f784(f243(x73861),x73863),x73864))+~P85(f784(f784(f243(x73861),x73862),x73864))+P85(f784(f784(f243(x73861),f784(f784(f186(x73861),x73862),x73863)),x73864))
% 11.41/11.19 [7387]~P101(x73871)+~P85(f784(f784(f242(x73871),x73873),x73874))+~P85(f784(f784(f242(x73871),x73872),x73874))+P85(f784(f784(f242(x73871),f784(f784(f186(x73871),x73872),x73873)),x73874))
% 11.41/11.19 [7388]~P101(x73881)+~P85(f784(f784(f242(x73881),x73883),x73884))+~P85(f784(f784(f242(x73881),x73882),x73884))+P85(f784(f784(f242(x73881),f784(f784(f186(x73881),x73882),x73883)),x73884))
% 11.41/11.19 [7389]~P101(x73891)+~P85(f784(f784(f242(x73891),x73893),x73894))+~P85(f784(f784(f242(x73891),x73892),x73894))+P85(f784(f784(f242(x73891),f784(f784(f186(x73891),x73892),x73893)),x73894))
% 11.41/11.19 [7390]~P98(x73901)+~P85(f784(f784(f242(x73901),x73903),x73904))+~P85(f784(f784(f242(x73901),x73902),x73904))+P85(f784(f784(f242(x73901),f784(f784(f110(x73901),x73902),x73903)),x73904))
% 11.41/11.19 [7391]~P98(x73911)+~P85(f784(f784(f242(x73911),x73913),x73914))+~P85(f784(f784(f242(x73911),x73912),x73914))+P85(f784(f784(f242(x73911),f784(f784(f110(x73911),x73912),x73913)),x73914))
% 11.41/11.19 [7392]~P98(x73921)+~P85(f784(f784(f242(x73921),x73923),x73924))+~P85(f784(f784(f242(x73921),x73922),x73924))+P85(f784(f784(f242(x73921),f784(f784(f110(x73921),x73922),x73923)),x73924))
% 11.41/11.19 [7632]~P4(x76321)+E(f784(f784(f89(x76321),f784(f784(f51(x76321),x76322),x76323)),f784(f784(f51(x76321),x76324),x76323)),f784(f784(f51(x76321),f784(f784(f89(x76321),x76322),x76324)),x76323))+~P85(f784(f784(f289(x76321),x76323),x76324))+~P85(f784(f784(f289(x76321),x76323),x76322))
% 11.41/11.19 [7709]~E(x77091,x77093)+E(f134(a859,f784(f304(a859,x77091),x77092)),f784(f784(f144(a859),x77093),x77094))+~E(f134(a859,f784(f304(a859,f784(f784(f89(a859),x77091),f87(a859))),x77092)),x77094)+~P85(f784(f784(f243(a859),x77091),x77092))
% 11.41/11.19 [7720]~P101(x77201)+P85(f784(f784(f243(x77201),x77202),x77203))+P85(f784(f784(f243(x77201),x77204),x77203))+~P85(f784(f784(f243(x77201),f784(f784(f246(x77201),x77204),x77202)),x77203))
% 11.41/11.19 [7721]~P101(x77211)+P85(f784(f784(f242(x77211),x77212),x77213))+P85(f784(f784(f242(x77211),x77214),x77213))+~P85(f784(f784(f242(x77211),f784(f784(f246(x77211),x77214),x77212)),x77213))
% 11.41/11.19 [8001]~P61(x80011)+~P85(f784(f784(f243(x80011),f2(x80011)),x80013))+~P85(f784(f784(f243(x80011),x80012),f784(f784(f293(x80011),x80014),x80013)))+P85(f784(f784(f243(x80011),f784(f784(f90(x80011),x80012),x80013)),x80014))
% 11.41/11.19 [8002]~P62(x80021)+~P85(f784(f784(f243(x80021),f2(x80021)),x80023))+~P85(f784(f784(f243(x80021),x80022),f784(f784(f293(x80021),x80024),x80023)))+P85(f784(f784(f243(x80021),f784(f784(f90(x80021),x80022),x80023)),x80024))
% 11.41/11.19 [8003]~P61(x80031)+~P85(f784(f784(f243(x80031),f2(x80031)),x80033))+~P85(f784(f784(f243(x80031),x80032),f784(f784(f90(x80031),x80034),x80033)))+P85(f784(f784(f243(x80031),f784(f784(f293(x80031),x80032),x80033)),x80034))
% 11.41/11.19 [8004]~P62(x80041)+~P85(f784(f784(f243(x80041),f2(x80041)),x80043))+~P85(f784(f784(f243(x80041),x80042),f784(f784(f90(x80041),x80044),x80043)))+P85(f784(f784(f243(x80041),f784(f784(f293(x80041),x80042),x80043)),x80044))
% 11.41/11.19 [8005]~P62(x80051)+~P85(f784(f784(f243(x80051),f2(x80051)),x80053))+~P85(f784(f784(f243(x80051),x80052),f784(f784(f90(x80051),x80054),x80053)))+P85(f784(f784(f243(x80051),f784(f784(f293(x80051),x80052),x80053)),x80054))
% 11.41/11.19 [8006]~P61(x80061)+~P85(f784(f784(f243(x80061),f2(x80061)),x80063))+~P85(f784(f784(f242(x80061),x80062),f784(f784(f293(x80061),x80064),x80063)))+P85(f784(f784(f242(x80061),f784(f784(f90(x80061),x80062),x80063)),x80064))
% 11.41/11.19 [8007]~P62(x80071)+~P85(f784(f784(f243(x80071),f2(x80071)),x80073))+~P85(f784(f784(f242(x80071),x80072),f784(f784(f293(x80071),x80074),x80073)))+P85(f784(f784(f242(x80071),f784(f784(f90(x80071),x80072),x80073)),x80074))
% 11.41/11.19 [8008]~P61(x80081)+~P85(f784(f784(f243(x80081),f2(x80081)),x80083))+~P85(f784(f784(f242(x80081),x80082),f784(f784(f90(x80081),x80084),x80083)))+P85(f784(f784(f242(x80081),f784(f784(f293(x80081),x80082),x80083)),x80084))
% 11.41/11.19 [8009]~P62(x80091)+~P85(f784(f784(f243(x80091),f2(x80091)),x80093))+~P85(f784(f784(f242(x80091),x80092),f784(f784(f90(x80091),x80094),x80093)))+P85(f784(f784(f242(x80091),f784(f784(f293(x80091),x80092),x80093)),x80094))
% 11.41/11.19 [8010]~P62(x80101)+~P85(f784(f784(f243(x80101),f2(x80101)),x80103))+~P85(f784(f784(f242(x80101),x80102),f784(f784(f90(x80101),x80104),x80103)))+P85(f784(f784(f242(x80101),f784(f784(f293(x80101),x80102),x80103)),x80104))
% 11.41/11.19 [8132]~P61(x81321)+~P85(f784(f784(f243(x81321),f2(x81321)),x81324))+P85(f784(f784(f243(x81321),x81322),f784(f784(f90(x81321),x81323),x81324)))+~P85(f784(f784(f243(x81321),f784(f784(f293(x81321),x81322),x81324)),x81323))
% 11.41/11.19 [8133]~P61(x81331)+~P85(f784(f784(f243(x81331),f2(x81331)),x81334))+P85(f784(f784(f243(x81331),x81332),f784(f784(f293(x81331),x81333),x81334)))+~P85(f784(f784(f243(x81331),f784(f784(f90(x81331),x81332),x81334)),x81333))
% 11.41/11.19 [8134]~P62(x81341)+~P85(f784(f784(f243(x81341),f2(x81341)),x81344))+P85(f784(f784(f243(x81341),x81342),f784(f784(f293(x81341),x81343),x81344)))+~P85(f784(f784(f243(x81341),f784(f784(f90(x81341),x81342),x81344)),x81343))
% 11.41/11.19 [8135]~P62(x81351)+~P85(f784(f784(f243(x81351),f2(x81351)),x81354))+P85(f784(f784(f243(x81351),x81352),f784(f784(f90(x81351),x81353),x81354)))+~P85(f784(f784(f243(x81351),f784(f784(f293(x81351),x81352),x81354)),x81353))
% 11.41/11.19 [8136]~P62(x81361)+~P85(f784(f784(f243(x81361),f2(x81361)),x81364))+P85(f784(f784(f243(x81361),x81362),f784(f784(f293(x81361),x81363),x81364)))+~P85(f784(f784(f243(x81361),f784(f784(f90(x81361),x81362),x81364)),x81363))
% 11.41/11.19 [8137]~P61(x81371)+~P85(f784(f784(f243(x81371),f2(x81371)),x81374))+P85(f784(f784(f242(x81371),x81372),f784(f784(f90(x81371),x81373),x81374)))+~P85(f784(f784(f242(x81371),f784(f784(f293(x81371),x81372),x81374)),x81373))
% 11.41/11.19 [8138]~P61(x81381)+~P85(f784(f784(f243(x81381),f2(x81381)),x81384))+P85(f784(f784(f242(x81381),x81382),f784(f784(f293(x81381),x81383),x81384)))+~P85(f784(f784(f242(x81381),f784(f784(f90(x81381),x81382),x81384)),x81383))
% 11.41/11.19 [8139]~P62(x81391)+~P85(f784(f784(f243(x81391),f2(x81391)),x81394))+P85(f784(f784(f242(x81391),x81392),f784(f784(f293(x81391),x81393),x81394)))+~P85(f784(f784(f242(x81391),f784(f784(f90(x81391),x81392),x81394)),x81393))
% 11.41/11.19 [8140]~P62(x81401)+~P85(f784(f784(f243(x81401),f2(x81401)),x81404))+P85(f784(f784(f242(x81401),x81402),f784(f784(f90(x81401),x81403),x81404)))+~P85(f784(f784(f242(x81401),f784(f784(f293(x81401),x81402),x81404)),x81403))
% 11.41/11.19 [8141]~P62(x81411)+~P85(f784(f784(f243(x81411),f2(x81411)),x81414))+P85(f784(f784(f242(x81411),x81412),f784(f784(f293(x81411),x81413),x81414)))+~P85(f784(f784(f242(x81411),f784(f784(f90(x81411),x81412),x81414)),x81413))
% 11.41/11.19 [8296]~P62(x82961)+~P85(f784(f784(f243(x82961),x82963),f2(x82961)))+~P85(f784(f784(f243(x82961),f784(f784(f293(x82961),x82964),x82963)),x82962))+P85(f784(f784(f243(x82961),f784(f784(f90(x82961),x82962),x82963)),x82964))
% 11.41/11.19 [8297]~P62(x82971)+~P85(f784(f784(f243(x82971),x82973),f2(x82971)))+~P85(f784(f784(f243(x82971),f784(f784(f90(x82971),x82974),x82973)),x82972))+P85(f784(f784(f243(x82971),f784(f784(f293(x82971),x82972),x82973)),x82974))
% 11.41/11.19 [8298]~P62(x82981)+~P85(f784(f784(f243(x82981),x82983),f2(x82981)))+~P85(f784(f784(f242(x82981),f784(f784(f293(x82981),x82984),x82983)),x82982))+P85(f784(f784(f242(x82981),f784(f784(f90(x82981),x82982),x82983)),x82984))
% 11.41/11.19 [8299]~P62(x82991)+~P85(f784(f784(f243(x82991),x82993),f2(x82991)))+~P85(f784(f784(f242(x82991),f784(f784(f90(x82991),x82994),x82993)),x82992))+P85(f784(f784(f242(x82991),f784(f784(f293(x82991),x82992),x82993)),x82994))
% 11.41/11.19 [8312]~P85(f784(x83121,x83124))+~P85(f784(f784(f243(a859),x83122),f784(f784(f90(a859),x83123),f784(a160,x83124))))+P85(f784(x83121,f784(f784(f51(a859),x83122),x83123)))+~P85(f784(f784(f242(a859),f784(f784(f90(a859),x83123),x83124)),x83122))
% 11.41/11.19 [8525]~P101(x85251)+~P85(f784(f71(x85251),x85254))+~P85(f784(f784(f347(x85251),x85252),x85254))+P85(f784(f784(f242(x85251),f784(f784(f186(x85251),x85252),x85253)),f784(f784(f74(x85251,x85251,f186(x85251)),x85253),x85254)))
% 11.41/11.19 [8526]~P98(x85261)+~P85(f784(f71(x85261),x85264))+~P85(f784(f784(f347(x85261),x85262),x85264))+P85(f784(f784(f242(x85261),f784(f784(f110(x85261),x85262),x85263)),f784(f784(f74(x85261,x85261,f110(x85261)),x85263),x85264)))
% 11.41/11.19 [8653]~P85(f784(f71(x86531),x86532))+E(f784(f50(x86531),f784(f784(f3(f869(x86531,a852)),x86532),f784(f784(f312(x86531),x86533),x86534))),f784(f784(f3(a859),f784(f50(x86531),f784(f784(f3(f869(x86531,a852)),x86532),x86534))),f87(a859)))+P85(f784(f784(f347(x86531),x86533),x86534))+~P85(f784(f784(f347(x86531),x86533),x86532))
% 11.41/11.19 [8717]E(f784(f784(f89(a1),f361(x87171,x87172,x87173,x87174)),f362(x87171,x87172,x87173,x87174)),x87174)+~P85(f784(f784(f243(a1),f2(a1)),x87173))+~P85(f784(f784(f242(a1),x87174),x87171))+P85(f784(f784(f242(a1),f784(f784(f3(a1),x87174),x87173)),x87171))
% 11.41/11.19 [8718]E(f784(f784(f89(a1),f369(x87181,x87182,x87183,x87184)),f370(x87181,x87182,x87183,x87184)),x87184)+~P85(f784(f784(f243(a1),f2(a1)),x87183))+~P85(f784(f784(f243(a1),x87184),x87181))+P85(f784(f784(f243(a1),f784(f784(f3(a1),x87184),x87183)),x87181))
% 11.41/11.19 [8903]~P85(f784(f784(f243(a1),f2(a1)),x89033))+~P85(f784(f784(f242(a1),x89034),x89031))+P85(f784(f784(f347(a1),f361(x89031,x89032,x89033,x89034)),x89032))+P85(f784(f784(f242(a1),f784(f784(f3(a1),x89034),x89033)),x89031))
% 11.41/11.19 [8904]~P85(f784(f784(f243(a1),f2(a1)),x89043))+~P85(f784(f784(f243(a1),x89044),x89041))+P85(f784(f784(f347(a1),f369(x89041,x89042,x89043,x89044)),x89042))+P85(f784(f784(f243(a1),f784(f784(f3(a1),x89044),x89043)),x89041))
% 11.41/11.19 [8982]~P85(f784(f784(f243(a1),f2(a1)),x89822))+~P85(f784(f784(f243(a1),x89821),x89823))+P85(f784(f784(f347(a1),f370(x89823,x89824,x89822,x89821)),f305(a1,f87(a1),x89822)))+P85(f784(f784(f243(a1),f784(f784(f3(a1),x89821),x89822)),x89823))
% 11.41/11.19 [8983]~P85(f784(f784(f243(a1),f2(a1)),x89832))+~P85(f784(f784(f242(a1),x89831),x89833))+P85(f784(f784(f347(a1),f362(x89833,x89834,x89832,x89831)),f305(a1,f87(a1),x89832)))+P85(f784(f784(f242(a1),f784(f784(f3(a1),x89831),x89832)),x89833))
% 11.41/11.19 [9004]~P85(f784(f784(f243(a1),f2(a1)),x90043))+~P85(f784(f784(f242(a1),f2(a1)),x90044))+~P85(f784(f784(f243(a1),x90044),x90041))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),f784(f784(f90(a1),x90041),f60(a1,x90042,x90043))),x90044)))
% 11.41/11.19 [9064]~P101(x90641)+~P85(f784(f71(x90641),x90644))+~P85(f784(f784(f242(x90641),x90642),f701(x90643,x90642,x90644,x90641)))+P85(f784(f784(f242(x90641),f784(f784(f246(x90641),x90642),x90643)),f784(f784(f74(x90641,x90641,f246(x90641)),x90643),x90644)))
% 11.41/11.19 [9065]~P99(x90651)+~P85(f784(f71(x90651),x90654))+~P85(f784(f784(f242(x90651),x90652),f705(x90653,x90652,x90654,x90651)))+P85(f784(f784(f242(x90651),f784(f784(f111(x90651),x90652),x90653)),f784(f784(f74(x90651,x90651,f111(x90651)),x90653),x90654)))
% 11.41/11.19 [9079]~P85(f784(f784(f242(a1),x90794),f2(a1)))+~P85(f784(f784(f243(a1),f2(a1)),x90792))+~P85(f784(f784(f243(a1),x90791),x90794))+P85(f784(f784(f243(a1),f784(f784(f90(a1),x90791),x90792)),f784(f784(f89(a1),f784(f784(f90(a1),x90791),f60(a1,x90793,x90792))),x90794)))
% 11.41/11.19 [9101]P85(f784(f71(x91011),x91012))+~P85(f784(f71(x91011),x91013))+~P85(f784(f784(f347(f869(x91011,a852)),x91012),f784(f784(f69(x91011),x91013),x91014)))+~P85(f784(f784(f242(f869(f868(x91011,x91011),a852)),x91014),f784(f784(f258(x91011,x91011),x91013),f784(f18(f869(x91011,a852),x91011),x91013))))
% 11.41/11.19 [9123]~P101(x91231)+~P85(f784(f71(x91231),x91234))+P85(f784(f784(f347(x91231),f701(x91232,x91233,x91234,x91231)),x91234))+P85(f784(f784(f242(x91231),f784(f784(f246(x91231),x91233),x91232)),f784(f784(f74(x91231,x91231,f246(x91231)),x91232),x91234)))
% 11.41/11.19 [9124]~P99(x91241)+~P85(f784(f71(x91241),x91244))+P85(f784(f784(f347(x91241),f705(x91242,x91243,x91244,x91241)),x91244))+P85(f784(f784(f242(x91241),f784(f784(f111(x91241),x91243),x91242)),f784(f784(f74(x91241,x91241,f111(x91241)),x91242),x91244)))
% 11.41/11.19 [9496]~P85(f784(f71(x94962),x94964))+~P85(f784(f71(x94961),x94963))+~P85(f784(f784(f242(a859),f784(f50(x94962),x94964)),f784(f50(x94961),x94963)))+P85(f784(f784(f242(f869(x94961,a852)),f784(f313(x94962,x94961,f538(x94963,x94961,x94964,x94962)),x94964)),x94963))
% 11.41/11.19 [9162]~P85(f784(f784(f347(x91621),x91622),x91624))+P85(f784(f784(f347(x91621),x91622),x91623))+~P85(f784(f784(f243(f869(x91621,a852)),x91624),f784(f784(f312(x91621),x91622),x91623)))+P85(f784(f784(f243(f869(x91621,a852)),f784(f784(f3(f869(x91621,a852)),x91624),f784(f784(f312(x91621),x91622),f187(f869(x91621,a852))))),x91623))
% 11.41/11.19 [9313]~P85(f784(f784(f347(x93131),x93132),x93134))+P85(f784(f784(f347(x93131),x93132),x93133))+P85(f784(f784(f243(f869(x93131,a852)),x93134),f784(f784(f312(x93131),x93132),x93133)))+~P85(f784(f784(f243(f869(x93131,a852)),f784(f784(f3(f869(x93131,a852)),x93134),f784(f784(f312(x93131),x93132),f187(f869(x93131,a852))))),x93133))
% 11.41/11.19 [9340]P85(f784(f784(f347(x93401),x93402),x93403))+~P85(f784(f784(f242(f869(x93401,a852)),x93404),x93403))+P85(f784(f784(f243(f869(x93401,a852)),x93404),f784(f784(f312(x93401),x93402),x93403)))+~P85(f784(f784(f243(f869(x93401,a852)),f784(f784(f3(f869(x93401,a852)),x93404),f784(f784(f312(x93401),x93402),f187(f869(x93401,a852))))),x93403))
% 11.41/11.19 [9345]~P85(f784(f784(f347(x93451),x93453),x93452))+~P85(f784(f784(f243(f869(x93451,a852)),x93452),x93454))+P85(f784(f784(f243(f869(x93451,a852)),x93452),f784(f784(f312(x93451),x93453),x93454)))+~P85(f784(f784(f243(f869(x93451,a852)),f784(f784(f3(f869(x93451,a852)),x93452),f784(f784(f312(x93451),x93453),f187(f869(x93451,a852))))),x93454))
% 11.41/11.19 [9357]~P85(f784(f784(f242(f869(x93571,a852)),x93572),x93574))+~P85(f784(f784(f243(f869(x93571,a852)),x93572),x93574))+P85(f784(f784(f243(f869(x93571,a852)),x93572),f784(f784(f312(x93571),x93573),x93574)))+~P85(f784(f784(f243(f869(x93571,a852)),f784(f784(f3(f869(x93571,a852)),x93572),f784(f784(f312(x93571),x93573),f187(f869(x93571,a852))))),x93574))
% 11.41/11.19 [9692]E(f784(f784(f155(x96921),f784(f784(f155(f860(x96921)),f170(x96921,x96922)),x96923)),x96924),f784(f784(f155(x96921),f784(f784(f155(f860(x96921)),x96922),x96924)),x96923))+~P85(f784(f784(f243(a859),x96923),f784(f188(f860(f860(x96921))),f170(x96921,x96922))))+~P15(a859,f784(f162(a859),f784(f784(f146(f860(x96921),a859),f188(f860(x96921))),x96922)))+~P85(f784(f784(f243(a859),x96924),f784(f188(f860(f860(x96921))),f784(f131(f860(x96921),f784(f784(f10(a859,a852,f860(x96921)),f784(f243(a859),x96923)),f188(f860(x96921)))),x96922))))
% 11.41/11.19 [9713]~P85(f784(f784(f347(f868(a859,a859)),x97134),x97131))+~P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),x97134),x97132)),a47))+~P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),x97131),x97133)),a48))+P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),x97131),f784(f784(f312(f868(a859,a859)),x97132),x97133))),a48))
% 11.41/11.19 [9714]~P85(f784(f784(f347(f868(a859,a859)),x97144),x97141))+~P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),x97144),x97142)),a79))+~P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),x97141),x97143)),a80))+P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),x97141),f784(f784(f312(f868(a859,a859)),x97142),x97143))),a80))
% 11.41/11.19 [9726]~P85(f784(f784(f347(f868(a859,a859)),x97264),x97263))+~P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),x97261),x97264)),a47))+~P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),x97262),x97263)),a49))+P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),f784(f784(f312(f868(a859,a859)),x97261),x97262)),x97263)),a49))
% 11.41/11.19 [9727]~P85(f784(f784(f347(f868(a859,a859)),x97274),x97273))+~P85(f784(f784(f347(f868(f868(a859,a859),f868(a859,a859))),f784(f784(f251(f868(a859,a859),f868(a859,a859)),x97271),x97274)),a79))+~P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),x97272),x97273)),a78))+P85(f784(f784(f347(f868(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852))),f784(f784(f251(f869(f868(a859,a859),a852),f869(f868(a859,a859),a852)),f784(f784(f312(f868(a859,a859)),x97271),x97272)),x97273)),a78))
% 11.41/11.19 [5926]~P8(x59264,x59261)+~P85(f784(f784(x59261,x59262),x59265))+P85(f784(f784(x59261,x59262),x59263))+~P85(f784(f784(x59261,x59265),x59263))
% 11.41/11.19 [5193]~P3(x51935)+E(x51931,x51932)+~E(x51933,x51934)+~E(f784(f784(f3(x51935),x51933),x51934),f784(f784(f3(x51935),x51931),x51932))
% 11.41/11.19 [5194]~P3(x51945)+E(x51941,x51942)+~E(x51943,x51944)+~E(f784(f784(f3(x51945),x51943),x51944),f784(f784(f3(x51945),x51941),x51942))
% 11.41/11.19 [6037]~P18(x60375,x60371,x60373)+E(f784(f784(x60371,x60372),f784(x60373,x60374)),f784(x60373,x60374))+~P85(f784(f71(x60375),x60374))+~P85(f784(f784(f347(x60375),x60372),x60374))
% 11.41/11.19 [6231]~P77(x62311)+~E(f784(f784(f3(x62311),x62314),x62315),f784(f784(f3(x62311),x62312),x62313))+~P85(f784(f784(f243(x62311),x62314),x62315))+P85(f784(f784(f243(x62311),x62312),x62313))
% 11.41/11.19 [6232]~P77(x62321)+~E(f784(f784(f3(x62321),x62324),x62325),f784(f784(f3(x62321),x62322),x62323))+~P85(f784(f784(f243(x62321),x62324),x62325))+P85(f784(f784(f243(x62321),x62322),x62323))
% 11.41/11.19 [6233]~P77(x62331)+~E(f784(f784(f3(x62331),x62334),x62335),f784(f784(f3(x62331),x62332),x62333))+~P85(f784(f784(f242(x62331),x62334),x62335))+P85(f784(f784(f242(x62331),x62332),x62333))
% 11.41/11.19 [6234]~P77(x62341)+~E(f784(f784(f3(x62341),x62344),x62345),f784(f784(f3(x62341),x62342),x62343))+~P85(f784(f784(f242(x62341),x62344),x62345))+P85(f784(f784(f242(x62341),x62342),x62343))
% 11.41/11.19 [7231]~E(x72312,f784(f784(f144(x72311),x72314),x72315))+P85(f784(f784(f347(f860(x72311)),x72312),f152(x72311,x72313)))+~P85(f784(f784(f347(f860(x72311)),x72315),f152(x72311,x72313)))+~P85(f784(f784(f347(x72311),x72314),x72313))
% 11.41/11.19 [7664]~E(f784(f188(f860(x76641)),x76643),f784(f188(f860(x76642)),x76644))+~E(f784(f784(f146(f868(x76641,x76642),x76642),f260(x76641,x76642)),x76645),x76644)+~E(f784(f784(f146(f868(x76641,x76642),x76641),f250(x76641,x76642)),x76645),x76643)+E(f784(f784(f173(x76641,x76642),x76643),x76644),x76645)
% 11.41/11.19 [7998]~P100(x79981)+P85(f784(f784(f243(f869(x79981,a852)),f305(x79981,x79982,x79983)),f305(x79981,x79984,x79985)))+~P85(f784(f784(f242(x79981),x79984),x79985))+P85(f784(f784(f242(x79981),x79982),x79983))
% 11.41/11.19 [8089]~P100(x80891)+P85(f784(f784(f242(f869(x80891,a852)),f305(x80891,x80892,x80893)),f305(x80891,x80894,x80895)))+~P85(f784(f784(f242(x80891),x80893),x80895))+~P85(f784(f784(f242(x80891),x80894),x80892))
% 11.41/11.19 [8205]~P101(x82051)+P85(f784(f784(f242(x82051),x82052),x82053))+P85(f784(f784(f242(x82051),x82054),x82053))+~P85(f784(f784(f242(f869(x82051,a852)),f784(f304(x82051,x82053),x82052)),f784(f304(x82051,x82054),x82055)))
% 11.41/11.19 [8206]~P101(x82061)+P85(f784(f784(f242(x82061),x82062),x82063))+P85(f784(f784(f242(x82061),x82062),x82064))+~P85(f784(f784(f242(f869(x82061,a852)),f784(f304(x82061,x82063),x82062)),f784(f304(x82061,x82065),x82064)))
% 11.41/11.19 [8446]~P100(x84461)+~P85(f784(f784(f243(f869(x84461,a852)),f305(x84461,x84464,x84462)),f305(x84461,x84465,x84463)))+P85(f784(f784(f242(x84461),x84462),x84463))+~P85(f784(f784(f242(x84461),x84464),x84462))
% 11.41/11.19 [8447]~P100(x84471)+~P85(f784(f784(f242(f869(x84471,a852)),f305(x84471,x84474,x84472)),f305(x84471,x84475,x84473)))+P85(f784(f784(f242(x84471),x84472),x84473))+~P85(f784(f784(f242(x84471),x84474),x84472))
% 11.41/11.19 [8448]~P100(x84481)+~P85(f784(f784(f243(f869(x84481,a852)),f305(x84481,x84483,x84484)),f305(x84481,x84482,x84485)))+P85(f784(f784(f242(x84481),x84482),x84483))+~P85(f784(f784(f242(x84481),x84483),x84484))
% 11.41/11.19 [8449]~P100(x84491)+~P85(f784(f784(f242(f869(x84491,a852)),f305(x84491,x84493,x84494)),f305(x84491,x84492,x84495)))+P85(f784(f784(f242(x84491),x84492),x84493))+~P85(f784(f784(f242(x84491),x84493),x84494))
% 11.41/11.19 [5925]~P18(x59252,x59255,x59253)+E(x59251,f187(f869(x59252,a852)))+~P85(f784(f71(x59252),x59251))+E(f784(x59253,f784(f784(f312(x59252),x59254),x59251)),f784(f784(x59255,x59254),f784(x59253,x59251)))
% 11.41/11.19 [6722]~E(x67221,x67222)+~E(f784(f784(f111(f869(x67223,a852)),x67224),x67225),f187(f869(x67223,a852)))+~P85(f784(f784(f347(x67223),x67222),x67225))+~P85(f784(f784(f347(x67223),x67221),x67224))
% 11.41/11.19 [6808]~P19(x68082,x68085,x68081)+~P85(f784(f71(x68082),x68084))+E(f784(x68081,f784(f784(f312(x68082),x68083),x68084)),f784(f784(f74(x68082,x68082,x68085),x68083),x68084))+P85(f784(f784(f347(x68082),x68083),x68084))
% 11.41/11.19 [6878]~P68(x68782)+~P85(f784(f71(x68781),x68785))+E(f784(f784(f8(x68781,x68782),x68783),f784(f784(f312(x68781),x68784),x68785)),f784(f784(f89(x68782),f784(x68783,x68784)),f784(f784(f8(x68781,x68782),x68783),x68785)))+P85(f784(f784(f347(x68781),x68784),x68785))
% 11.41/11.19 [6879]~P68(x68792)+~P85(f784(f71(x68791),x68795))+E(f784(f784(f8(x68791,x68792),x68793),f784(f784(f312(x68791),x68794),x68795)),f784(f784(f89(x68792),f784(x68793,x68794)),f784(f784(f8(x68791,x68792),x68793),x68795)))+P85(f784(f784(f347(x68791),x68794),x68795))
% 11.41/11.19 [6880]~P71(x68802)+~P85(f784(f71(x68801),x68805))+E(f784(f784(f11(x68801,x68802),x68803),f784(f784(f312(x68801),x68804),x68805)),f784(f784(f90(x68802),f784(x68803,x68804)),f784(f784(f11(x68801,x68802),x68803),x68805)))+P85(f784(f784(f347(x68801),x68804),x68805))
% 11.41/11.19 [6881]~P71(x68812)+~P85(f784(f71(x68811),x68815))+E(f784(f784(f11(x68811,x68812),x68813),f784(f784(f312(x68811),x68814),x68815)),f784(f784(f90(x68812),f784(x68813,x68814)),f784(f784(f11(x68811,x68812),x68813),x68815)))+P85(f784(f784(f347(x68811),x68814),x68815))
% 11.41/11.19 [7289]~P86(x72891)+~P85(f784(f71(x72894),x72895))+~P85(f784(f784(f347(x72894),x72893),x72895))+P85(f784(f784(f289(x72891),f784(x72892,x72893)),f784(f784(f11(x72894,x72891),x72892),x72895)))
% 11.41/11.19 [7402]~P19(x74022,x74025,x74021)+~P85(f784(f71(x74022),x74024))+E(f784(x74021,f784(f784(f312(x74022),x74023),x74024)),x74023)+~E(f784(f784(f3(f869(x74022,a852)),x74024),f784(f784(f312(x74022),x74023),f187(f869(x74022,a852)))),f187(f869(x74022,a852)))
% 11.41/11.19 [7712]~P85(f784(x77121,x77123))+~P85(f784(f784(f194(x77122),x77123),x77125))+~P85(f784(f784(f194(f37(x77121,x77122)),x77125),x77124))+P85(f784(f784(f194(f37(x77121,x77122)),x77123),x77124))
% 11.41/11.19 [7713]~P85(f784(x77131,x77133))+~P85(f784(f784(f194(x77132),x77133),x77135))+~P85(f784(f784(f194(f37(x77131,x77132)),x77135),x77134))+P85(f784(f784(f194(f37(x77131,x77132)),x77133),x77134))
% 11.41/11.19 [7731]~P86(x77311)+~P85(f784(f784(f289(x77311),x77312),x77314))+~P85(f784(f784(f242(a859),x77313),x77315))+P85(f784(f784(f289(x77311),f784(f784(f252(x77311),x77312),x77313)),f784(f784(f252(x77311),x77314),x77315)))
% 11.41/11.19 [7765]~P4(x77651)+E(f784(f784(f51(x77651),f784(f784(f90(x77651),x77652),x77653)),f784(f784(f90(x77651),x77654),x77655)),f784(f784(f90(x77651),f784(f784(f51(x77651),x77652),x77654)),f784(f784(f51(x77651),x77653),x77655)))+~P85(f784(f784(f289(x77651),x77655),x77653))+~P85(f784(f784(f289(x77651),x77654),x77652))
% 11.41/11.19 [7769]~P80(x77691)+~P85(f784(f784(f243(x77691),x77693),x77695))+~P85(f784(f784(f243(x77691),x77692),x77694))+P85(f784(f784(f243(x77691),f784(f784(f89(x77691),x77692),x77693)),f784(f784(f89(x77691),x77694),x77695)))
% 11.41/11.19 [7770]~P80(x77701)+~P85(f784(f784(f242(x77701),x77702),x77704))+~P85(f784(f784(f243(x77701),x77703),x77705))+P85(f784(f784(f243(x77701),f784(f784(f89(x77701),x77702),x77703)),f784(f784(f89(x77701),x77704),x77705)))
% 11.41/11.19 [7771]~P80(x77711)+~P85(f784(f784(f242(x77711),x77713),x77715))+~P85(f784(f784(f243(x77711),x77712),x77714))+P85(f784(f784(f243(x77711),f784(f784(f89(x77711),x77712),x77713)),f784(f784(f89(x77711),x77714),x77715)))
% 11.41/11.19 [7772]~P78(x77721)+~P85(f784(f784(f242(x77721),x77723),x77725))+~P85(f784(f784(f242(x77721),x77722),x77724))+P85(f784(f784(f242(x77721),f784(f784(f89(x77721),x77722),x77723)),f784(f784(f89(x77721),x77724),x77725)))
% 11.41/11.19 [7773]~P101(x77731)+~P85(f784(f784(f242(x77731),x77733),x77735))+~P85(f784(f784(f242(x77731),x77732),x77734))+P85(f784(f784(f242(x77731),f784(f784(f246(x77731),x77732),x77733)),f784(f784(f246(x77731),x77734),x77735)))
% 11.41/11.19 [7774]~P101(x77741)+~P85(f784(f784(f242(x77741),x77743),x77745))+~P85(f784(f784(f242(x77741),x77742),x77744))+P85(f784(f784(f242(x77741),f784(f784(f186(x77741),x77742),x77743)),f784(f784(f186(x77741),x77744),x77745)))
% 11.41/11.19 [7775]~P98(x77751)+~P85(f784(f784(f242(x77751),x77753),x77755))+~P85(f784(f784(f242(x77751),x77752),x77754))+P85(f784(f784(f242(x77751),f784(f784(f110(x77751),x77752),x77753)),f784(f784(f110(x77751),x77754),x77755)))
% 11.41/11.19 [7776]~P99(x77761)+~P85(f784(f784(f242(x77761),x77763),x77765))+~P85(f784(f784(f242(x77761),x77762),x77764))+P85(f784(f784(f242(x77761),f784(f784(f111(x77761),x77762),x77763)),f784(f784(f111(x77761),x77764),x77765)))
% 11.41/11.19 [7777]~P86(x77771)+~P85(f784(f784(f289(x77771),x77773),x77775))+~P85(f784(f784(f289(x77771),x77772),x77774))+P85(f784(f784(f289(x77771),f784(f784(f90(x77771),x77772),x77773)),f784(f784(f90(x77771),x77774),x77775)))
% 11.41/11.19 [7909]~P111(x79095)+E(x79091,x79092)+E(x79093,x79094)+~E(f784(f784(f89(x79095),f784(f784(f90(x79095),x79093),x79091)),f784(f784(f90(x79095),x79094),x79092)),f784(f784(f89(x79095),f784(f784(f90(x79095),x79093),x79092)),f784(f784(f90(x79095),x79094),x79091)))
% 11.41/11.19 [7910]~P111(x79105)+E(x79101,x79102)+E(x79103,x79104)+~E(f784(f784(f89(x79105),f784(f784(f90(x79105),x79103),x79101)),f784(f784(f90(x79105),x79104),x79102)),f784(f784(f89(x79105),f784(f784(f90(x79105),x79103),x79102)),f784(f784(f90(x79105),x79104),x79101)))
% 11.41/11.19 [8046]P32(x80461,x80462,x80463)+~P31(x80461,x80464,x80465)+~P32(x80461,x80462,f616(x80465,x80464,x80461,x80462))+~P85(f784(f784(f347(f858(x80461)),x80463),x80465))
% 11.41/11.19 [8109]~P101(x81094)+~P85(f784(f132(x81091),x81093))+P85(f784(f784(f347(x81091),x81092),f784(f164(x81091),x81093)))+P85(f784(f132(x81091),f784(f784(f142(x81091,x81094,x81095),x81092),x81093)))
% 11.41/11.19 [8251]~P68(x82511)+E(f784(f784(f89(x82511),f784(f784(f8(a859,x82511),x82512),f784(f304(a859,x82513),x82514))),f784(f784(f8(a859,x82511),x82512),f784(f304(a859,x82514),x82515))),f784(f784(f8(a859,x82511),x82512),f784(f304(a859,x82513),x82515)))+~P85(f784(f784(f242(a859),x82514),x82515))+~P85(f784(f784(f242(a859),x82513),x82514))
% 11.41/11.19 [8252]~P3(x82521)+E(f784(f784(f3(x82521),f784(f784(f8(a859,x82521),x82522),f784(f304(a859,x82523),x82524))),f784(f784(f8(a859,x82521),x82522),f784(f304(a859,x82523),x82525))),f784(f784(f8(a859,x82521),x82522),f784(f304(a859,x82525),x82524)))+~P85(f784(f784(f242(a859),x82525),x82524))+~P85(f784(f784(f242(a859),x82523),x82525))
% 11.41/11.19 [8570]~P60(x85702)+E(x85701,f2(x85702))+E(x85703,f2(x85702))+E(f784(f784(f293(x85702),f784(f784(f89(x85702),f784(f784(f90(x85702),x85704),x85701)),f784(f784(f90(x85702),x85705),x85703))),f784(f784(f90(x85702),x85703),x85701)),f784(f784(f89(x85702),f784(f784(f293(x85702),x85704),x85703)),f784(f784(f293(x85702),x85705),x85701)))
% 11.41/11.19 [8571]~P60(x85712)+E(x85711,f2(x85712))+E(x85713,f2(x85712))+E(f784(f784(f293(x85712),f784(f784(f3(x85712),f784(f784(f90(x85712),x85714),x85711)),f784(f784(f90(x85712),x85715),x85713))),f784(f784(f90(x85712),x85713),x85711)),f784(f784(f3(x85712),f784(f784(f293(x85712),x85714),x85713)),f784(f784(f293(x85712),x85715),x85711)))
% 11.41/11.19 [8580]~E(x85802,f784(x85803,x85801))+E(x85801,f534(x85802,x85803,x85804,x85805))+~P26(x85805,x85804,x85803,f249(f869(x85805,a852)))+~P85(f784(f784(f347(x85804),x85802),f784(f313(x85805,x85804,x85803),f249(f869(x85805,a852)))))
% 11.41/11.19 [8765]~P113(x87651)+~P85(f784(f784(f243(x87651),f784(f84(x87651),x87652)),x87654))+P85(f784(f784(f243(x87651),f784(f784(f90(x87651),f784(f84(x87651),x87652)),f784(f84(x87651),x87653))),f784(f784(f90(x87651),x87654),x87655)))+~P85(f784(f784(f243(x87651),f784(f84(x87651),x87653)),x87655))
% 11.41/11.19 [8779]~P31(x87791,x87795,x87794)+P32(x87791,x87792,x87793)+P85(f784(f784(f347(f858(x87791)),f616(x87794,x87795,x87791,x87792)),x87795))+~P85(f784(f784(f347(f858(x87791)),x87793),x87794))
% 11.41/11.19 [8861]~P26(x88611,x88613,x88615,x88612)+~P85(f784(f71(x88613),x88614))+P85(f784(f784(f242(a859),f784(f50(x88611),x88612)),f784(f50(x88613),x88614)))+~P85(f784(f784(f242(f869(x88613,a852)),f784(f313(x88611,x88613,x88615),x88612)),x88614))
% 11.41/11.19 [8930]~P68(x89302)+~P26(x89301,x89301,x89304,x89305)+~P85(f784(f71(x89301),x89305))+E(f784(f784(f8(x89301,x89302),f784(f82(x89301,x89302,x89301,x89303),x89304)),x89305),f784(f784(f8(x89301,x89302),x89303),f784(f313(x89301,x89301,x89304),x89305)))
% 11.41/11.19 [8931]~P71(x89312)+~P26(x89311,x89311,x89314,x89315)+~P85(f784(f71(x89311),x89315))+E(f784(f784(f11(x89311,x89312),f784(f82(x89311,x89312,x89311,x89313),x89314)),x89315),f784(f784(f11(x89311,x89312),x89313),f784(f313(x89311,x89311,x89314),x89315)))
% 11.41/11.19 [9011]~E(f535(x90112,x90114,x90111,x90113,x90115),x90115)+~E(x90112,f784(x90114,x90115))+~P26(x90113,x90111,x90114,f249(f869(x90113,a852)))+P85(f784(f784(f347(x90111),x90112),f784(f313(x90113,x90111,x90114),f249(f869(x90113,a852)))))
% 11.41/11.19 [9043]~P35(x90431,x90432)+~P85(f784(f784(f347(x90431),x90433),x90434))+~P85(f784(f784(f347(x90431),x90435),x90434))+~P85(f784(f784(f347(f868(x90431,x90431)),f784(f784(f251(x90431,x90431),x90435),f697(x90432,x90431,x90434))),x90432))
% 11.41/11.19 [9078]~P26(x90782,x90783,x90785,x90781)+E(x90781,f187(f869(x90782,a852)))+E(f784(f313(x90783,x90782,f536(x90784,x90783,x90782,x90781)),x90784),x90781)+~P85(f784(f784(f242(f869(x90783,a852)),f784(f313(x90782,x90783,x90785),x90781)),x90784))
% 11.41/11.19 [9116]~E(x91162,f784(x91161,x91165))+~P26(x91164,x91163,x91161,f249(f869(x91164,a852)))+E(f784(x91161,f535(x91162,x91161,x91163,x91164,x91165)),x91162)+P85(f784(f784(f347(x91163),x91162),f784(f313(x91164,x91163,x91161),f249(f869(x91164,a852)))))
% 11.41/11.19 [9519]~P101(x95195)+~P6(x95195)+P85(f784(f784(f347(x95191),f403(x95192,x95193,x95191,x95194,x95195)),x95193))+~P85(f784(f784(f243(x95195),x95194),f784(f784(f54(x95191,x95195),x95193),x95192)))
% 11.41/11.19 [9524]~P101(x95241)+~P6(x95241)+P85(f784(f784(f243(x95241),x95242),f784(x95243,f403(x95243,x95244,x95245,x95242,x95241))))+~P85(f784(f784(f243(x95241),x95242),f784(f784(f54(x95245,x95241),x95244),x95243)))
% 11.41/11.19 [9599]~P65(x95991)+~P85(f784(f76(x95991,x95991,f90(x95991),x95992,x95993),x95995))+P85(f784(f784(f347(x95991),x95992),x95993))+P85(f784(f76(x95991,x95991,f90(x95991),x95994,f784(f784(f312(x95991),x95992),x95993)),f784(f784(f90(x95991),x95994),x95995)))
% 11.41/11.19 [9809]~P68(x98092)+~P85(f784(f71(x98091),x98095))+E(f784(f784(f8(x98091,x98092),f784(f784(f9(x98091,x98092,x98092),f784(f784(f20(x98091,x98092,f869(x98092,x98092)),f784(f784(f10(a852,f869(x98092,f869(x98092,x98092)),x98091),f105(x98092)),f784(a343,x98093))),x98094)),f2(x98092))),x98095),f2(x98092))+P85(f784(f784(f347(x98091),x98093),x98095))
% 11.41/11.19 [9810]~P71(x98102)+~P85(f784(f71(x98101),x98105))+E(f784(f784(f11(x98101,x98102),f784(f784(f9(x98101,x98102,x98102),f784(f784(f20(x98101,x98102,f869(x98102,x98102)),f784(f784(f10(a852,f869(x98102,f869(x98102,x98102)),x98101),f105(x98102)),f784(a343,x98103))),x98104)),f87(x98102))),x98105),f87(x98102))+P85(f784(f784(f347(x98101),x98103),x98105))
% 11.41/11.19 [9811]~P68(x98112)+~P85(f784(f71(x98111),x98115))+E(f784(f784(f8(x98111,x98112),f784(f784(f9(x98111,x98112,x98112),f784(f784(f20(x98111,x98112,f869(x98112,x98112)),f784(f784(f10(a852,f869(x98112,f869(x98112,x98112)),x98111),f105(x98112)),f784(a343,x98113))),x98114)),f2(x98112))),x98115),f784(x98114,x98113))+~P85(f784(f784(f347(x98111),x98113),x98115))
% 11.41/11.19 [9812]~P71(x98122)+~P85(f784(f71(x98121),x98125))+E(f784(f784(f11(x98121,x98122),f784(f784(f9(x98121,x98122,x98122),f784(f784(f20(x98121,x98122,f869(x98122,x98122)),f784(f784(f10(a852,f869(x98122,f869(x98122,x98122)),x98121),f105(x98122)),f784(a343,x98123))),x98124)),f87(x98122))),x98125),f784(x98124,x98123))+~P85(f784(f784(f347(x98121),x98123),x98125))
% 11.41/11.19 [9877]~P68(x98772)+~P85(f784(f71(x98771),x98775))+E(f784(f784(f8(x98771,x98772),f784(f784(f9(x98771,x98772,x98772),f784(f784(f20(x98771,x98772,f869(x98772,x98772)),f784(f784(f10(a852,f869(x98772,f869(x98772,x98772)),x98771),f105(x98772)),f784(f784(f9(x98771,x98771,a852),a343),x98773))),x98774)),f2(x98772))),x98775),f2(x98772))+P85(f784(f784(f347(x98771),x98773),x98775))
% 11.41/11.19 [9878]~P71(x98782)+~P85(f784(f71(x98781),x98785))+E(f784(f784(f11(x98781,x98782),f784(f784(f9(x98781,x98782,x98782),f784(f784(f20(x98781,x98782,f869(x98782,x98782)),f784(f784(f10(a852,f869(x98782,f869(x98782,x98782)),x98781),f105(x98782)),f784(f784(f9(x98781,x98781,a852),a343),x98783))),x98784)),f87(x98782))),x98785),f87(x98782))+P85(f784(f784(f347(x98781),x98783),x98785))
% 11.41/11.19 [9880]~P68(x98802)+~P85(f784(f71(x98801),x98805))+E(f784(f784(f8(x98801,x98802),f784(f784(f9(x98801,x98802,x98802),f784(f784(f20(x98801,x98802,f869(x98802,x98802)),f784(f784(f10(a852,f869(x98802,f869(x98802,x98802)),x98801),f105(x98802)),f784(f784(f9(x98801,x98801,a852),a343),x98803))),x98804)),f2(x98802))),x98805),f784(x98804,x98803))+~P85(f784(f784(f347(x98801),x98803),x98805))
% 11.41/11.19 [9881]~P71(x98812)+~P85(f784(f71(x98811),x98815))+E(f784(f784(f11(x98811,x98812),f784(f784(f9(x98811,x98812,x98812),f784(f784(f20(x98811,x98812,f869(x98812,x98812)),f784(f784(f10(a852,f869(x98812,f869(x98812,x98812)),x98811),f105(x98812)),f784(f784(f9(x98811,x98811,a852),a343),x98813))),x98814)),f87(x98812))),x98815),f784(x98814,x98813))+~P85(f784(f784(f347(x98811),x98813),x98815))
% 11.41/11.19 [7768]~P3(x77682)+~P85(f784(f71(x77681),x77684))+E(f784(f784(f8(x77681,x77682),x77683),f784(f784(f3(f869(x77681,a852)),x77684),f784(f784(f312(x77681),x77685),f187(f869(x77681,a852))))),f784(f784(f8(x77681,x77682),x77683),x77684))+P85(f784(f784(f347(x77681),x77685),x77684))
% 11.41/11.19 [8258]~P123(x82582)+~P85(f784(f71(x82581),x82584))+E(f784(f784(f8(x82581,x82582),x82583),f784(f784(f3(f869(x82581,a852)),x82584),f784(f784(f312(x82581),x82585),f187(f869(x82581,a852))))),f784(f784(f3(x82582),f784(f784(f8(x82581,x82582),x82583),x82584)),f784(x82583,x82585)))+~P85(f784(f784(f347(x82581),x82585),x82584))
% 11.41/11.19 [8259]~P3(x82592)+~P85(f784(f71(x82591),x82594))+E(f784(f784(f8(x82591,x82592),x82593),f784(f784(f3(f869(x82591,a852)),x82594),f784(f784(f312(x82591),x82595),f187(f869(x82591,a852))))),f784(f784(f3(x82592),f784(f784(f8(x82591,x82592),x82593),x82594)),f784(x82593,x82595)))+~P85(f784(f784(f347(x82591),x82595),x82594))
% 11.41/11.19 [8270]~P86(x82701)+~P85(f784(f784(f242(a859),x82703),x82705))+~P85(f784(f784(f289(x82701),f784(f784(f252(x82701),x82702),x82705)),x82704))+P85(f784(f784(f289(x82701),f784(f784(f252(x82701),x82702),x82703)),x82704))
% 11.41/11.19 [8287]~P3(x82871)+~P85(f784(f71(x82872),x82874))+E(f784(f784(f3(x82871),f784(f784(f8(x82872,x82871),x82873),x82874)),f784(f784(f8(x82872,x82871),x82873),x82875)),f784(f784(f8(x82872,x82871),x82873),f784(f784(f3(f869(x82872,a852)),x82874),x82875)))+~P85(f784(f784(f242(f869(x82872,a852)),x82875),x82874))
% 11.41/11.19 [8308]P85(f784(f71(x83081),f784(x83082,x83083)))+~P85(f784(f71(x83084),x83085))+~P85(f784(f784(f347(x83084),x83083),x83085))+~P85(f784(f71(x83081),f784(f784(f54(x83084,f869(x83081,a852)),x83085),x83082)))
% 11.41/11.19 [8730]~P9(x87301,x87305,x87304)+~E(f784(f287(x87301,x87301,x87304),f784(f784(f312(x87301),x87302),f187(f869(x87301,a852)))),f784(f287(x87301,x87301,x87304),f784(f784(f312(x87301),x87303),f187(f869(x87301,a852)))))+~P85(f784(f784(f347(x87301),x87303),x87305))+P85(f784(f784(f347(f868(x87301,x87301)),f784(f784(f251(x87301,x87301),x87302),x87303)),x87304))
% 11.41/11.19 [9002]~P85(f784(x90021,x90025))+P85(f784(x90021,f398(x90021,x90022,x90023,x90024)))+P85(f784(x90021,f395(x90021,x90022,x90023,x90024)))+~P85(f784(f784(f347(x90024),x90025),f784(f784(f110(f869(x90024,a852)),x90023),x90022)))
% 11.41/11.19 [9165]~P85(f784(x91651,x91655))+P85(f784(x91651,f395(x91651,x91652,x91653,x91654)))+P85(f784(f784(f347(x91654),f398(x91651,x91652,x91653,x91654)),x91652))+~P85(f784(f784(f347(x91654),x91655),f784(f784(f110(f869(x91654,a852)),x91653),x91652)))
% 11.41/11.19 [9166]~P85(f784(x91661,x91665))+P85(f784(x91661,f398(x91661,x91662,x91663,x91664)))+P85(f784(f784(f347(x91664),f395(x91661,x91662,x91663,x91664)),x91663))+~P85(f784(f784(f347(x91664),x91665),f784(f784(f110(f869(x91664,a852)),x91663),x91662)))
% 11.41/11.19 [9170]P85(f784(x91701,x91702))+~P85(f784(x91701,f397(x91701,x91703,x91704,x91705)))+~P85(f784(x91701,f396(x91701,x91703,x91704,x91705)))+~P85(f784(f784(f347(x91705),x91702),f784(f784(f110(f869(x91705,a852)),x91704),x91703)))
% 11.41/11.19 [9202]E(x92021,x92022)+~P85(f784(f784(f347(f868(x92023,x92023)),f784(f784(f251(x92023,x92023),x92021),x92022)),f310(x92023,x92025)))+P85(f784(f784(f347(x92023),x92021),x92024))+~P85(f784(f784(f242(f869(f868(x92023,x92023),a852)),x92025),f784(f784(f258(x92023,x92023),x92024),f784(f18(f869(x92023,a852),x92023),x92024))))
% 11.41/11.19 [9219]P85(f784(x92191,x92192))+~P85(f784(x92191,f396(x92191,x92194,x92195,x92193)))+P85(f784(f784(f347(x92193),f397(x92191,x92194,x92195,x92193)),x92194))+~P85(f784(f784(f347(x92193),x92192),f784(f784(f110(f869(x92193,a852)),x92195),x92194)))
% 11.41/11.19 [9220]P85(f784(x92201,x92202))+~P85(f784(x92201,f397(x92201,x92204,x92205,x92203)))+P85(f784(f784(f347(x92203),f396(x92201,x92204,x92205,x92203)),x92205))+~P85(f784(f784(f347(x92203),x92202),f784(f784(f110(f869(x92203,a852)),x92205),x92204)))
% 11.41/11.19 [9282]P85(f784(x92821,x92822))+P85(f784(f784(f347(x92823),f397(x92821,x92824,x92825,x92823)),x92824))+P85(f784(f784(f347(x92823),f396(x92821,x92824,x92825,x92823)),x92825))+~P85(f784(f784(f347(x92823),x92822),f784(f784(f110(f869(x92823,a852)),x92825),x92824)))
% 11.41/11.19 [9284]~P85(f784(x92842,x92845))+P85(f784(f784(f347(x92841),f398(x92842,x92843,x92844,x92841)),x92843))+P85(f784(f784(f347(x92841),f395(x92842,x92843,x92844,x92841)),x92844))+~P85(f784(f784(f347(x92841),x92845),f784(f784(f110(f869(x92841,a852)),x92844),x92843)))
% 11.41/11.19 [9429]~P9(x94291,x94295,x94294)+~P85(f784(f784(f347(x94291),x94293),x94295))+P85(f784(f784(f347(f868(x94291,x94291)),f784(f784(f251(x94291,x94291),x94292),x94293)),x94294))+~P85(f784(f784(f242(f869(x94291,a852)),f784(f287(x94291,x94291,x94294),f784(f784(f312(x94291),x94293),f187(f869(x94291,a852))))),f784(f287(x94291,x94291,x94294),f784(f784(f312(x94291),x94292),f187(f869(x94291,a852))))))
% 11.41/11.19 [9549]~P101(x95495)+~P6(x95495)+P85(f784(f784(f347(x95491),f679(x95492,x95493,x95494,x95491,x95495)),x95494))+~P85(f784(f784(f243(x95495),f784(f784(f55(x95491,x95495),x95494),x95493)),x95492))
% 11.41/11.19 [9583]~P67(x95835)+~P78(x95835)+P85(f784(f784(f347(x95831),f765(x95832,x95833,x95834,x95831,x95835)),f784(f164(x95831),x95834)))+P85(f784(f784(f242(x95835),f784(f157(x95835),f784(f784(f146(x95831,x95835),x95833),x95834))),f784(f157(x95835),f784(f784(f146(x95831,x95835),x95832),x95834))))
% 11.41/11.19 [9682]~P101(x96821)+~P6(x96821)+P85(f784(f784(f243(x96821),f784(x96822,f679(x96823,x96822,x96824,x96825,x96821))),x96823))+~P85(f784(f784(f243(x96821),f784(f784(f55(x96825,x96821),x96824),x96822)),x96823))
% 11.41/11.19 [9826]~P67(x98261)+~P78(x98261)+~P85(f784(f784(f242(x98261),f784(x98263,f765(x98265,x98263,x98264,x98262,x98261))),f784(x98265,f765(x98265,x98263,x98264,x98262,x98261))))+P85(f784(f784(f242(x98261),f784(f157(x98261),f784(f784(f146(x98262,x98261),x98263),x98264))),f784(f157(x98261),f784(f784(f146(x98262,x98261),x98265),x98264))))
% 11.41/11.19 [8588]~P68(x85881)+~P85(f784(f71(x85884),x85885))+~P85(f784(f784(f347(x85884),x85883),x85885))+E(f784(f784(f89(x85881),f784(x85882,x85883)),f784(f784(f8(x85884,x85881),x85882),f784(f784(f3(f869(x85884,a852)),x85885),f784(f784(f312(x85884),x85883),f187(f869(x85884,a852)))))),f784(f784(f8(x85884,x85881),x85882),x85885))
% 11.41/11.19 [8589]~P68(x85891)+~P85(f784(f71(x85894),x85895))+~P85(f784(f784(f347(x85894),x85893),x85895))+E(f784(f784(f89(x85891),f784(x85892,x85893)),f784(f784(f8(x85894,x85891),x85892),f784(f784(f3(f869(x85894,a852)),x85895),f784(f784(f312(x85894),x85893),f187(f869(x85894,a852)))))),f784(f784(f8(x85894,x85891),x85892),x85895))
% 11.41/11.19 [8590]~P71(x85901)+~P85(f784(f71(x85904),x85905))+~P85(f784(f784(f347(x85904),x85903),x85905))+E(f784(f784(f90(x85901),f784(x85902,x85903)),f784(f784(f11(x85904,x85901),x85902),f784(f784(f3(f869(x85904,a852)),x85905),f784(f784(f312(x85904),x85903),f187(f869(x85904,a852)))))),f784(f784(f11(x85904,x85901),x85902),x85905))
% 11.41/11.19 [8643]~P19(x86431,x86434,x86435)+~P85(f784(f71(x86431),x86432))+E(f784(f784(f3(f869(x86431,a852)),x86432),f784(f784(f312(x86431),x86433),f187(f869(x86431,a852)))),f187(f869(x86431,a852)))+E(f784(f784(x86434,x86433),f784(x86435,f784(f784(f3(f869(x86431,a852)),x86432),f784(f784(f312(x86431),x86433),f187(f869(x86431,a852)))))),f784(x86435,f784(f784(f312(x86431),x86433),x86432)))
% 11.41/11.19 [8977]~P68(x89771)+~P85(f784(f71(x89772),x89775))+~P85(f784(f71(x89772),x89774))+E(f784(f784(f89(x89771),f784(f784(f8(x89772,x89771),x89773),f784(f784(f110(f869(x89772,a852)),x89774),x89775))),f784(f784(f8(x89772,x89771),x89773),f784(f784(f111(f869(x89772,a852)),x89774),x89775))),f784(f784(f89(x89771),f784(f784(f8(x89772,x89771),x89773),x89774)),f784(f784(f8(x89772,x89771),x89773),x89775)))
% 11.41/11.19 [8978]~P71(x89781)+~P85(f784(f71(x89782),x89785))+~P85(f784(f71(x89782),x89784))+E(f784(f784(f90(x89781),f784(f784(f11(x89782,x89781),x89783),f784(f784(f110(f869(x89782,a852)),x89784),x89785))),f784(f784(f11(x89782,x89781),x89783),f784(f784(f111(f869(x89782,a852)),x89784),x89785))),f784(f784(f90(x89781),f784(f784(f11(x89782,x89781),x89783),x89784)),f784(f784(f11(x89782,x89781),x89783),x89785)))
% 11.41/11.19 [8979]~P71(x89791)+~P85(f784(f71(x89792),x89795))+~P85(f784(f71(x89792),x89794))+E(f784(f784(f90(x89791),f784(f784(f11(x89792,x89791),x89793),f784(f784(f110(f869(x89792,a852)),x89794),x89795))),f784(f784(f11(x89792,x89791),x89793),f784(f784(f111(f869(x89792,a852)),x89794),x89795))),f784(f784(f90(x89791),f784(f784(f11(x89792,x89791),x89793),x89794)),f784(f784(f11(x89792,x89791),x89793),x89795)))
% 11.41/11.19 [9115]~P3(x91151)+~P85(f784(f71(x91152),x91155))+~P85(f784(f71(x91152),x91154))+E(f784(f784(f3(x91151),f784(f784(f89(x91151),f784(f784(f8(x91152,x91151),x91153),x91154)),f784(f784(f8(x91152,x91151),x91153),x91155))),f784(f784(f8(x91152,x91151),x91153),f784(f784(f111(f869(x91152,a852)),x91154),x91155))),f784(f784(f8(x91152,x91151),x91153),f784(f784(f110(f869(x91152,a852)),x91154),x91155)))
% 11.41/11.19 [9296]~P26(x92961,x92962,x92963,x92965)+~P26(x92961,x92962,x92963,x92964)+P26(x92961,x92962,x92963,f784(f784(f110(f869(x92961,a852)),x92964),x92965))+~E(f784(f784(f111(f869(x92962,a852)),f784(f313(x92961,x92962,x92963),f784(f784(f3(f869(x92961,a852)),x92964),x92965))),f784(f313(x92961,x92962,x92963),f784(f784(f3(f869(x92961,a852)),x92965),x92964))),f187(f869(x92962,a852)))
% 11.41/11.19 [9402]E(x94021,f2(a1))+~P85(f784(f784(f243(a1),f2(a1)),x94023))+~P85(f784(f64(x94022,x94021),f784(f784(f251(a1,a1),x94024),x94025)))+P85(f784(f64(x94022,f784(f784(f90(a1),x94021),x94023)),f784(f784(f251(a1,a1),f784(f784(f51(a1),x94024),x94023)),f784(f784(f89(a1),f784(f784(f90(a1),x94021),f60(a1,x94024,x94023))),x94025))))
% 11.41/11.19 [9411]~P85(f784(f784(f243(a859),f2(a859)),x94113))+~P85(f784(f784(f243(a859),f2(a859)),x94112))+~P85(f784(f63(x94111,x94112),f784(f784(f251(a859,a859),x94114),x94115)))+P85(f784(f63(x94111,f784(f784(f90(a859),x94112),x94113)),f784(f784(f251(a859,a859),f784(f784(f51(a859),x94114),x94113)),f784(f784(f89(a859),f784(f784(f90(a859),x94112),f60(a859,x94114,x94113))),x94115))))
% 11.41/11.19 [9461]E(f784(f784(f89(a1),f371(x94611,x94612,x94613,x94614,x94615)),f372(x94611,x94612,x94613,x94614,x94615)),x94615)+~P85(f784(f784(f289(a1),x94614),x94613))+~P85(f784(f784(f289(a1),x94614),f784(f784(f89(a1),x94615),x94611)))+P85(f784(f784(f289(a1),x94614),f784(f784(f89(a1),f784(f784(f3(a1),x94615),x94613)),x94611)))
% 11.41/11.19 [9462]E(f784(f784(f3(a1),f377(x94621,x94622,x94623,x94624,x94625)),f373(x94621,x94622,x94623,x94624,x94625)),x94625)+~P85(f784(f784(f289(a1),x94624),x94623))+~P85(f784(f784(f289(a1),x94624),f784(f784(f89(a1),x94625),x94621)))+P85(f784(f784(f289(a1),x94624),f784(f784(f89(a1),f784(f784(f89(a1),x94625),x94623)),x94621)))
% 11.41/11.19 [9463]~P71(x94631)+~P85(f784(f71(x94632),x94635))+~P85(f784(f71(x94632),x94634))+E(f784(f784(f90(x94631),f784(f784(f784(f75(x94631,x94632,f90(x94631)),x94633),f87(x94631)),f784(f784(f110(f869(x94632,a852)),x94634),x94635))),f784(f784(f784(f75(x94631,x94632,f90(x94631)),x94633),f87(x94631)),f784(f784(f111(f869(x94632,a852)),x94634),x94635))),f784(f784(f90(x94631),f784(f784(f784(f75(x94631,x94632,f90(x94631)),x94633),f87(x94631)),x94634)),f784(f784(f784(f75(x94631,x94632,f90(x94631)),x94633),f87(x94631)),x94635)))
% 11.41/11.19 [9465]~E(f784(f784(f165(x94651),x94655),x94652),f784(f784(f165(x94651),x94655),x94653))+P85(f784(f784(f347(f868(f860(x94651),f860(x94651))),f784(f784(f251(f860(x94651),f860(x94651)),x94652),x94653)),f141(x94651,x94654)))+~P85(f784(f784(f243(a859),x94655),f784(f784(f246(a859),f784(f188(f860(x94651)),x94652)),f784(f188(f860(x94651)),x94653))))+~P85(f784(f784(f347(f868(x94651,x94651)),f784(f784(f251(x94651,x94651),f784(f784(f155(x94651),x94652),x94655)),f784(f784(f155(x94651),x94653),x94655))),x94654))
% 11.41/11.19 [9474]E(f784(f784(f89(a1),f378(x94741,x94742,x94743,x94744,x94745)),f379(x94741,x94742,x94743,x94744,x94745)),x94745)+~P85(f784(f784(f289(a1),x94744),x94743))+P85(f784(f784(f289(a1),x94744),f784(f784(f89(a1),x94745),x94741)))+~P85(f784(f784(f289(a1),x94744),f784(f784(f89(a1),f784(f784(f3(a1),x94745),x94743)),x94741)))
% 11.41/11.19 [9475]E(f784(f784(f3(a1),f380(x94751,x94752,x94753,x94754,x94755)),f381(x94751,x94752,x94753,x94754,x94755)),x94755)+~P85(f784(f784(f289(a1),x94754),x94753))+P85(f784(f784(f289(a1),x94754),f784(f784(f89(a1),x94755),x94751)))+~P85(f784(f784(f289(a1),x94754),f784(f784(f89(a1),f784(f784(f89(a1),x94755),x94753)),x94751)))
% 11.41/11.19 [9558]~P85(f784(f784(f289(a1),x95584),x95583))+P85(f784(f784(f347(a1),f371(x95581,x95582,x95583,x95584,x95585)),x95582))+~P85(f784(f784(f289(a1),x95584),f784(f784(f89(a1),x95585),x95581)))+P85(f784(f784(f289(a1),x95584),f784(f784(f89(a1),f784(f784(f3(a1),x95585),x95583)),x95581)))
% 11.41/11.19 [9559]~P85(f784(f784(f289(a1),x95594),x95593))+P85(f784(f784(f347(a1),f377(x95591,x95592,x95593,x95594,x95595)),x95592))+~P85(f784(f784(f289(a1),x95594),f784(f784(f89(a1),x95595),x95591)))+P85(f784(f784(f289(a1),x95594),f784(f784(f89(a1),f784(f784(f89(a1),x95595),x95593)),x95591)))
% 11.41/11.19 [9567]~P85(f784(f784(f289(a1),x95674),x95673))+P85(f784(f784(f347(a1),f372(x95671,x95672,x95673,x95674,x95675)),f305(a1,f87(a1),x95673)))+~P85(f784(f784(f289(a1),x95674),f784(f784(f89(a1),x95675),x95671)))+P85(f784(f784(f289(a1),x95674),f784(f784(f89(a1),f784(f784(f3(a1),x95675),x95673)),x95671)))
% 11.41/11.19 [9568]~P85(f784(f784(f289(a1),x95684),x95683))+P85(f784(f784(f347(a1),f373(x95681,x95682,x95683,x95684,x95685)),f305(a1,f87(a1),x95683)))+~P85(f784(f784(f289(a1),x95684),f784(f784(f89(a1),x95685),x95681)))+P85(f784(f784(f289(a1),x95684),f784(f784(f89(a1),f784(f784(f89(a1),x95685),x95683)),x95681)))
% 11.41/11.19 [9569]~P112(x95695)+~P78(x95695)+P85(f784(f784(f347(x95691),f450(x95692,x95693,x95694,x95691,x95695)),x95694))+P85(f784(f784(f242(x95695),f784(f784(f8(x95691,x95695),x95693),x95694)),f784(f784(f90(x95695),f784(f109(x95695),f784(f50(x95691),x95694))),x95692)))
% 11.41/11.19 [9570]~P85(f784(f784(f289(a1),x95704),x95703))+P85(f784(f784(f347(a1),f378(x95701,x95702,x95703,x95704,x95705)),x95702))+P85(f784(f784(f289(a1),x95704),f784(f784(f89(a1),x95705),x95701)))+~P85(f784(f784(f289(a1),x95704),f784(f784(f89(a1),f784(f784(f3(a1),x95705),x95703)),x95701)))
% 11.41/11.19 [9571]~P85(f784(f784(f289(a1),x95714),x95713))+P85(f784(f784(f347(a1),f380(x95711,x95712,x95713,x95714,x95715)),x95712))+P85(f784(f784(f289(a1),x95714),f784(f784(f89(a1),x95715),x95711)))+~P85(f784(f784(f289(a1),x95714),f784(f784(f89(a1),f784(f784(f89(a1),x95715),x95713)),x95711)))
% 11.41/11.19 [9573]~P85(f784(f784(f289(a1),x95731),x95735))+P85(f784(f784(f347(a1),f379(x95733,x95734,x95735,x95731,x95732)),f305(a1,f87(a1),x95735)))+P85(f784(f784(f289(a1),x95731),f784(f784(f89(a1),x95732),x95733)))+~P85(f784(f784(f289(a1),x95731),f784(f784(f89(a1),f784(f784(f3(a1),x95732),x95735)),x95733)))
% 11.41/11.19 [9574]~P85(f784(f784(f289(a1),x95741),x95745))+P85(f784(f784(f347(a1),f381(x95743,x95744,x95745,x95741,x95742)),f305(a1,f87(a1),x95745)))+P85(f784(f784(f289(a1),x95741),f784(f784(f89(a1),x95742),x95743)))+~P85(f784(f784(f289(a1),x95741),f784(f784(f89(a1),f784(f784(f89(a1),x95742),x95745)),x95743)))
% 11.41/11.19 [9742]~P112(x97421)+~P78(x97421)+~P85(f784(f784(f242(x97421),f784(x97423,f450(x97425,x97423,x97424,x97422,x97421))),x97425))+P85(f784(f784(f242(x97421),f784(f784(f8(x97422,x97421),x97423),x97424)),f784(f784(f90(x97421),f784(f109(x97421),f784(f50(x97422),x97424))),x97425)))
% 11.41/11.19 [8615]E(f784(f784(f130(x86151),x86152),x86153),f784(f784(f130(x86151),x86154),x86155))+~E(f784(f784(f165(x86151),f784(f188(f860(x86151)),x86152)),x86154),x86152)+~E(f784(f784(f130(x86151),f784(f784(f133(x86151),f784(f188(f860(x86151)),x86152)),x86154)),x86155),x86153)+P85(f784(f784(f242(a859),f784(f188(f860(x86151)),x86154)),f784(f188(f860(x86151)),x86152)))
% 11.41/11.19 [8728]E(f784(f784(f130(x87281),x87282),x87283),f784(f784(f130(x87281),x87284),x87285))+~E(f784(f784(f165(x87281),f784(f188(f860(x87281)),x87282)),x87284),x87282)+~E(x87283,f784(f784(f130(x87281),f784(f784(f133(x87281),f784(f188(f860(x87281)),x87282)),x87284)),x87285))+~P85(f784(f784(f242(a859),f784(f188(f860(x87281)),x87282)),f784(f188(f860(x87281)),x87284)))
% 11.41/11.19 [9896]~P85(f784(x98965,x98964))+~P85(f784(f71(x98962),f784(f266(x98962),x98965)))+P85(f784(f71(x98961),f784(f266(x98961),f784(f784(f9(x98961,x98962,a852),x98963),x98964))))+~P85(f784(f71(x98961),f784(f266(x98961),f784(f784(f10(f869(x98962,a852),a852,x98961),f96(x98962)),f784(f784(f10(f869(x98962,a852),f869(x98962,a852),x98961),f784(f20(x98962,a852,a852),f784(f784(f10(a852,f869(a852,a852),x98962),a344),x98965))),x98963)))))
% 11.41/11.19 [7913]~P38(x79132,x79133,x79134,x79136)+~P38(f37(x79131,x79132),x79136,x79134,x79135)+P38(f37(x79131,x79132),x79133,x79134,x79135)+~P85(f784(x79131,x79133))
% 11.41/11.19 [7914]~P38(x79142,x79143,x79144,x79146)+~P38(f37(x79141,x79142),x79146,x79144,x79145)+P38(f37(x79141,x79142),x79143,x79144,x79145)+~P85(f784(x79141,x79143))
% 11.41/11.19 [8422]~P20(x84225,x84221,x84226,x84222)+E(f784(f82(x84221,x84221,x84221,f784(x84222,x84223)),f784(x84222,x84224)),f784(f82(x84221,x84221,x84221,f784(x84222,x84224)),f784(x84222,x84223)))+~P85(f784(f71(x84225),x84224))+~P85(f784(f71(x84225),x84223))
% 11.41/11.19 [7824]~P26(x78241,x78242,x78244,x78243)+~E(f784(x78244,x78246),x78245)+E(f784(f86(x78241,x78242,x78243,x78244),x78245),x78246)+~P85(f784(f784(f347(x78241),x78246),x78243))
% 11.41/11.19 [8016]~P21(x80166,x80161,x80164,x80162)+E(f784(f82(x80161,x80161,x80161,f784(x80162,x80163)),f784(x80164,x80165)),f784(x80162,x80163))+~P85(f784(f71(x80166),x80163))+~P85(f784(f784(f347(x80166),x80165),x80163))
% 11.41/11.19 [9154]~P20(x91543,x91541,x91546,x91542)+E(f784(f82(x91541,x91541,x91541,f784(x91542,f784(f784(f3(f869(x91543,a852)),x91544),f784(f784(f312(x91543),x91545),f187(f869(x91543,a852)))))),f784(x91546,x91545)),f784(x91542,x91544))+~P85(f784(f71(x91543),x91544))+~P85(f784(f784(f347(x91543),x91545),x91544))
% 11.41/11.19 [6886]~P4(x68861)+~E(f60(x68861,x68863,x68864),f60(x68861,x68866,x68864))+~E(f60(x68861,x68862,x68864),f60(x68861,x68865,x68864))+E(f60(x68861,f784(f784(f89(x68861),x68862),x68863),x68864),f60(x68861,f784(f784(f89(x68861),x68865),x68866),x68864))
% 11.41/11.19 [6887]~P4(x68871)+~E(f60(x68871,x68873,x68874),f60(x68871,x68876,x68874))+~E(f60(x68871,x68872,x68874),f60(x68871,x68875,x68874))+E(f60(x68871,f784(f784(f90(x68871),x68872),x68873),x68874),f60(x68871,f784(f784(f90(x68871),x68875),x68876),x68874))
% 11.41/11.19 [6888]~P5(x68881)+~E(f60(x68881,x68883,x68884),f60(x68881,x68886,x68884))+~E(f60(x68881,x68882,x68884),f60(x68881,x68885,x68884))+E(f60(x68881,f784(f784(f3(x68881),x68882),x68883),x68884),f60(x68881,f784(f784(f3(x68881),x68885),x68886),x68884))
% 11.41/11.19 [7715]~P17(x77151,x77152,x77153)+~P85(f784(f71(x77151),x77156))+E(f784(f784(f74(x77151,x77152,x77153),x77154),f784(f784(f312(x77151),x77155),x77156)),f784(f784(f74(x77151,x77152,x77153),f784(f784(x77153,x77155),x77154)),x77156))+P85(f784(f784(f347(x77151),x77155),x77156))
% 11.41/11.19 [7782]~P6(x77821)+P85(f784(f784(f242(x77821),x77822),f784(x77823,x77824)))+~P85(f784(f784(f347(x77825),x77824),x77826))+~P85(f784(f784(f242(x77821),x77822),f784(f784(f55(x77825,x77821),x77826),x77823)))
% 11.41/11.19 [7941]~P17(x79411,x79412,x79413)+~P85(f784(f71(x79411),x79416))+E(f784(f784(f74(x79411,x79412,x79413),x79414),f784(f784(f312(x79411),x79415),x79416)),f784(f784(x79413,x79415),f784(f784(f74(x79411,x79412,x79413),x79414),x79416)))+P85(f784(f784(f347(x79411),x79415),x79416))
% 11.41/11.19 [8031]~P101(x80313)+~P85(f784(x80312,x80315))+~P15(x80313,f784(f784(f146(x80311,x80313),x80314),x80316))+E(f784(f131(x80311,x80312),f784(f784(f142(x80311,x80313,x80314),x80315),x80316)),f784(f784(f142(x80311,x80313,x80314),x80315),f784(f131(x80311,x80312),x80316)))
% 11.41/11.19 [8054]E(x80541,x80542)+E(x80543,f2(a1))+~P85(f784(f64(x80544,x80543),f784(f784(f251(a1,a1),x80545),x80542)))+~P85(f784(f64(x80544,x80543),f784(f784(f251(a1,a1),x80546),x80541)))
% 11.41/11.19 [8055]E(x80551,x80552)+E(x80553,f2(a1))+~P85(f784(f64(x80554,x80553),f784(f784(f251(a1,a1),x80552),x80555)))+~P85(f784(f64(x80554,x80553),f784(f784(f251(a1,a1),x80551),x80556)))
% 11.41/11.19 [8077]~P20(x80772,x80775,x80776,x80771)+~P85(f784(f71(x80772),x80774))+E(f784(x80771,f784(f784(f312(x80772),x80773),x80774)),f784(f82(x80775,x80775,x80775,f784(x80771,x80774)),f784(x80776,x80773)))+P85(f784(f784(f347(x80772),x80773),x80774))
% 11.41/11.19 [8290]~P21(x82905,x82901,x82906,x82902)+E(f784(f82(x82901,x82901,x82901,f784(x82902,x82903)),f784(x82902,x82904)),f784(x82902,x82903))+~P85(f784(f71(x82905),x82903))+~P85(f784(f784(f242(f869(x82905,a852)),x82904),x82903))
% 11.41/11.19 [9342]~P26(x93421,x93422,x93424,x93423)+~P85(f784(f784(f347(x93422),x93425),f784(f313(x93421,x93422,x93424),x93423)))+P85(f784(f784(f347(x93421),f784(f86(x93421,x93422,x93423,x93424),x93425)),x93426))+~P85(f784(f784(f242(f869(x93421,a852)),x93423),x93426))
% 11.41/11.19 [9693]~P68(x96932)+~E(f508(x96931,x96933,x96935,x96936,x96934,x96932),f509(x96931,x96933,x96935,x96936,x96934,x96932))+~P85(f784(f71(x96934),x96936))+E(f784(f784(f8(x96931,x96932),x96933),f784(f313(x96934,x96931,x96935),x96936)),f784(f784(f8(x96934,x96932),f784(f82(x96931,x96932,x96934,x96933),x96935)),x96936))
% 11.41/11.19 [9722]~P68(x97226)+E(f784(x97221,f508(x97222,x97223,x97221,x97224,x97225,x97226)),f784(x97221,f509(x97222,x97223,x97221,x97224,x97225,x97226)))+E(f784(f784(f8(x97222,x97226),x97223),f784(f313(x97225,x97222,x97221),x97224)),f784(f784(f8(x97225,x97226),f784(f82(x97222,x97226,x97225,x97223),x97221)),x97224))+~P85(f784(f71(x97225),x97224))
% 11.41/11.19 [9776]~P68(x97762)+~E(f784(x97763,f784(x97765,f509(x97761,x97763,x97765,x97766,x97764,x97762))),f2(x97762))+~P85(f784(f71(x97764),x97766))+E(f784(f784(f8(x97761,x97762),x97763),f784(f313(x97764,x97761,x97765),x97766)),f784(f784(f8(x97764,x97762),f784(f82(x97761,x97762,x97764,x97763),x97765)),x97766))
% 11.41/11.19 [9839]~P68(x98392)+~P85(f784(f71(x98394),x98396))+E(f784(f784(f8(x98391,x98392),x98393),f784(f313(x98394,x98391,x98395),x98396)),f784(f784(f8(x98394,x98392),f784(f82(x98391,x98392,x98394,x98393),x98395)),x98396))+P85(f784(f784(f347(x98394),f509(x98391,x98393,x98395,x98396,x98394,x98392)),x98396))
% 11.41/11.19 [9840]~P68(x98402)+~P85(f784(f71(x98404),x98406))+E(f784(f784(f8(x98401,x98402),x98403),f784(f313(x98404,x98401,x98405),x98406)),f784(f784(f8(x98404,x98402),f784(f82(x98401,x98402,x98404,x98403),x98405)),x98406))+P85(f784(f784(f347(x98404),f508(x98401,x98403,x98405,x98406,x98404,x98402)),x98406))
% 11.41/11.19 [9959]~P71(x99591)+~P85(f784(f71(x99592),x99596))+E(f784(f784(f784(f75(x99591,x99592,f90(x99591)),f784(f784(f20(x99592,f869(x99593,a852),x99591),f784(f784(f9(x99592,x99591,f869(f869(x99593,a852),x99591)),f784(f784(f10(f869(x99593,x99591),f869(x99591,f869(f869(x99593,a852),x99591)),x99592),f75(x99591,x99593,f90(x99591))),x99594)),f87(x99591))),x99595)),f87(x99591)),x99596),f784(f784(f784(f75(x99591,f868(x99592,x99593),f90(x99591)),f784(f261(x99592,x99593,x99591),x99594)),f87(x99591)),f784(f784(f258(x99592,x99593),x99596),x99595)))+P85(f784(f784(f347(x99592),f554(x99594,x99595,x99593,x99596,x99592,x99591)),x99596))
% 11.41/11.19 [9977]~P71(x99771)+~P85(f784(f71(x99772),x99776))+E(f784(f784(f784(f75(x99771,x99772,f90(x99771)),f784(f784(f20(x99772,f869(x99773,a852),x99771),f784(f784(f9(x99772,x99771,f869(f869(x99773,a852),x99771)),f784(f784(f10(f869(x99773,x99771),f869(x99771,f869(f869(x99773,a852),x99771)),x99772),f75(x99771,x99773,f90(x99771))),x99774)),f87(x99771))),x99775)),f87(x99771)),x99776),f784(f784(f784(f75(x99771,f868(x99772,x99773),f90(x99771)),f784(f261(x99772,x99773,x99771),x99774)),f87(x99771)),f784(f784(f258(x99772,x99773),x99776),x99775)))+~P85(f784(f71(x99773),f784(x99775,f554(x99774,x99775,x99773,x99776,x99772,x99771))))
% 11.41/11.19 [8204]~P21(x82042,x82045,x82046,x82041)+~P85(f784(f71(x82042),x82044))+~P85(f784(f71(x82042),x82043))+E(f784(x82041,f784(f784(f110(f869(x82042,a852)),x82043),x82044)),f784(f82(x82045,x82045,x82045,f784(x82041,x82043)),f784(x82041,x82044)))
% 11.41/11.19 [8424]~P6(x84241)+P85(f784(f784(f242(x84241),f784(x84242,x84243)),x84244))+~P85(f784(f784(f347(x84245),x84243),x84246))+~P85(f784(f784(f242(x84241),f784(f784(f54(x84245,x84241),x84246),x84242)),x84244))
% 11.41/11.19 [8798]~P26(x87982,x87981,x87983,x87986)+E(f784(f784(f3(f869(x87981,a852)),f784(f313(x87982,x87981,x87983),x87984)),f784(f313(x87982,x87981,x87983),x87985)),f784(f313(x87982,x87981,x87983),f784(f784(f3(f869(x87982,a852)),x87984),x87985)))+~P85(f784(f784(f242(f869(x87982,a852)),x87985),x87986))+~P85(f784(f784(f242(f869(x87982,a852)),x87984),x87986))
% 11.41/11.19 [8799]~P26(x87992,x87991,x87993,x87996)+E(f784(f784(f111(f869(x87991,a852)),f784(f313(x87992,x87991,x87993),x87994)),f784(f313(x87992,x87991,x87993),x87995)),f784(f313(x87992,x87991,x87993),f784(f784(f111(f869(x87992,a852)),x87994),x87995)))+~P85(f784(f784(f242(f869(x87992,a852)),x87995),x87996))+~P85(f784(f784(f242(f869(x87992,a852)),x87994),x87996))
% 11.41/11.19 [9045]E(x90451,x90452)+~P52(x90453,x90454,x90455)+~P85(f784(f784(f347(f868(x90453,x90454)),f784(f784(f251(x90453,x90454),x90456),x90452)),x90455))+~P85(f784(f784(f347(f868(x90453,x90454)),f784(f784(f251(x90453,x90454),x90456),x90451)),x90455))
% 11.41/11.19 [9046]E(x90461,x90462)+~P52(x90463,x90464,x90465)+~P85(f784(f784(f347(f868(x90463,x90464)),f784(f784(f251(x90463,x90464),x90466),x90462)),x90465))+~P85(f784(f784(f347(f868(x90463,x90464)),f784(f784(f251(x90463,x90464),x90466),x90461)),x90465))
% 11.41/11.19 [9634]~P68(x96341)+~P85(f784(f71(x96343),x96346))+~P85(f784(f71(x96342),x96345))+E(f784(f784(f89(x96341),f784(f784(f8(x96342,x96341),f784(f82(f870(x96342,x96343),x96341,x96342,x96344),f322(x96342,x96343))),x96345)),f784(f784(f8(x96343,x96341),f784(f82(f870(x96342,x96343),x96341,x96343,x96344),f326(x96343,x96342))),x96346)),f784(f784(f8(f870(x96342,x96343),x96341),x96344),f327(x96342,x96343,x96345,x96346)))
% 11.41/11.19 [9772]~P65(x97721)+~E(f784(x97723,f637(x97724,x97726,x97723,x97725,x97722,x97721)),f784(x97726,f637(x97724,x97726,x97723,x97725,x97722,x97721)))+~P85(f784(f71(x97722),x97725))+E(f784(f784(f784(f75(x97721,x97722,f90(x97721)),x97723),x97724),x97725),f784(f784(f784(f75(x97721,x97722,f90(x97721)),x97726),x97724),x97725))
% 11.41/11.19 [9834]~P65(x98341)+~P85(f784(f71(x98342),x98345))+E(f784(f784(f784(f75(x98341,x98342,f90(x98341)),x98343),x98344),x98345),f784(f784(f784(f75(x98341,x98342,f90(x98341)),x98346),x98344),x98345))+P85(f784(f784(f347(x98342),f637(x98344,x98343,x98346,x98345,x98342,x98341)),x98345))
% 11.41/11.19 [8628]~P65(x86281)+~P85(f784(f71(x86282),x86286))+P85(f784(f784(f347(x86282),x86285),x86286))+E(f784(f784(f784(f75(x86281,x86282,f90(x86281)),x86283),x86284),f784(f784(f312(x86282),x86285),x86286)),f784(f784(f90(x86281),f784(x86283,x86285)),f784(f784(f784(f75(x86281,x86282,f90(x86281)),x86283),x86284),x86286)))
% 11.41/11.19 [8672]~P9(x86721,x86726,x86723)+~P13(x86721,f869(x86722,a852),x86723,x86725)+~P85(f784(f784(f347(x86721),x86724),x86726))+E(f784(f784(f54(x86721,f869(x86722,a852)),f784(f287(x86721,x86721,x86723),f784(f784(f312(x86721),x86724),f187(f869(x86721,a852))))),x86725),f784(x86725,x86724))
% 11.41/11.19 [8780]~P17(x87803,x87804,x87801)+~P85(f784(f71(x87803),x87806))+~P85(f784(f784(f347(x87803),x87802),x87806))+E(f784(f784(x87801,x87802),f784(f784(f74(x87803,x87804,x87801),x87805),f784(f784(f3(f869(x87803,a852)),x87806),f784(f784(f312(x87803),x87802),f187(f869(x87803,a852)))))),f784(f784(f74(x87803,x87804,x87801),x87805),x87806))
% 11.41/11.19 [9056]~P20(x90563,x90561,x90566,x90562)+~P85(f784(f71(x90563),x90565))+~P85(f784(f71(x90563),x90564))+E(f784(f82(x90561,x90561,x90561,f784(x90562,f784(f784(f110(f869(x90563,a852)),x90564),x90565))),f784(x90562,f784(f784(f111(f869(x90563,a852)),x90564),x90565))),f784(f82(x90561,x90561,x90561,f784(x90562,x90564)),f784(x90562,x90565)))
% 11.41/11.19 [9361]~E(x93613,f784(f784(f151(x93611,x93612),x93615),x93616))+P85(f784(f784(f347(f868(f860(x93611),f860(x93611))),f784(f784(f251(f860(x93611),f860(x93611)),x93612),x93613)),f149(x93611,x93614)))+~P85(f784(f784(f243(a859),x93615),f784(f188(f860(x93611)),x93612)))+~P85(f784(f784(f347(f868(x93611,x93611)),f784(f784(f251(x93611,x93611),f784(f784(f155(x93611),x93612),x93615)),x93616)),x93614))
% 11.41/11.19 [9856]~P68(x98562)+~P85(f784(f71(x98561),x98566))+P85(f784(f784(f347(x98561),f556(x98564,x98565,x98563,x98566,x98561,x98562)),x98566))+E(f784(f784(f8(x98561,x98562),f784(f784(f20(x98561,f869(x98563,a852),x98562),f784(f784(f10(f869(x98563,x98562),f869(f869(x98563,a852),x98562),x98561),f8(x98563,x98562)),x98564)),x98565)),x98566),f784(f784(f8(f868(x98561,x98563),x98562),f784(f261(x98561,x98563,x98562),x98564)),f784(f784(f258(x98561,x98563),x98566),x98565)))
% 11.41/11.19 [9857]~P71(x98572)+~P85(f784(f71(x98571),x98576))+P85(f784(f784(f347(x98571),f557(x98574,x98575,x98573,x98576,x98571,x98572)),x98576))+E(f784(f784(f11(x98571,x98572),f784(f784(f20(x98571,f869(x98573,a852),x98572),f784(f784(f10(f869(x98573,x98572),f869(f869(x98573,a852),x98572),x98571),f11(x98573,x98572)),x98574)),x98575)),x98576),f784(f784(f11(f868(x98571,x98573),x98572),f784(f261(x98571,x98573,x98572),x98574)),f784(f784(f258(x98571,x98573),x98576),x98575)))
% 11.41/11.19 [9894]~P68(x98942)+~P85(f784(f71(x98941),x98946))+~P85(f784(f71(x98943),f784(x98945,f556(x98944,x98945,x98943,x98946,x98941,x98942))))+E(f784(f784(f8(x98941,x98942),f784(f784(f20(x98941,f869(x98943,a852),x98942),f784(f784(f10(f869(x98943,x98942),f869(f869(x98943,a852),x98942),x98941),f8(x98943,x98942)),x98944)),x98945)),x98946),f784(f784(f8(f868(x98941,x98943),x98942),f784(f261(x98941,x98943,x98942),x98944)),f784(f784(f258(x98941,x98943),x98946),x98945)))
% 11.41/11.19 [9895]~P71(x98952)+~P85(f784(f71(x98951),x98956))+~P85(f784(f71(x98953),f784(x98955,f557(x98954,x98955,x98953,x98956,x98951,x98952))))+E(f784(f784(f11(x98951,x98952),f784(f784(f20(x98951,f869(x98953,a852),x98952),f784(f784(f10(f869(x98953,x98952),f869(f869(x98953,a852),x98952),x98951),f11(x98953,x98952)),x98954)),x98955)),x98956),f784(f784(f11(f868(x98951,x98953),x98952),f784(f261(x98951,x98953,x98952),x98954)),f784(f784(f258(x98951,x98953),x98956),x98955)))
% 11.41/11.19 [9879]~P71(x98792)+~P85(f784(f71(x98791),x98796))+P85(f784(f784(f347(x98791),x98793),x98796))+E(f784(f784(f11(x98791,x98792),f784(f784(f9(x98791,x98792,x98792),f784(f784(f20(x98791,x98792,f869(x98792,x98792)),f784(f784(f10(a852,f869(x98792,f869(x98792,x98792)),x98791),f105(x98792)),f784(f784(f9(x98791,x98791,a852),a343),x98793))),x98794)),x98795)),x98796),f784(f784(f252(x98792),x98795),f784(f50(x98791),x98796)))
% 11.41/11.19 [9882]~P71(x98822)+~P85(f784(f71(x98821),x98826))+~P85(f784(f784(f347(x98821),x98823),x98826))+E(f784(f784(f11(x98821,x98822),f784(f784(f9(x98821,x98822,x98822),f784(f784(f20(x98821,x98822,f869(x98822,x98822)),f784(f784(f10(a852,f869(x98822,f869(x98822,x98822)),x98821),f105(x98822)),f784(f784(f9(x98821,x98821,a852),a343),x98823))),x98824)),x98825)),x98826),f784(f784(f90(x98822),f784(x98824,x98823)),f784(f784(f252(x98822),x98825),f784(f784(f3(a859),f784(f50(x98821),x98826)),f87(a859)))))
% 11.41/11.19 [9946]~P85(f784(f71(x99461),x99465))+~P85(f784(f71(x99462),x99463))+P85(f784(f784(f347(x99462),f590(x99466,x99464,x99463,x99462,x99465,x99461)),x99463))+E(f784(f784(f8(x99461,a859),f784(f784(f10(f869(x99462,a852),a859,x99461),f50(x99462)),f784(f784(f10(f869(x99462,a852),f869(x99462,a852),x99461),f266(x99462)),f784(f784(f10(f869(x99462,a852),f869(x99462,a852),x99461),f784(f20(x99462,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99462),a344),f784(f784(f9(x99462,f869(x99462,a852),a852),f347(x99462)),x99463)))),x99464)))),x99465),f784(f784(f90(a859),x99466),f784(f50(x99462),x99463)))
% 11.41/11.19 [9947]~P85(f784(f71(x99471),x99475))+~P85(f784(f71(x99472),x99473))+P85(f784(f784(f347(x99472),f591(x99476,x99474,x99473,x99472,x99475,x99471)),x99473))+E(f784(f784(f8(x99471,a859),f784(f784(f10(f869(x99472,a852),a859,x99471),f50(x99472)),f784(f784(f10(f869(x99472,a852),f869(x99472,a852),x99471),f266(x99472)),f784(f784(f10(f869(x99472,a852),f869(x99472,a852),x99471),f784(f20(x99472,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99472),a344),f784(f784(f9(x99472,f869(x99472,a852),a852),f347(x99472)),x99473)))),x99474)))),x99475),f784(f784(f8(x99472,a859),x99476),x99473))
% 11.41/11.19 [9983]~P85(f784(f71(x99832),x99833))+~P85(f784(f71(x99831),x99835))+~E(f784(f50(x99831),f784(f266(x99831),f784(f784(f20(x99831,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99831),a344),f784(f784(f9(x99831,f869(x99831,a852),a852),f347(x99831)),x99835))),f784(f784(f9(x99831,x99832,a852),x99834),f590(x99836,x99834,x99833,x99832,x99835,x99831))))),x99836)+E(f784(f784(f8(x99831,a859),f784(f784(f10(f869(x99832,a852),a859,x99831),f50(x99832)),f784(f784(f10(f869(x99832,a852),f869(x99832,a852),x99831),f266(x99832)),f784(f784(f10(f869(x99832,a852),f869(x99832,a852),x99831),f784(f20(x99832,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99832),a344),f784(f784(f9(x99832,f869(x99832,a852),a852),f347(x99832)),x99833)))),x99834)))),x99835),f784(f784(f90(a859),x99836),f784(f50(x99832),x99833)))
% 11.41/11.19 [9985]~P85(f784(f71(x99852),x99853))+~P85(f784(f71(x99851),x99855))+~E(f784(f50(x99851),f784(f266(x99851),f784(f784(f20(x99851,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99851),a344),f784(f784(f9(x99851,f869(x99851,a852),a852),f347(x99851)),x99855))),f784(f784(f9(x99851,x99852,a852),x99854),f591(x99856,x99854,x99853,x99852,x99855,x99851))))),f784(x99856,f591(x99856,x99854,x99853,x99852,x99855,x99851)))+E(f784(f784(f8(x99851,a859),f784(f784(f10(f869(x99852,a852),a859,x99851),f50(x99852)),f784(f784(f10(f869(x99852,a852),f869(x99852,a852),x99851),f266(x99852)),f784(f784(f10(f869(x99852,a852),f869(x99852,a852),x99851),f784(f20(x99852,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99852),a344),f784(f784(f9(x99852,f869(x99852,a852),a852),f347(x99852)),x99853)))),x99854)))),x99855),f784(f784(f8(x99852,a859),x99856),x99853))
% 11.41/11.19 [9633]E(x96331,x96332)+~P17(x96333,x96334,x96335)+~P85(f784(f76(x96333,x96334,x96335,x96336,x96337),x96332))+~P85(f784(f76(x96333,x96334,x96335,x96336,x96337),x96331))
% 11.41/11.19 [9432]P85(f784(x94321,x94322))+~P85(f784(f784(f347(x94327),x94322),f784(x94326,x94324)))+~P85(f784(x94321,f399(x94321,x94326,x94325,x94323,x94327)))+~P85(f784(f784(f347(x94323),x94324),x94325))
% 11.41/11.19 [9871]~P17(x98717,x98716,x98711)+E(f784(f784(x98711,x98712),f676(x98712,x98713,x98714,x98715,x98711,x98716,x98717)),x98713)+~P85(f784(f76(x98717,x98716,x98711,x98715,x98714),x98713))+~P85(f784(f784(f347(x98717),x98712),x98714))
% 11.41/11.19 [9931]~P17(x99311,x99312,x99313)+~P85(f784(f76(x99311,x99312,x99313,x99314,x99315),x99317))+P85(f784(f76(x99311,x99312,x99313,x99314,f784(f784(f3(f869(x99311,a852)),x99315),f784(f784(f312(x99311),x99316),f187(f869(x99311,a852))))),f676(x99316,x99317,x99315,x99314,x99313,x99312,x99311)))+~P85(f784(f784(f347(x99311),x99316),x99315))
% 11.41/11.19 [9338]~P65(x93381)+~P26(x93385,x93382,x93386,x93387)+~P85(f784(f71(x93385),x93387))+E(f784(f784(f784(f75(x93381,x93382,f90(x93381)),x93383),x93384),f784(f313(x93385,x93382,x93386),x93387)),f784(f784(f784(f75(x93381,x93385,f90(x93381)),f784(f82(x93382,x93381,x93385,x93383),x93386)),x93384),x93387))
% 11.41/11.19 [9455]~E(f784(f784(f312(x94551),x94555),x94556),f784(f784(f312(x94551),x94552),x94553))+~P85(f784(f76(x94551,x94551,x94554,x94552,x94553),x94557))+P85(f784(f784(f347(x94551),x94552),x94553))+P85(f784(f72(x94551,x94554,f784(f784(f312(x94551),x94555),x94556)),x94557))
% 11.41/11.19 [9537]P85(f784(x95371,x95372))+~P85(f784(f784(f347(x95373),x95372),f784(x95374,x95377)))+~P85(f784(f784(f347(x95376),x95377),x95375))+P85(f784(f784(f347(x95373),f399(x95371,x95374,x95375,x95376,x95373)),f784(f784(f54(x95376,f869(x95373,a852)),x95375),x95374)))
% 11.41/11.19 [9550]~P26(x95502,x95501,x95505,x95504)+~P26(x95501,x95503,x95506,f784(f313(x95502,x95501,x95505),x95504))+E(f784(f784(f82(x95501,x95502,x95503,f86(x95502,x95501,x95504,x95505)),f86(x95501,x95503,f784(f313(x95502,x95501,x95505),x95504),x95506)),x95507),f784(f86(x95502,x95503,x95504,f784(f82(x95501,x95503,x95502,x95506),x95505)),x95507))+~P85(f784(f784(f347(x95503),x95507),f784(f313(x95501,x95503,x95506),f784(f313(x95502,x95501,x95505),x95504))))
% 11.41/11.19 [9872]~P17(x98727,x98726,x98721)+E(f784(f784(x98721,x98722),f704(x98723,x98724,x98722,x98725,x98721,x98726,x98727)),x98723)+P85(f784(f784(f347(x98727),x98722),x98724))+~P85(f784(f76(x98727,x98726,x98721,x98725,f784(f784(f312(x98727),x98722),x98724)),x98723))
% 11.41/11.19 [9930]~P17(x99301,x99304,x99305)+P85(f784(f76(x99301,x99304,x99305,x99306,x99303),f704(x99307,x99303,x99302,x99306,x99305,x99304,x99301)))+P85(f784(f784(f347(x99301),x99302),x99303))+~P85(f784(f76(x99301,x99304,x99305,x99306,f784(f784(f312(x99301),x99302),x99303)),x99307))
% 11.41/11.19 [9617]E(x96171,f2(a1))+~P85(f784(f64(x96173,x96171),f784(f784(f251(a1,a1),x96175),x96177)))+~P85(f784(f64(x96172,x96171),f784(f784(f251(a1,a1),x96174),x96176)))+P85(f784(f64(f784(f784(f89(a1),x96172),x96173),x96171),f784(f784(f251(a1,a1),f784(f784(f89(a1),f784(f784(f89(a1),x96174),x96175)),f784(f784(f51(a1),f784(f784(f89(a1),x96176),x96177)),x96171))),f60(a1,f784(f784(f89(a1),x96176),x96177),x96171))))
% 11.41/11.19 [9619]~P85(f784(f784(f243(a859),f2(a859)),x96193))+~P85(f784(f63(x96192,x96193),f784(f784(f251(a859,a859),x96195),x96197)))+~P85(f784(f63(x96191,x96193),f784(f784(f251(a859,a859),x96194),x96196)))+P85(f784(f63(f784(f784(f89(a859),x96191),x96192),x96193),f784(f784(f251(a859,a859),f784(f784(f89(a859),f784(f784(f89(a859),x96194),x96195)),f784(f784(f51(a859),f784(f784(f89(a859),x96196),x96197)),x96193))),f60(a859,f784(f784(f89(a859),x96196),x96197),x96193))))
% 11.41/11.19 [9982]~P68(x99822)+~P85(f784(f71(x99823),x99825))+~P85(f784(f71(x99821),x99827))+E(f784(f784(f8(x99821,x99822),f784(f784(f20(x99821,f869(x99823,a852),x99822),f784(f784(f10(f869(x99823,x99822),f869(f869(x99823,a852),x99822),x99821),f8(x99823,x99822)),x99824)),f784(f784(f10(f869(x99823,a852),f869(x99823,a852),x99821),f266(x99823)),f784(f784(f10(f869(x99823,a852),f869(x99823,a852),x99821),f784(f20(x99823,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99823),a344),f784(f784(f9(x99823,f869(x99823,a852),a852),f347(x99823)),x99825)))),x99826)))),x99827),f784(f784(f8(x99823,x99822),f784(f784(f20(x99823,f869(x99821,a852),x99822),f784(f784(f10(f869(x99821,x99822),f869(f869(x99821,a852),x99822),x99823),f8(x99821,x99822)),f784(f9(x99821,x99823,x99822),x99824))),f784(f784(f10(f869(x99821,a852),f869(x99821,a852),x99823),f266(x99821)),f784(f784(f10(f869(x99821,a852),f869(x99821,a852),x99823),f784(f20(x99821,a852,a852),f784(f784(f10(a852,f869(a852,a852),x99821),a344),f784(f784(f9(x99821,f869(x99821,a852),a852),f347(x99821)),x99827)))),f784(f9(x99821,x99823,a852),x99826))))),x99825))
% 11.41/11.19 [9495]~P23(x94957,x94956,x94951,x94958,x94952,x94954)+E(f784(f784(x94951,f784(x94952,x94953)),f784(x94954,x94955)),f784(x94954,x94955))+~P85(f784(f71(x94956),x94955))+~P85(f784(f784(f347(x94956),x94953),x94955))
% 11.41/11.19 [9499]~P14(x94996,x94991,x94992,x94998,x94993,x94994)+~P9(x94996,x94997,x94998)+P13(x94991,x94992,x94993,f784(x94994,x94995))+~P85(f784(f784(f347(x94996),x94995),x94997))
% 11.41/11.19 [7742]~P38(x77424,x77425,x77426,x77423)+~P32(x77428,x77426,f784(f784(f784(f100(x77428),x77427),x77424),x77421))+P85(f784(f784(x77421,x77422),x77423))+~P85(f784(f784(x77427,x77422),x77425))
% 11.41/11.19 [9143]~P20(x91437,x91431,x91438,x91433)+~P85(f784(f71(x91437),x91435))+~P85(f784(f71(x91437),x91434))+E(f784(f82(x91431,x91431,x91432,f784(x91433,x91434)),f784(f82(x91431,x91431,x91432,f784(x91433,x91435)),x91436)),f784(f82(x91431,x91431,x91432,f784(x91433,x91435)),f784(f82(x91431,x91431,x91432,f784(x91433,x91434)),x91436)))
% 11.41/11.19 [9209]~P26(x92092,x92092,x92095,x92096)+~P22(x92093,x92092,x92097,x92098,x92091)+~P85(f784(f71(x92092),x92096))+E(f784(f784(x92091,f784(f82(x92092,x92093,x92092,x92094),x92095)),x92096),f784(f784(x92091,x92094),f784(f313(x92092,x92092,x92095),x92096)))
% 11.41/11.19 [9497]~P24(x94977,x94972,x94975,x94978,x94976,x94971)+~P85(f784(f71(x94972),x94974))+E(f784(x94971,f784(f784(f312(x94972),x94973),x94974)),f784(f784(x94975,f784(x94976,x94973)),f784(x94971,x94974)))+P85(f784(f784(f347(x94972),x94973),x94974))
% 11.41/11.19 [9504]~P23(x95046,x95045,x95041,x95047,x95048,x95042)+E(f784(f784(x95041,f784(x95042,x95043)),f784(x95042,x95044)),f784(x95042,x95044))+~P85(f784(f71(x95045),x95044))+~P85(f784(f784(f242(f869(x95045,a852)),x95043),x95044))
% 11.41/11.19 [9130]P85(f784(f784(f347(f868(f860(x91301),f860(x91301))),f784(f784(f251(f860(x91301),f860(x91301)),x91302),x91303)),f149(x91301,x91304)))+~E(x91303,f784(f784(f130(x91301),x91305),f784(f784(f144(x91301),x91306),x91307)))+~E(x91302,f784(f784(f130(x91301),x91305),f784(f784(f144(x91301),x91308),x91307)))+~P85(f784(f784(f347(f868(x91301,x91301)),f784(f784(f251(x91301,x91301),x91308),x91306)),x91304))
% 11.41/11.19 [9500]~P23(x95006,x95002,x95005,x95007,x95008,x95001)+~P85(f784(f71(x95002),x95004))+~P85(f784(f71(x95002),x95003))+E(f784(x95001,f784(f784(f110(f869(x95002,a852)),x95003),x95004)),f784(f784(x95005,f784(x95001,x95003)),f784(x95001,x95004)))
% 11.41/11.19 [10021]~P26(x100214,x100212,x100215,x100218)+E(f784(f784(f55(x100211,f869(x100212,a852)),x100213),f784(f784(f10(f869(x100214,a852),f869(x100212,a852),x100211),f313(x100214,x100212,x100215)),x100216)),f784(f313(x100214,x100212,x100215),f784(f784(f55(x100211,f869(x100214,a852)),x100213),x100216)))+~P85(f784(f784(f347(x100211),x100217),x100213))+P85(f784(f784(f347(x100211),f690(x100217,x100216,x100213,x100211,x100218,x100215,x100212,x100214)),x100213))
% 11.41/11.19 [10039]~P26(x100394,x100392,x100395,x100397)+E(f784(f784(f55(x100391,f869(x100392,a852)),x100393),f784(f784(f10(f869(x100394,a852),f869(x100392,a852),x100391),f313(x100394,x100392,x100395)),x100396)),f784(f313(x100394,x100392,x100395),f784(f784(f55(x100391,f869(x100394,a852)),x100393),x100396)))+~P85(f784(f784(f347(x100391),x100398),x100393))+~P85(f784(f784(f242(f869(x100394,a852)),f784(x100396,f690(x100398,x100396,x100393,x100391,x100397,x100395,x100392,x100394))),x100397))
% 11.41/11.19 [9555]~P24(x95557,x95555,x95551,x95558,x95552,x95554)+~P85(f784(f71(x95555),x95556))+~P85(f784(f784(f347(x95555),x95553),x95556))+E(f784(f784(x95551,f784(x95552,x95553)),f784(x95554,f784(f784(f3(f869(x95555,a852)),x95556),f784(f784(f312(x95555),x95553),f187(f869(x95555,a852)))))),f784(x95554,x95556))
% 11.41/11.19 [9565]~P24(x95656,x95653,x95651,x95657,x95658,x95652)+~P85(f784(f71(x95653),x95655))+~P85(f784(f71(x95653),x95654))+E(f784(f784(x95651,f784(x95652,f784(f784(f110(f869(x95653,a852)),x95654),x95655))),f784(x95652,f784(f784(f111(f869(x95653,a852)),x95654),x95655))),f784(f784(x95651,f784(x95652,x95654)),f784(x95652,x95655)))
% 11.41/11.19 [9653]P40(x96531,x96532,x96533,x96534,x96535,f784(f784(x96533,x96536),x96537))+~P40(x96531,x96532,x96533,x96534,f784(f784(f3(f869(x96531,a852)),x96535),f784(f784(f312(x96531),x96538),f187(f869(x96531,a852)))),x96539)+~E(f784(f784(x96533,x96536),x96537),f784(f784(x96533,x96538),x96539))+~P85(f784(f784(f347(x96531),x96538),x96535))
% 11.41/11.19 [9592]~P14(x95926,x95927,x95928,x95929,x959210,x95921)+E(f784(f784(x95921,x95922),x95923),f784(f784(x95921,x95924),x95925))+~P85(f784(f784(f347(f868(x95927,x95927)),f784(f784(f251(x95927,x95927),x95923),x95925)),x959210))+~P85(f784(f784(f347(f868(x95926,x95926)),f784(f784(f251(x95926,x95926),x95922),x95924)),x95929))
% 11.41/11.19 [6815]E(x68151,x68152)+~P85(f784(f784(f242(a1),f2(a1)),x68152))+~P85(f784(f784(f242(a1),f2(a1)),x68151))+~P85(f784(f784(f289(a1),x68152),x68151))+~P85(f784(f784(f289(a1),x68151),x68152))
% 11.41/11.19 [9360]E(x93601,f2(a1))+E(x93602,f2(a1))+E(f784(f784(f95(a1,f868(a1,a1)),f784(f784(a222,x93602),x93601)),f784(f784(f20(a1,a1,f868(a1,a1)),f784(f784(f10(a1,f869(a1,f868(a1,a1)),a1),f251(a1,a1)),f784(f51(a1),x93602))),f784(f51(a1),x93601))),f220(x93602,x93601))+P85(f784(f784(f243(a1),x93601),f2(a1)))+~P85(f784(f334(f868(a1,a1),a226),f784(f784(f251(a1,a1),x93602),x93601)))
% 11.41/11.19 [9211]~P93(x92112)+E(x92111,f187(f869(x92112,a852)))+~P85(f784(f71(x92112),x92111))+P85(f784(f784(f347(x92112),f15(x92112,x92111)),x92111))+~P85(f784(f784(f347(x92112),f784(f784(f110(x92112),f453(x92111,x92112)),f454(x92111,x92112))),f784(f784(f312(x92112),f453(x92111,x92112)),f784(f784(f312(x92112),f454(x92111,x92112)),f187(f869(x92112,a852))))))
% 11.41/11.19 [9212]~P101(x92122)+E(x92121,f187(f869(x92122,a852)))+~P85(f784(f71(x92122),x92121))+P85(f784(f784(f347(x92122),f16(x92122,x92121)),x92121))+~P85(f784(f784(f347(x92122),f784(f784(f186(x92122),f455(x92121,x92122)),f456(x92121,x92122))),f784(f784(f312(x92122),f455(x92121,x92122)),f784(f784(f312(x92122),f456(x92121,x92122)),f187(f869(x92122,a852))))))
% 11.41/11.19 [9213]~P101(x92132)+E(x92131,f187(f869(x92132,a852)))+~P85(f784(f71(x92132),x92131))+P85(f784(f784(f347(x92132),f17(x92132,x92131)),x92131))+~P85(f784(f784(f347(x92132),f784(f784(f246(x92132),f457(x92131,x92132)),f458(x92131,x92132))),f784(f784(f312(x92132),f457(x92131,x92132)),f784(f784(f312(x92132),f458(x92131,x92132)),f187(f869(x92132,a852))))))
% 11.41/11.19 [9214]~P93(x92142)+E(x92141,f187(f869(x92142,a852)))+~P85(f784(f71(x92142),x92141))+P85(f784(f784(f347(x92142),f12(x92142,x92141)),x92141))+~P85(f784(f784(f347(x92142),f784(f784(f111(x92142),f525(x92141,x92142)),f526(x92141,x92142))),f784(f784(f312(x92142),f525(x92141,x92142)),f784(f784(f312(x92142),f526(x92141,x92142)),f187(f869(x92142,a852))))))
% 11.41/11.19 [9242]~P65(x92422)+E(x92421,f187(f869(x92422,a852)))+~P85(f784(f71(x92422),x92421))+P85(f784(f784(f347(x92422),f784(f73(x92422,f90(x92422)),x92421)),x92421))+~P85(f784(f784(f347(x92422),f784(f784(f90(x92422),f577(x92421,x92422)),f578(x92421,x92422))),f784(f784(f312(x92422),f577(x92421,x92422)),f784(f784(f312(x92422),f578(x92421,x92422)),f187(f869(x92422,a852))))))
% 11.41/11.19 [9248]~P101(x92482)+E(x92481,f187(f869(x92482,a852)))+~P85(f784(f71(x92482),x92481))+P85(f784(f784(f347(x92482),f13(x92482,f186(x92482),x92481)),x92481))+~P85(f784(f784(f347(x92482),f784(f784(f186(x92482),f468(x92481,x92482)),f469(x92481,x92482))),f784(f784(f312(x92482),f468(x92481,x92482)),f784(f784(f312(x92482),f469(x92481,x92482)),f187(f869(x92482,a852))))))
% 11.41/11.19 [9249]~P101(x92492)+E(x92491,f187(f869(x92492,a852)))+~P85(f784(f71(x92492),x92491))+P85(f784(f784(f347(x92492),f14(x92492,f246(x92492),x92491)),x92491))+~P85(f784(f784(f347(x92492),f784(f784(f246(x92492),f470(x92491,x92492)),f471(x92491,x92492))),f784(f784(f312(x92492),f470(x92491,x92492)),f784(f784(f312(x92492),f471(x92491,x92492)),f187(f869(x92492,a852))))))
% 11.41/11.19 [6431]~P81(x64312)+E(x64311,f2(x64312))+~E(f784(f784(f89(x64312),x64313),x64311),f2(x64312))+~P85(f784(f784(f242(x64312),f2(x64312)),x64313))+~P85(f784(f784(f242(x64312),f2(x64312)),x64311))
% 11.41/11.19 [6432]~P81(x64322)+E(x64321,f2(x64322))+~E(f784(f784(f89(x64322),x64321),x64323),f2(x64322))+~P85(f784(f784(f242(x64322),f2(x64322)),x64323))+~P85(f784(f784(f242(x64322),f2(x64322)),x64321))
% 11.41/11.19 [6633]~P85(f784(f784(f289(a859),x66332),x66331))+~P85(f784(f784(f289(a859),x66331),x66333))+P85(f784(f784(f289(a859),x66332),x66333))+P85(f784(f784(f289(a859),x66331),x66332))+P85(f784(f784(f289(a859),x66333),x66331))
% 11.41/11.19 [6814]~P85(f784(f784(f289(a859),x68141),x68143))+~P85(f784(f784(f289(a859),x68143),x68142))+~P85(f784(f784(f289(a859),x68142),x68141))+P85(f784(f784(f289(a859),x68141),x68142))+P85(f784(f784(f289(a859),x68143),x68141))
% 11.41/11.19 [7145]~P101(x71451)+E(f17(x71451,x71452),x71453)+~P85(f784(f71(x71451),x71452))+~P85(f784(f784(f242(x71451),x71453),f641(x71453,x71452,x71451)))+~P85(f784(f784(f347(x71451),x71453),x71452))
% 11.41/11.19 [7180]~P101(x71801)+~P15(x71801,x71802)+~P15(x71801,x71803)+P15(x71801,f784(f784(f130(x71801),x71802),x71803))+P85(f784(f784(f347(x71801),f776(x71803,x71802,x71801)),f784(f164(x71801),x71802)))
% 11.41/11.19 [7181]~P101(x71811)+~P15(x71811,x71812)+~P15(x71811,x71813)+P15(x71811,f784(f784(f130(x71811),x71812),x71813))+P85(f784(f784(f347(x71811),f777(x71813,x71812,x71811)),f784(f164(x71811),x71813)))
% 11.41/11.19 [7247]~P101(x72471)+E(f16(x72471,x72472),x72473)+~P85(f784(f71(x72471),x72472))+P85(f784(f784(f347(x72471),f643(x72473,x72472,x72471)),x72472))+~P85(f784(f784(f347(x72471),x72473),x72472))
% 11.41/11.19 [7248]~P101(x72481)+E(f17(x72481,x72482),x72483)+~P85(f784(f71(x72481),x72482))+P85(f784(f784(f347(x72481),f641(x72483,x72482,x72481)),x72482))+~P85(f784(f784(f347(x72481),x72483),x72482))
% 11.41/11.19 [7845]~P101(x78451)+E(f16(x78451,x78452),x78453)+~P85(f784(f71(x78451),x78452))+~P85(f784(f784(f347(x78451),x78453),x78452))+~P85(f784(f784(f242(x78451),f643(x78453,x78452,x78451)),x78453))
% 11.41/11.19 [8155]~P101(x81551)+~P15(x81551,x81552)+~P15(x81551,x81553)+P15(x81551,f784(f784(f130(x81551),x81552),x81553))+~P85(f784(f784(f242(x81551),f776(x81553,x81552,x81551)),f777(x81553,x81552,x81551)))
% 11.41/11.19 [8886]~P93(x88862)+E(x88861,f187(f869(x88862,a852)))+~E(f784(f784(f110(x88862),f784(x88863,f490(x88861,x88863,x88862))),f784(x88863,f491(x88861,x88863,x88862))),f784(x88863,f784(f784(f110(x88862),f490(x88861,x88863,x88862)),f491(x88861,x88863,x88862))))+E(f15(x88862,f784(f313(x88862,x88862,x88863),x88861)),f784(x88863,f15(x88862,x88861)))+~P85(f784(f71(x88862),x88861))
% 11.41/11.19 [8887]~P101(x88872)+E(x88871,f187(f869(x88872,a852)))+~E(f784(f784(f186(x88872),f784(x88873,f479(x88871,x88873,x88872))),f784(x88873,f487(x88871,x88873,x88872))),f784(x88873,f784(f784(f186(x88872),f479(x88871,x88873,x88872)),f487(x88871,x88873,x88872))))+E(f16(x88872,f784(f313(x88872,x88872,x88873),x88871)),f784(x88873,f16(x88872,x88871)))+~P85(f784(f71(x88872),x88871))
% 11.41/11.19 [8888]~P101(x88882)+E(x88881,f187(f869(x88882,a852)))+~E(f784(f784(f246(x88882),f784(x88883,f488(x88881,x88883,x88882))),f784(x88883,f489(x88881,x88883,x88882))),f784(x88883,f784(f784(f246(x88882),f488(x88881,x88883,x88882)),f489(x88881,x88883,x88882))))+E(f17(x88882,f784(f313(x88882,x88882,x88883),x88881)),f784(x88883,f17(x88882,x88881)))+~P85(f784(f71(x88882),x88881))
% 11.41/11.19 [8889]~P93(x88892)+E(x88891,f187(f869(x88892,a852)))+~E(f784(f784(f111(x88892),f784(x88893,f531(x88891,x88893,x88892))),f784(x88893,f532(x88891,x88893,x88892))),f784(x88893,f784(f784(f111(x88892),f531(x88891,x88893,x88892)),f532(x88891,x88893,x88892))))+E(f12(x88892,f784(f313(x88892,x88892,x88893),x88891)),f784(x88893,f12(x88892,x88891)))+~P85(f784(f71(x88892),x88891))
% 11.41/11.19 [8953]~P101(x89532)+E(x89531,f187(f869(x89532,a852)))+~E(f784(f784(f186(x89532),f784(x89533,f480(x89531,x89533,x89532))),f784(x89533,f482(x89531,x89533,x89532))),f784(x89533,f784(f784(f186(x89532),f480(x89531,x89533,x89532)),f482(x89531,x89533,x89532))))+E(f13(x89532,f186(x89532),f784(f313(x89532,x89532,x89533),x89531)),f784(x89533,f13(x89532,f186(x89532),x89531)))+~P85(f784(f71(x89532),x89531))
% 11.41/11.19 [8954]~P101(x89542)+E(x89541,f187(f869(x89542,a852)))+~E(f784(f784(f246(x89542),f784(x89543,f483(x89541,x89543,x89542))),f784(x89543,f484(x89541,x89543,x89542))),f784(x89543,f784(f784(f246(x89542),f483(x89541,x89543,x89542)),f484(x89541,x89543,x89542))))+E(f14(x89542,f246(x89542),f784(f313(x89542,x89542,x89543),x89541)),f784(x89543,f14(x89542,f246(x89542),x89541)))+~P85(f784(f71(x89542),x89541))
% 11.41/11.19 [6051]~P93(x60512)+E(x60511,f187(f869(x60512,a852)))+~P85(f784(f71(x60512),x60511))+E(f15(x60512,f784(f784(f312(x60512),x60513),x60511)),f784(f784(f110(x60512),x60513),f15(x60512,x60511)))+P85(f784(f784(f347(x60512),x60513),x60511))
% 11.41/11.19 [6052]~P101(x60522)+E(x60521,f187(f869(x60522,a852)))+~P85(f784(f71(x60522),x60521))+E(f16(x60522,f784(f784(f312(x60522),x60523),x60521)),f784(f784(f186(x60522),x60523),f16(x60522,x60521)))+P85(f784(f784(f347(x60522),x60523),x60521))
% 11.41/11.19 [6053]~P101(x60532)+E(x60531,f187(f869(x60532,a852)))+~P85(f784(f71(x60532),x60531))+E(f17(x60532,f784(f784(f312(x60532),x60533),x60531)),f784(f784(f246(x60532),x60533),f17(x60532,x60531)))+P85(f784(f784(f347(x60532),x60533),x60531))
% 11.41/11.19 [6054]~P93(x60542)+E(x60541,f187(f869(x60542,a852)))+~P85(f784(f71(x60542),x60541))+E(f12(x60542,f784(f784(f312(x60542),x60543),x60541)),f784(f784(f111(x60542),x60543),f12(x60542,x60541)))+P85(f784(f784(f347(x60542),x60543),x60541))
% 11.41/11.19 [6448]~P65(x64482)+E(x64481,f187(f869(x64482,a852)))+~P85(f784(f71(x64482),x64481))+E(f784(f73(x64482,f90(x64482)),f784(f784(f312(x64482),x64483),x64481)),f784(f784(f90(x64482),x64483),f784(f73(x64482,f90(x64482)),x64481)))+P85(f784(f784(f347(x64482),x64483),x64481))
% 11.41/11.19 [6537]~P101(x65372)+E(x65371,f187(f869(x65372,a852)))+~P85(f784(f71(x65372),x65371))+E(f13(x65372,f186(x65372),f784(f784(f312(x65372),x65373),x65371)),f784(f784(f186(x65372),x65373),f13(x65372,f186(x65372),x65371)))+P85(f784(f784(f347(x65372),x65373),x65371))
% 11.41/11.19 [6538]~P101(x65382)+E(x65381,f187(f869(x65382,a852)))+~P85(f784(f71(x65382),x65381))+E(f14(x65382,f246(x65382),f784(f784(f312(x65382),x65383),x65381)),f784(f784(f246(x65382),x65383),f14(x65382,f246(x65382),x65381)))+P85(f784(f784(f347(x65382),x65383),x65381))
% 11.41/11.19 [6984]~P101(x69842)+E(f784(f784(f246(x69842),f17(x69842,x69841)),f17(x69842,x69843)),f17(x69842,x69843))+E(x69841,f187(f869(x69842,a852)))+~P85(f784(f71(x69842),x69843))+~P85(f784(f784(f242(f869(x69842,a852)),x69841),x69843))
% 11.41/11.19 [6985]~P101(x69852)+E(f784(f784(f186(x69852),f16(x69852,x69851)),f16(x69852,x69853)),f16(x69852,x69853))+E(x69851,f187(f869(x69852,a852)))+~P85(f784(f71(x69852),x69853))+~P85(f784(f784(f242(f869(x69852,a852)),x69851),x69853))
% 11.41/11.19 [6986]~P93(x69862)+E(f784(f784(f110(x69862),f15(x69862,x69861)),f15(x69862,x69863)),f15(x69862,x69863))+E(x69861,f187(f869(x69862,a852)))+~P85(f784(f71(x69862),x69863))+~P85(f784(f784(f242(f869(x69862,a852)),x69861),x69863))
% 11.41/11.19 [6987]~P93(x69872)+E(f784(f784(f111(x69872),f12(x69872,x69871)),f12(x69872,x69873)),f12(x69872,x69873))+E(x69871,f187(f869(x69872,a852)))+~P85(f784(f71(x69872),x69873))+~P85(f784(f784(f242(f869(x69872,a852)),x69871),x69873))
% 11.41/11.19 [7303]~P101(x73032)+E(x73031,f187(f869(x73032,a852)))+~P85(f784(f71(x73032),x73033))+P85(f784(f784(f242(x73032),f16(x73032,x73031)),f16(x73032,x73033)))+~P85(f784(f784(f242(f869(x73032,a852)),x73031),x73033))
% 11.41/11.19 [7304]~P101(x73042)+E(x73041,f187(f869(x73042,a852)))+~P85(f784(f71(x73042),x73043))+P85(f784(f784(f242(x73042),f17(x73042,x73043)),f17(x73042,x73041)))+~P85(f784(f784(f242(f869(x73042,a852)),x73041),x73043))
% 11.41/11.19 [7366]~P93(x73661)+E(f15(x73661,x73662),x73663)+~P85(f784(f71(x73661),x73662))+~E(f784(f784(f3(f869(x73661,a852)),x73662),f784(f784(f312(x73661),x73663),f187(f869(x73661,a852)))),f187(f869(x73661,a852)))+~P85(f784(f784(f347(x73661),x73663),x73662))
% 11.41/11.19 [7367]~P101(x73671)+E(f16(x73671,x73672),x73673)+~P85(f784(f71(x73671),x73672))+~E(f784(f784(f3(f869(x73671,a852)),x73672),f784(f784(f312(x73671),x73673),f187(f869(x73671,a852)))),f187(f869(x73671,a852)))+~P85(f784(f784(f347(x73671),x73673),x73672))
% 11.41/11.19 [7368]~P101(x73681)+E(f17(x73681,x73682),x73683)+~P85(f784(f71(x73681),x73682))+~E(f784(f784(f3(f869(x73681,a852)),x73682),f784(f784(f312(x73681),x73683),f187(f869(x73681,a852)))),f187(f869(x73681,a852)))+~P85(f784(f784(f347(x73681),x73683),x73682))
% 11.41/11.19 [7369]~P93(x73691)+E(f12(x73691,x73692),x73693)+~P85(f784(f71(x73691),x73692))+~E(f784(f784(f3(f869(x73691,a852)),x73692),f784(f784(f312(x73691),x73693),f187(f869(x73691,a852)))),f187(f869(x73691,a852)))+~P85(f784(f784(f347(x73691),x73693),x73692))
% 11.41/11.19 [7468]~P101(x74681)+E(f13(x74681,f186(x74681),x74682),x74683)+~P85(f784(f71(x74681),x74682))+~E(f784(f784(f3(f869(x74681,a852)),x74682),f784(f784(f312(x74681),x74683),f187(f869(x74681,a852)))),f187(f869(x74681,a852)))+~P85(f784(f784(f347(x74681),x74683),x74682))
% 11.41/11.19 [7469]~P101(x74691)+E(f14(x74691,f246(x74691),x74692),x74693)+~P85(f784(f71(x74691),x74692))+~E(f784(f784(f3(f869(x74691,a852)),x74692),f784(f784(f312(x74691),x74693),f187(f869(x74691,a852)))),f187(f869(x74691,a852)))+~P85(f784(f784(f347(x74691),x74693),x74692))
% 11.41/11.19 [7506]~P101(x75062)+E(x75061,f187(f869(x75062,a852)))+~P85(f784(f71(x75062),x75061))+~P85(f784(f784(f243(x75062),x75063),f563(x75063,x75061,x75062)))+P85(f784(f784(f243(x75062),x75063),f784(f73(x75062,f246(x75062)),x75061)))
% 11.41/11.19 [7507]~P101(x75072)+E(x75071,f187(f869(x75072,a852)))+~P85(f784(f71(x75072),x75071))+~P85(f784(f784(f242(x75072),x75073),f564(x75073,x75071,x75072)))+P85(f784(f784(f242(x75072),x75073),f784(f73(x75072,f246(x75072)),x75071)))
% 11.41/11.19 [7508]~P99(x75082)+E(x75081,f187(f869(x75082,a852)))+~P85(f784(f71(x75082),x75081))+~P85(f784(f784(f242(x75082),x75083),f565(x75083,x75081,x75082)))+P85(f784(f784(f242(x75082),x75083),f784(f73(x75082,f111(x75082)),x75081)))
% 11.41/11.19 [7596]~P99(x75962)+E(x75961,f187(f869(x75962,a852)))+~P85(f784(f71(x75962),x75961))+P85(f784(f784(f347(x75962),f565(x75963,x75961,x75962)),x75961))+P85(f784(f784(f242(x75962),x75963),f784(f73(x75962,f111(x75962)),x75961)))
% 11.41/11.19 [7597]~P101(x75972)+E(x75971,f187(f869(x75972,a852)))+~P85(f784(f71(x75972),x75971))+P85(f784(f784(f347(x75972),f564(x75973,x75971,x75972)),x75971))+P85(f784(f784(f242(x75972),x75973),f784(f73(x75972,f246(x75972)),x75971)))
% 11.41/11.19 [7598]~P101(x75982)+E(x75981,f187(f869(x75982,a852)))+~P85(f784(f71(x75982),x75981))+P85(f784(f784(f347(x75982),f563(x75983,x75981,x75982)),x75981))+P85(f784(f784(f243(x75982),x75983),f784(f73(x75982,f246(x75982)),x75981)))
% 11.41/11.19 [7717]~P101(x77172)+E(x77171,f187(f869(x77172,a852)))+E(f784(f784(f246(x77172),f14(x77172,f246(x77172),x77171)),f14(x77172,f246(x77172),x77173)),f14(x77172,f246(x77172),x77173))+~P85(f784(f71(x77172),x77173))+~P85(f784(f784(f242(f869(x77172,a852)),x77171),x77173))
% 11.41/11.19 [7718]~P101(x77182)+E(x77181,f187(f869(x77182,a852)))+E(f784(f784(f186(x77182),f13(x77182,f186(x77182),x77181)),f13(x77182,f186(x77182),x77183)),f13(x77182,f186(x77182),x77183))+~P85(f784(f71(x77182),x77183))+~P85(f784(f784(f242(f869(x77182,a852)),x77181),x77183))
% 11.41/11.19 [7919]~E(f687(x79191,x79193,x79192),f688(x79191,x79193,x79192))+~E(f784(f50(x79192),f689(x79191,x79193,x79192)),x79191)+E(f784(f784(f90(a859),x79191),f784(f50(f869(x79192,a852)),x79193)),f784(f50(x79192),f52(f869(x79192,a852),x79193)))+~P85(f784(f71(x79192),f52(f869(x79192,a852),x79193)))+~P85(f784(f71(f869(x79192,a852)),x79193))
% 11.41/11.19 [8093]~P101(x80932)+E(x80931,f187(f869(x80932,a852)))+~P85(f784(f71(x80932),x80933))+P85(f784(f784(f242(x80932),f784(f73(x80932,f246(x80932)),x80933)),f784(f73(x80932,f246(x80932)),x80931)))+~P85(f784(f784(f242(f869(x80932,a852)),x80931),x80933))
% 11.41/11.19 [8396]~E(f687(x83961,x83963,x83962),f688(x83961,x83963,x83962))+E(f784(f784(f90(a859),x83961),f784(f50(f869(x83962,a852)),x83963)),f784(f50(x83962),f52(f869(x83962,a852),x83963)))+P85(f784(f784(f347(f869(x83962,a852)),f689(x83961,x83963,x83962)),x83963))+~P85(f784(f71(x83962),f52(f869(x83962,a852),x83963)))+~P85(f784(f71(f869(x83962,a852)),x83963))
% 11.41/11.19 [8420]~E(f784(f50(x84202),f689(x84201,x84203,x84202)),x84201)+E(f784(f784(f90(a859),x84201),f784(f50(f869(x84202,a852)),x84203)),f784(f50(x84202),f52(f869(x84202,a852),x84203)))+P85(f784(f784(f347(f869(x84202,a852)),f688(x84201,x84203,x84202)),x84203))+~P85(f784(f71(x84202),f52(f869(x84202,a852),x84203)))+~P85(f784(f71(f869(x84202,a852)),x84203))
% 11.41/11.19 [8421]~E(f784(f50(x84212),f689(x84211,x84213,x84212)),x84211)+E(f784(f784(f90(a859),x84211),f784(f50(f869(x84212,a852)),x84213)),f784(f50(x84212),f52(f869(x84212,a852),x84213)))+P85(f784(f784(f347(f869(x84212,a852)),f687(x84211,x84213,x84212)),x84213))+~P85(f784(f71(x84212),f52(f869(x84212,a852),x84213)))+~P85(f784(f71(f869(x84212,a852)),x84213))
% 11.41/11.19 [8450]~E(f784(f50(x84502),f689(x84501,x84503,x84502)),x84501)+~E(f784(f784(f111(f869(x84502,a852)),f688(x84501,x84503,x84502)),f687(x84501,x84503,x84502)),f187(f869(x84502,a852)))+E(f784(f784(f90(a859),x84501),f784(f50(f869(x84502,a852)),x84503)),f784(f50(x84502),f52(f869(x84502,a852),x84503)))+~P85(f784(f71(f869(x84502,a852)),x84503))+~P85(f784(f71(x84502),f52(f869(x84502,a852),x84503)))
% 11.41/11.19 [8676]E(f784(f784(f90(a859),x86761),f784(f50(f869(x86762,a852)),x86763)),f784(f50(x86762),f52(f869(x86762,a852),x86763)))+P85(f784(f784(f347(f869(x86762,a852)),f689(x86761,x86763,x86762)),x86763))+P85(f784(f784(f347(f869(x86762,a852)),f688(x86761,x86763,x86762)),x86763))+~P85(f784(f71(f869(x86762,a852)),x86763))+~P85(f784(f71(x86762),f52(f869(x86762,a852),x86763)))
% 11.41/11.19 [8677]E(f784(f784(f90(a859),x86771),f784(f50(f869(x86772,a852)),x86773)),f784(f50(x86772),f52(f869(x86772,a852),x86773)))+P85(f784(f784(f347(f869(x86772,a852)),f689(x86771,x86773,x86772)),x86773))+P85(f784(f784(f347(f869(x86772,a852)),f687(x86771,x86773,x86772)),x86773))+~P85(f784(f71(f869(x86772,a852)),x86773))+~P85(f784(f71(x86772),f52(f869(x86772,a852),x86773)))
% 11.41/11.19 [8702]~E(f784(f784(f111(f869(x87022,a852)),f688(x87021,x87023,x87022)),f687(x87021,x87023,x87022)),f187(f869(x87022,a852)))+E(f784(f784(f90(a859),x87021),f784(f50(f869(x87022,a852)),x87023)),f784(f50(x87022),f52(f869(x87022,a852),x87023)))+~P85(f784(f71(f869(x87022,a852)),x87023))+P85(f784(f784(f347(f869(x87022,a852)),f689(x87021,x87023,x87022)),x87023))+~P85(f784(f71(x87022),f52(f869(x87022,a852),x87023)))
% 11.41/11.19 [8932]~P92(x89322)+E(x89321,f187(f869(x89322,a852)))+~E(f784(f784(f90(x89322),f784(x89323,f576(x89321,x89323,x89322))),f784(x89323,f579(x89321,x89323,x89322))),f784(x89323,f784(f784(f90(x89322),f576(x89321,x89323,x89322)),f579(x89321,x89323,x89322))))+~P85(f784(f71(x89322),x89321))+E(f784(f73(x89322,f90(x89322)),f784(f313(x89322,x89322,x89323),x89321)),f784(x89323,f784(f73(x89322,f90(x89322)),x89321)))
% 11.41/11.19 [9807]P85(f784(f784(x98071,x98072),x98073))+P85(f784(f784(f243(a1),f835(x98071,x98073,x98072)),f836(x98071,x98073,x98072)))+P85(f784(f784(f242(a1),f836(x98071,x98073,x98072)),f2(a1)))+P85(f784(f784(x98071,f835(x98071,x98073,x98072)),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f836(x98071,x98073,x98072))))+~P85(f784(f334(f868(a1,a1),a70),f784(f784(f251(a1,a1),x98072),x98073)))
% 11.41/11.19 [9813]P85(f784(f784(x98131,x98132),x98133))+P85(f784(f784(f242(a1),f834(x98131,x98133,x98132)),f2(a1)))+P85(f784(f784(x98131,f833(x98131,x98133,x98132)),f784(f784(f90(a1),f784(f113(a1),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f834(x98131,x98133,x98132))))+P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),f833(x98131,x98133,x98132)),f834(x98131,x98133,x98132))))+~P85(f784(f334(f868(a1,a1),a67),f784(f784(f251(a1,a1),x98132),x98133)))
% 11.41/11.19 [7890]~P113(x78901)+~P85(f784(f784(f242(x78901),x78902),f87(x78901)))+~P85(f784(f784(f242(x78901),f2(x78901)),x78902))+~P85(f784(f784(f242(x78901),f2(x78901)),x78903))+P85(f784(f784(f242(x78901),f784(f784(f90(x78901),x78902),x78903)),x78903))
% 11.41/11.19 [7891]~P113(x78911)+~P85(f784(f784(f242(x78911),x78913),f87(x78911)))+~P85(f784(f784(f242(x78911),f2(x78911)),x78913))+~P85(f784(f784(f242(x78911),f2(x78911)),x78912))+P85(f784(f784(f242(x78911),f784(f784(f90(x78911),x78912),x78913)),x78912))
% 11.41/11.19 [8236]~P101(x82362)+E(x82361,f187(f869(x82362,a852)))+~P85(f784(f71(x82362),x82361))+P85(f784(f784(f243(x82362),f571(x82363,x82361,x82362)),x82363))+~P85(f784(f784(f243(x82362),f784(f73(x82362,f246(x82362)),x82361)),x82363))
% 11.41/11.19 [8237]~P101(x82372)+E(x82371,f187(f869(x82372,a852)))+~P85(f784(f71(x82372),x82371))+P85(f784(f784(f242(x82372),f572(x82373,x82371,x82372)),x82373))+~P85(f784(f784(f242(x82372),f784(f73(x82372,f246(x82372)),x82371)),x82373))
% 11.41/11.19 [8238]~P101(x82382)+E(x82381,f187(f869(x82382,a852)))+~P85(f784(f71(x82382),x82381))+P85(f784(f784(f347(x82382),f572(x82383,x82381,x82382)),x82381))+~P85(f784(f784(f242(x82382),f784(f73(x82382,f246(x82382)),x82381)),x82383))
% 11.41/11.19 [8239]~P101(x82392)+E(x82391,f187(f869(x82392,a852)))+~P85(f784(f71(x82392),x82391))+P85(f784(f784(f347(x82392),f571(x82393,x82391,x82392)),x82391))+~P85(f784(f784(f243(x82392),f784(f73(x82392,f246(x82392)),x82391)),x82393))
% 11.41/11.19 [8325]~P85(f784(x83251,x83253))+P85(f784(x83251,f363(x83251,x83252)))+P85(f784(x83251,f358(x83251,x83252)))+~P85(f784(f784(f243(a1),f2(a1)),x83252))+P85(f784(x83251,f784(f784(f3(a1),f358(x83251,x83252)),f784(f784(f90(a1),f364(x83251,x83252)),x83252))))
% 11.41/11.19 [8541]~P85(f784(x85411,x85413))+P85(f784(x85411,f358(x85411,x85412)))+~P85(f784(f784(f243(a1),f2(a1)),x85412))+P85(f784(f784(f347(a1),f363(x85411,x85412)),f305(a1,f87(a1),x85412)))+P85(f784(x85411,f784(f784(f3(a1),f358(x85411,x85412)),f784(f784(f90(a1),f364(x85411,x85412)),x85412))))
% 11.41/11.19 [8720]~P85(f784(x87201,x87203))+~P85(f784(x87201,f358(x87201,x87202)))+P85(f784(x87201,f363(x87201,x87202)))+~P85(f784(f784(f243(a1),f2(a1)),x87202))+~P85(f784(x87201,f784(f784(f3(a1),f358(x87201,x87202)),f784(f784(f90(a1),f364(x87201,x87202)),x87202))))
% 11.41/11.19 [8826]~P85(f784(x88261,x88263))+~P85(f784(x88261,f358(x88261,x88262)))+~P85(f784(f784(f243(a1),f2(a1)),x88262))+P85(f784(f784(f347(a1),f363(x88261,x88262)),f305(a1,f87(a1),x88262)))+~P85(f784(x88261,f784(f784(f3(a1),f358(x88261,x88262)),f784(f784(f90(a1),f364(x88261,x88262)),x88262))))
% 11.41/11.19 [8639]~P93(x86391)+~P85(f784(f71(x86391),x86392))+E(f784(f784(f3(f869(x86391,a852)),x86392),f784(f784(f312(x86391),x86393),f187(f869(x86391,a852)))),f187(f869(x86391,a852)))+~P85(f784(f784(f347(x86391),x86393),x86392))+E(f784(f784(f110(x86391),x86393),f15(x86391,f784(f784(f3(f869(x86391,a852)),x86392),f784(f784(f312(x86391),x86393),f187(f869(x86391,a852)))))),f15(x86391,x86392))
% 11.41/11.19 [8640]~P101(x86401)+~P85(f784(f71(x86401),x86402))+E(f784(f784(f3(f869(x86401,a852)),x86402),f784(f784(f312(x86401),x86403),f187(f869(x86401,a852)))),f187(f869(x86401,a852)))+~P85(f784(f784(f347(x86401),x86403),x86402))+E(f784(f784(f186(x86401),x86403),f16(x86401,f784(f784(f3(f869(x86401,a852)),x86402),f784(f784(f312(x86401),x86403),f187(f869(x86401,a852)))))),f16(x86401,x86402))
% 11.41/11.19 [8641]~P101(x86411)+~P85(f784(f71(x86411),x86412))+E(f784(f784(f3(f869(x86411,a852)),x86412),f784(f784(f312(x86411),x86413),f187(f869(x86411,a852)))),f187(f869(x86411,a852)))+~P85(f784(f784(f347(x86411),x86413),x86412))+E(f784(f784(f246(x86411),x86413),f17(x86411,f784(f784(f3(f869(x86411,a852)),x86412),f784(f784(f312(x86411),x86413),f187(f869(x86411,a852)))))),f17(x86411,x86412))
% 11.41/11.19 [8642]~P93(x86421)+~P85(f784(f71(x86421),x86422))+E(f784(f784(f3(f869(x86421,a852)),x86422),f784(f784(f312(x86421),x86423),f187(f869(x86421,a852)))),f187(f869(x86421,a852)))+~P85(f784(f784(f347(x86421),x86423),x86422))+E(f784(f784(f111(x86421),x86423),f12(x86421,f784(f784(f3(f869(x86421,a852)),x86422),f784(f784(f312(x86421),x86423),f187(f869(x86421,a852)))))),f12(x86421,x86422))
% 11.41/11.19 [8697]~P101(x86971)+~P85(f784(f71(x86971),x86972))+E(f784(f784(f3(f869(x86971,a852)),x86972),f784(f784(f312(x86971),x86973),f187(f869(x86971,a852)))),f187(f869(x86971,a852)))+~P85(f784(f784(f347(x86971),x86973),x86972))+E(f784(f784(f186(x86971),x86973),f13(x86971,f186(x86971),f784(f784(f3(f869(x86971,a852)),x86972),f784(f784(f312(x86971),x86973),f187(f869(x86971,a852)))))),f13(x86971,f186(x86971),x86972))
% 11.41/11.19 [8698]~P101(x86981)+~P85(f784(f71(x86981),x86982))+E(f784(f784(f3(f869(x86981,a852)),x86982),f784(f784(f312(x86981),x86983),f187(f869(x86981,a852)))),f187(f869(x86981,a852)))+~P85(f784(f784(f347(x86981),x86983),x86982))+E(f784(f784(f246(x86981),x86983),f14(x86981,f246(x86981),f784(f784(f3(f869(x86981,a852)),x86982),f784(f784(f312(x86981),x86983),f187(f869(x86981,a852)))))),f14(x86981,f246(x86981),x86982))
% 11.41/11.19 [8708]~P101(x87081)+~P85(f784(f71(x87081),x87083))+~P85(f784(f71(x87081),x87082))+E(f784(f784(f111(f869(x87081,a852)),x87082),x87083),f187(f869(x87081,a852)))+E(f784(f784(f246(x87081),f17(x87081,f784(f784(f110(f869(x87081,a852)),x87082),x87083))),f17(x87081,f784(f784(f111(f869(x87081,a852)),x87082),x87083))),f784(f784(f246(x87081),f17(x87081,x87082)),f17(x87081,x87083)))
% 11.41/11.19 [8709]~P101(x87091)+~P85(f784(f71(x87091),x87093))+~P85(f784(f71(x87091),x87092))+E(f784(f784(f111(f869(x87091,a852)),x87092),x87093),f187(f869(x87091,a852)))+E(f784(f784(f186(x87091),f16(x87091,f784(f784(f110(f869(x87091,a852)),x87092),x87093))),f16(x87091,f784(f784(f111(f869(x87091,a852)),x87092),x87093))),f784(f784(f186(x87091),f16(x87091,x87092)),f16(x87091,x87093)))
% 11.41/11.19 [8710]~P93(x87101)+~P85(f784(f71(x87101),x87103))+~P85(f784(f71(x87101),x87102))+E(f784(f784(f111(f869(x87101,a852)),x87102),x87103),f187(f869(x87101,a852)))+E(f784(f784(f110(x87101),f15(x87101,f784(f784(f110(f869(x87101,a852)),x87102),x87103))),f15(x87101,f784(f784(f111(f869(x87101,a852)),x87102),x87103))),f784(f784(f110(x87101),f15(x87101,x87102)),f15(x87101,x87103)))
% 11.41/11.19 [8711]~P93(x87111)+~P85(f784(f71(x87111),x87113))+~P85(f784(f71(x87111),x87112))+E(f784(f784(f111(f869(x87111,a852)),x87112),x87113),f187(f869(x87111,a852)))+E(f784(f784(f111(x87111),f12(x87111,f784(f784(f110(f869(x87111,a852)),x87112),x87113))),f12(x87111,f784(f784(f111(f869(x87111,a852)),x87112),x87113))),f784(f784(f111(x87111),f12(x87111,x87112)),f12(x87111,x87113)))
% 11.41/11.19 [8906]~P101(x89061)+~P85(f784(f71(x89061),x89063))+~P85(f784(f71(x89061),x89062))+E(f784(f784(f111(f869(x89061,a852)),x89062),x89063),f187(f869(x89061,a852)))+E(f784(f784(f246(x89061),f14(x89061,f246(x89061),f784(f784(f110(f869(x89061,a852)),x89062),x89063))),f14(x89061,f246(x89061),f784(f784(f111(f869(x89061,a852)),x89062),x89063))),f784(f784(f246(x89061),f14(x89061,f246(x89061),x89062)),f14(x89061,f246(x89061),x89063)))
% 11.41/11.19 [8907]~P101(x89071)+~P85(f784(f71(x89071),x89073))+~P85(f784(f71(x89071),x89072))+E(f784(f784(f111(f869(x89071,a852)),x89072),x89073),f187(f869(x89071,a852)))+E(f784(f784(f186(x89071),f13(x89071,f186(x89071),f784(f784(f110(f869(x89071,a852)),x89072),x89073))),f13(x89071,f186(x89071),f784(f784(f111(f869(x89071,a852)),x89072),x89073))),f784(f784(f186(x89071),f13(x89071,f186(x89071),x89072)),f13(x89071,f186(x89071),x89073)))
% 11.41/11.19 [9650]~P120(x96503)+E(x96501,x96502)+~P85(f784(f784(f242(x96503),f2(x96503)),x96502))+~P85(f784(f784(f242(x96503),f2(x96503)),x96501))+~E(f784(f784(f252(x96503),x96501),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))),f784(f784(f252(x96503),x96502),f784(f113(a859),f784(f784(f89(a1),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)),f784(f784(f3(a1),f784(f784(f89(a1),a92),a92)),a106)))))
% 11.41/11.19 [5002]~P90(x50021)+~P59(x50021)+~E(x50024,f2(x50021))+~E(f784(f113(x50021),x50022),f2(x50021))+E(f784(f113(x50021),x50022),f784(f784(f293(x50021),x50023),x50024))
% 11.41/11.19 [5003]~P90(x50031)+~P59(x50031)+~E(x50033,f2(x50031))+~E(f784(f113(x50031),x50034),f2(x50031))+E(f784(f784(f293(x50031),x50032),x50033),f784(f113(x50031),x50034))
% 11.41/11.19 [5097]~P90(x50972)+~P59(x50972)+~E(x50971,f2(x50972))+~E(f784(f113(x50972),x50974),f2(x50972))+E(x50971,f784(f784(f293(x50972),x50973),f784(f113(x50972),x50974)))
% 11.41/11.19 [5098]~P90(x50981)+~P59(x50981)+~E(x50984,f2(x50981))+~E(f784(f113(x50981),x50983),f2(x50981))+E(f784(f784(f293(x50981),x50982),f784(f113(x50981),x50983)),x50984)
% 11.41/11.19 [5122]~P90(x51221)+~P59(x51221)+~E(x51223,f2(x51221))+E(f784(f113(x51221),x51222),f2(x51221))+~E(f784(f113(x51221),x51222),f784(f784(f293(x51221),x51224),x51223))
% 11.41/11.19 [5123]~P90(x51231)+~P59(x51231)+~E(x51233,f2(x51231))+E(f784(f113(x51231),x51232),f2(x51231))+~E(f784(f784(f293(x51231),x51234),x51233),f784(f113(x51231),x51232))
% 11.41/11.19 [5280]~P90(x52802)+~P59(x52802)+E(x52801,f2(x52802))+~E(f784(f113(x52802),x52803),f2(x52802))+~E(x52801,f784(f784(f293(x52802),x52804),f784(f113(x52802),x52803)))
% 11.41/11.19 [5281]~P90(x52812)+~P59(x52812)+E(x52811,f2(x52812))+~E(f784(f113(x52812),x52813),f2(x52812))+~E(f784(f784(f293(x52812),x52814),f784(f113(x52812),x52813)),x52811)
% 11.41/11.19 [5501]~P90(x55012)+~P59(x55012)+~E(x55011,f2(x55012))+E(x55011,f784(f784(f293(x55012),x55013),f784(f113(x55012),x55014)))+~E(f784(f784(f90(x55012),x55011),f784(f113(x55012),x55014)),x55013)
% 11.41/11.19 [5502]~P90(x55021)+~P59(x55021)+~E(x55024,f2(x55021))+~E(x55022,f784(f784(f90(x55021),x55024),f784(f113(x55021),x55023)))+E(f784(f784(f293(x55021),x55022),f784(f113(x55021),x55023)),x55024)
% 11.41/11.19 [5564]~P90(x55641)+~P59(x55641)+E(f784(f113(x55641),x55642),f2(x55641))+~E(f784(f784(f293(x55641),x55643),f784(f113(x55641),x55642)),x55644)+E(x55643,f784(f784(f90(x55641),x55644),f784(f113(x55641),x55642)))
% 11.41/11.19 [5565]~P90(x55651)+~P59(x55651)+E(f784(f113(x55651),x55652),f2(x55651))+~E(f784(f784(f90(x55651),x55653),f784(f113(x55651),x55652)),x55654)+E(x55653,f784(f784(f293(x55651),x55654),f784(f113(x55651),x55652)))
% 11.41/11.19 [5566]~P90(x55661)+~P59(x55661)+E(f784(f113(x55661),x55662),f2(x55661))+~E(x55663,f784(f784(f293(x55661),x55664),f784(f113(x55661),x55662)))+E(f784(f784(f90(x55661),x55663),f784(f113(x55661),x55662)),x55664)
% 11.41/11.19 [5567]~P90(x55671)+~P59(x55671)+E(f784(f113(x55671),x55672),f2(x55671))+~E(x55673,f784(f784(f90(x55671),x55674),f784(f113(x55671),x55672)))+E(f784(f784(f293(x55671),x55673),f784(f113(x55671),x55672)),x55674)
% 11.41/11.19 [5775]~P4(x57752)+E(x57751,f2(x57752))+~E(f784(f784(f51(x57752),x57753),x57751),x57754)+E(x57753,f784(f784(f90(x57752),x57754),x57751))+~P85(f784(f784(f289(x57752),x57751),x57753))
% 11.41/11.19 [5776]~P4(x57762)+E(x57761,f2(x57762))+~E(x57763,f784(f784(f90(x57762),x57764),x57761))+E(f784(f784(f51(x57762),x57763),x57761),x57764)+~P85(f784(f784(f289(x57762),x57761),x57763))
% 11.41/11.19 [6235]E(f416(x62351,x62352,x62353),x62354)+E(f784(x62351,x62354),f2(a859))+~E(f784(f784(f8(x62353,a859),x62351),x62352),f87(a859))+~P85(f784(f71(x62353),x62352))+~P85(f784(f784(f347(x62353),x62354),x62352))
% 11.41/11.19 [6303]E(f418(x63031,x63032,x63033),x63034)+E(f784(x63031,x63034),f2(a859))+~E(f784(f784(f8(x63033,a859),x63031),x63032),f784(a160,f2(a859)))+~P85(f784(f71(x63033),x63032))+~P85(f784(f784(f347(x63033),x63034),x63032))
% 11.41/11.19 [6417]~P101(x64171)+~P6(x64171)+P85(f784(f784(f243(x64171),x64172),f52(x64171,x64173)))+~P85(f784(f784(f347(x64171),x64174),x64173))+~P85(f784(f784(f243(x64171),x64172),x64174))
% 11.41/11.19 [6594]~P101(x65941)+~P6(x65941)+~P85(f784(f784(f347(x65941),x65944),x65942))+P85(f784(f784(f243(x65941),f53(x65941,x65942)),x65943))+~P85(f784(f784(f243(x65941),x65944),x65943))
% 11.41/11.19 [6869]~P120(x68693)+E(x68691,x68692)+~E(f784(f784(f252(x68693),x68691),f784(a160,x68694)),f784(f784(f252(x68693),x68692),f784(a160,x68694)))+~P85(f784(f784(f242(x68693),f2(x68693)),x68692))+~P85(f784(f784(f242(x68693),f2(x68693)),x68691))
% 11.41/11.19 [7078]~E(f420(x70782,x70783,x70781,x70784),x70784)+~E(f784(x70782,x70784),f87(a859))+E(f784(f784(f8(x70781,a859),x70782),x70783),f87(a859))+~P85(f784(f71(x70781),x70783))+~P85(f784(f784(f347(x70781),x70784),x70783))
% 11.41/11.19 [7085]~P86(x70854)+~P129(x70854)+E(f784(x70851,f464(x70851,x70852,x70853,x70854)),f2(x70854))+~E(f784(f784(f11(x70853,x70854),x70851),x70852),f2(x70854))+~P85(f784(f71(x70853),x70852))
% 11.41/11.19 [7167]~E(f419(x71672,x71673,x71671,x71674),x71674)+~E(f784(x71672,x71674),f784(a160,f2(a859)))+E(f784(f784(f8(x71671,a859),x71672),x71673),f784(a160,f2(a859)))+~P85(f784(f71(x71671),x71673))+~P85(f784(f784(f347(x71671),x71674),x71673))
% 11.41/11.19 [7929]~E(f784(x79292,x79294),f87(a859))+~E(f784(x79292,f420(x79292,x79293,x79291,x79294)),f2(a859))+E(f784(f784(f8(x79291,a859),x79292),x79293),f87(a859))+~P85(f784(f71(x79291),x79293))+~P85(f784(f784(f347(x79291),x79294),x79293))
% 11.41/11.19 [7974]~E(f784(x79742,x79744),f784(a160,f2(a859)))+~E(f784(x79742,f419(x79742,x79743,x79741,x79744)),f2(a859))+E(f784(f784(f8(x79741,a859),x79742),x79743),f784(a160,f2(a859)))+~P85(f784(f71(x79741),x79743))+~P85(f784(f784(f347(x79741),x79744),x79743))
% 11.41/11.19 [8052]~P139(x80522)+~P115(x80522)+~P85(f784(x80521,x80524))+~P85(f784(f784(f289(x80522),x80523),f784(f784(f89(x80522),x80524),f2(x80522))))+P85(f784(x80521,f784(f784(f90(x80522),x80523),f846(x80523,x80521,x80522))))
% 11.41/11.19 [8544]E(x85441,x85442)+E(f784(f784(f89(a1),f441(x85443,x85442,x85444,x85441)),f442(x85443,x85442,x85444,x85441)),x85441)+~E(f784(f784(f3(a1),x85441),x85444),x85442)+~P85(f784(f784(f243(a1),f2(a1)),x85444))+~P85(f784(f784(f347(a1),x85442),x85443))
% 11.41/11.19 [8545]E(x85451,x85452)+E(f784(f784(f3(a1),f443(x85453,x85452,x85454,x85451)),f444(x85453,x85452,x85454,x85451)),x85451)+~E(f784(f784(f89(a1),x85451),x85454),x85452)+~P85(f784(f784(f243(a1),f2(a1)),x85454))+~P85(f784(f784(f347(a1),x85452),x85453))
% 11.41/11.19 [8707]E(f784(x87071,f826(x87072,x87071,x87073,x87074)),x87072)+P85(f784(f784(f242(a859),x87074),f827(x87072,x87071,x87073,x87074)))+~P85(f784(f784(f242(a1),x87072),f784(x87071,x87073)))+~P85(f784(f784(f243(a859),x87074),x87073))+~P85(f784(f784(f242(a1),f784(x87071,x87074)),x87072))
% 11.41/11.19 [8724]~P86(x87244)+~P129(x87244)+~E(f784(f784(f11(x87241,x87244),x87242),x87243),f2(x87244))+~P85(f784(f71(x87241),x87243))+P85(f784(f784(f347(x87241),f464(x87242,x87243,x87241,x87244)),x87243))
% 11.41/11.19 [8757]~E(f784(x87572,x87574),f87(a859))+E(f784(f784(f8(x87571,a859),x87572),x87573),f87(a859))+~P85(f784(f71(x87571),x87573))+~P85(f784(f784(f347(x87571),x87574),x87573))+P85(f784(f784(f347(x87571),f420(x87572,x87573,x87571,x87574)),x87573))
% 11.41/11.19 [8766]E(x87661,x87662)+~E(f784(f784(f89(a1),x87662),x87664),x87661)+~P85(f784(f784(f243(a1),f2(a1)),x87664))+~P85(f784(f784(f347(a1),x87661),x87663))+P85(f784(f784(f347(a1),f443(x87663,x87661,x87664,x87662)),x87663))
% 11.41/11.19 [8767]E(x87671,x87672)+~E(f784(f784(f3(a1),x87672),x87674),x87671)+~P85(f784(f784(f243(a1),f2(a1)),x87674))+~P85(f784(f784(f347(a1),x87671),x87673))+P85(f784(f784(f347(a1),f441(x87673,x87671,x87674,x87672)),x87673))
% 11.41/11.19 [8769]~E(f784(x87692,x87694),f784(a160,f2(a859)))+E(f784(f784(f8(x87691,a859),x87692),x87693),f784(a160,f2(a859)))+~P85(f784(f71(x87691),x87693))+~P85(f784(f784(f347(x87691),x87694),x87693))+P85(f784(f784(f347(x87691),f419(x87692,x87693,x87691,x87694)),x87693))
% 11.41/11.19 [8773]P56(x87732,x87733,x87734,x87731)+E(x87731,f187(f869(x87732,a852)))+~P85(f784(f71(x87732),x87734))+~P85(f784(f71(x87732),x87731))+P85(f784(f784(f347(x87732),f545(x87731,x87734,x87733,x87732)),x87734))
% 11.41/11.19 [8839]E(x88391,x88392)+~E(f784(f784(f89(a1),x88392),x88394),x88391)+~P85(f784(f784(f243(a1),f2(a1)),x88394))+~P85(f784(f784(f347(a1),x88391),x88393))+P85(f784(f784(f347(a1),f444(x88393,x88391,x88394,x88392)),f305(a1,f87(a1),x88394)))
% 11.41/11.19 [8840]E(x88401,x88402)+~E(f784(f784(f3(a1),x88402),x88404),x88401)+~P85(f784(f784(f243(a1),f2(a1)),x88404))+~P85(f784(f784(f347(a1),x88401),x88403))+P85(f784(f784(f347(a1),f442(x88403,x88401,x88404,x88402)),f305(a1,f87(a1),x88404)))
% 11.41/11.19 [8912]P85(f784(f784(f242(a859),x89121),f826(x89122,x89123,x89124,x89121)))+~P85(f784(f784(f242(a1),x89122),f784(x89123,x89124)))+P85(f784(f784(f242(a859),x89121),f827(x89122,x89123,x89124,x89121)))+~P85(f784(f784(f243(a859),x89121),x89124))+~P85(f784(f784(f242(a1),f784(x89123,x89121)),x89122))
% 11.41/11.19 [9019]E(f784(x90191,f826(x90192,x90191,x90193,x90194)),x90192)+~P85(f784(f784(f242(a1),x90192),f784(x90191,x90193)))+P85(f784(f784(f243(a859),f827(x90192,x90191,x90193,x90194)),x90193))+~P85(f784(f784(f243(a859),x90194),x90193))+~P85(f784(f784(f242(a1),f784(x90191,x90194)),x90192))
% 11.41/11.19 [9125]~P85(f784(f784(f289(a859),x91254),x91251))+~P85(f784(f784(f289(a859),x91254),x91253))+~P85(f784(f784(f289(a859),x91252),x91251))+P85(f784(f784(f289(a859),x91251),x91252))+P85(f784(f784(f243(f869(a859,a852)),f292(a859,f289(a859),x91253,x91252)),f292(a859,f289(a859),x91254,x91251)))
% 11.41/11.19 [9126]~P85(f784(f784(f289(a859),x91262),x91261))+~P85(f784(f784(f289(a859),x91263),x91264))+~P85(f784(f784(f289(a859),x91262),x91264))+P85(f784(f784(f289(a859),x91261),x91262))+P85(f784(f784(f243(f869(a859,a852)),f292(a859,f289(a859),x91261,x91263)),f292(a859,f289(a859),x91262,x91264)))
% 11.41/11.19 [9137]~P85(f784(f784(f242(a1),x91372),f784(x91373,x91374)))+P85(f784(f784(f242(a859),x91371),f827(x91372,x91373,x91374,x91371)))+P85(f784(f784(f242(a859),f826(x91372,x91373,x91374,x91371)),x91374))+~P85(f784(f784(f243(a859),x91371),x91374))+~P85(f784(f784(f242(a1),f784(x91373,x91371)),x91372))
% 11.41/11.19 [9138]~P85(f784(f784(f242(a1),x91382),f784(x91383,x91384)))+P85(f784(f784(f242(a859),x91381),f826(x91382,x91383,x91384,x91381)))+P85(f784(f784(f243(a859),f827(x91382,x91383,x91384,x91381)),x91384))+~P85(f784(f784(f243(a859),x91381),x91384))+~P85(f784(f784(f242(a1),f784(x91383,x91381)),x91382))
% 11.41/11.19 [9224]~P85(f784(f784(f242(a1),x92241),f784(x92242,x92243)))+P85(f784(f784(f242(a859),f826(x92241,x92242,x92243,x92244)),x92243))+~P85(f784(f784(f243(a859),x92244),x92243))+~P85(f784(f784(f242(a1),f784(x92242,x92244)),x92241))+P85(f784(f784(f243(a859),f827(x92241,x92242,x92243,x92244)),x92243))
% 11.41/11.19 [9309]E(x93091,f187(f869(x93092,a852)))+~P85(f784(f71(x93092),x93094))+~P85(f784(f71(x93092),x93091))+P85(f784(f784(f347(f868(f869(x93092,a852),f869(x93092,a852))),f784(f784(f251(f869(x93092,a852),f869(x93092,a852)),x93094),x93091)),f338(x93092,x93093)))+P85(f784(f784(f347(x93092),f547(x93093,x93091,x93094,x93092)),x93094))
% 11.41/11.19 [9310]E(x93101,f187(f869(x93102,a852)))+~P85(f784(f71(x93102),x93104))+~P85(f784(f71(x93102),x93101))+P85(f784(f784(f347(f868(f869(x93102,a852),f869(x93102,a852))),f784(f784(f251(f869(x93102,a852),f869(x93102,a852)),x93104),x93101)),f338(x93102,x93103)))+P85(f784(f784(f347(x93102),f635(x93103,x93101,x93104,x93102)),x93104))
% 11.41/11.19 [9960]E(f784(x99601,f826(x99602,x99601,x99603,x99604)),x99602)+~P85(f784(f784(f242(a1),x99602),f784(x99601,x99603)))+~P85(f784(f784(f242(a1),f784(f84(a1),f784(f784(f3(a1),f784(x99601,f784(f784(f89(a859),f827(x99602,x99601,x99603,x99604)),f87(a859)))),f784(x99601,f827(x99602,x99601,x99603,x99604))))),f87(a1)))+~P85(f784(f784(f243(a859),x99604),x99603))+~P85(f784(f784(f242(a1),f784(x99601,x99604)),x99602))
% 11.41/11.19 [9961]~P85(f784(f784(f242(a1),x99612),f784(x99613,x99614)))+P85(f784(f784(f242(a859),x99611),f826(x99612,x99613,x99614,x99611)))+~P85(f784(f784(f242(a1),f784(f84(a1),f784(f784(f3(a1),f784(x99613,f784(f784(f89(a859),f827(x99612,x99613,x99614,x99611)),f87(a859)))),f784(x99613,f827(x99612,x99613,x99614,x99611))))),f87(a1)))+~P85(f784(f784(f243(a859),x99611),x99614))+~P85(f784(f784(f242(a1),f784(x99613,x99611)),x99612))
% 11.41/11.19 [9962]~P85(f784(f784(f242(a1),x99621),f784(x99622,x99623)))+~P85(f784(f784(f242(a1),f784(f84(a1),f784(f784(f3(a1),f784(x99622,f784(f784(f89(a859),f827(x99621,x99622,x99623,x99624)),f87(a859)))),f784(x99622,f827(x99621,x99622,x99623,x99624))))),f87(a1)))+~P85(f784(f784(f243(a859),x99624),x99623))+~P85(f784(f784(f242(a1),f784(x99622,x99624)),x99621))+P85(f784(f784(f242(a859),f826(x99621,x99622,x99623,x99624)),x99623))
% 11.41/11.19 [5523]~P90(x55232)+~P59(x55232)+E(x55231,f2(x55232))+~E(f784(f784(f293(x55232),x55233),x55231),f784(f113(x55232),x55234))+E(x55233,f784(f784(f90(x55232),f784(f113(x55232),x55234)),x55231))
% 11.41/11.19 [5524]~P90(x55242)+~P59(x55242)+E(x55241,f2(x55242))+~E(f784(f113(x55242),x55243),f784(f784(f293(x55242),x55244),x55241))+E(f784(f784(f90(x55242),f784(f113(x55242),x55243)),x55241),x55244)
% 11.41/11.19 [5675]~P90(x56752)+~P59(x56752)+E(x56751,f2(x56752))+E(f784(f113(x56752),x56753),f784(f784(f293(x56752),x56754),x56751))+~E(f784(f784(f90(x56752),f784(f113(x56752),x56753)),x56751),x56754)
% 11.41/11.19 [5676]~P90(x56762)+~P59(x56762)+E(x56761,f2(x56762))+E(f784(f784(f293(x56762),x56763),x56761),f784(f113(x56762),x56764))+~E(x56763,f784(f784(f90(x56762),f784(f113(x56762),x56764)),x56761))
% 11.41/11.19 [5812]~P90(x58121)+~P59(x58121)+~E(f784(f113(x58121),x58122),f2(x58121))+E(f784(f113(x58121),x58122),f784(f784(f293(x58121),x58123),x58124))+~E(f784(f784(f90(x58121),f784(f113(x58121),x58122)),x58124),x58123)
% 11.41/11.19 [5813]~P90(x58131)+~P59(x58131)+~E(f784(f113(x58131),x58134),f2(x58131))+E(f784(f784(f293(x58131),x58132),x58133),f784(f113(x58131),x58134))+~E(x58132,f784(f784(f90(x58131),f784(f113(x58131),x58134)),x58133))
% 11.41/11.19 [7135]~P61(x71351)+P85(f784(f784(f243(x71351),x71352),f2(x71351)))+~P85(f784(f784(f243(x71351),x71353),f2(x71351)))+P85(f784(f784(f243(x71351),f2(x71351)),x71352))+P85(f784(f784(f243(x71351),x71353),f784(f784(f293(x71351),x71354),x71352)))
% 11.41/11.19 [7136]~P61(x71361)+P85(f784(f784(f243(x71361),x71362),f2(x71361)))+~P85(f784(f784(f242(x71361),x71363),f2(x71361)))+P85(f784(f784(f243(x71361),f2(x71361)),x71362))+P85(f784(f784(f242(x71361),x71363),f784(f784(f293(x71361),x71364),x71362)))
% 11.41/11.19 [7407]~P61(x74071)+P85(f784(f784(f243(x74071),x74072),f2(x74071)))+P85(f784(f784(f243(x74071),x74073),f2(x74071)))+P85(f784(f784(f243(x74071),f2(x74071)),x74073))+~P85(f784(f784(f243(x74071),x74072),f784(f784(f293(x74071),x74074),x74073)))
% 11.41/11.19 [7408]~P61(x74081)+P85(f784(f784(f243(x74081),x74082),f2(x74081)))+P85(f784(f784(f242(x74081),x74083),f2(x74081)))+P85(f784(f784(f243(x74081),f2(x74081)),x74082))+~P85(f784(f784(f242(x74081),x74083),f784(f784(f293(x74081),x74084),x74082)))
% 11.41/11.19 [7525]E(x75251,x75252)+~E(f784(f784(f155(x75253),x75254),x75251),f784(f784(f155(x75253),x75254),x75252))+~P85(f784(f132(x75253),x75254))+~P85(f784(f784(f243(a859),x75252),f784(f188(f860(x75253)),x75254)))+~P85(f784(f784(f243(a859),x75251),f784(f188(f860(x75253)),x75254)))
% 11.41/11.19 [7526]E(x75261,x75262)+~E(f784(f784(f155(x75263),x75264),x75261),f784(f784(f155(x75263),x75264),x75262))+~P85(f784(f132(x75263),x75264))+~P85(f784(f784(f243(a859),x75262),f784(f188(f860(x75263)),x75264)))+~P85(f784(f784(f243(a859),x75261),f784(f188(f860(x75263)),x75264)))
% 11.41/11.19 [7892]~P61(x78921)+~P85(f784(f784(f243(x78921),x78923),f2(x78921)))+P85(f784(f784(f243(x78921),f2(x78921)),x78922))+~P85(f784(f784(f243(x78921),x78924),f784(f784(f90(x78921),x78923),x78922)))+P85(f784(f784(f243(x78921),x78923),f784(f784(f293(x78921),x78924),x78922)))
% 11.41/11.19 [7893]~P61(x78931)+~P85(f784(f784(f242(x78931),x78933),f2(x78931)))+P85(f784(f784(f243(x78931),f2(x78931)),x78932))+~P85(f784(f784(f242(x78931),x78934),f784(f784(f90(x78931),x78933),x78932)))+P85(f784(f784(f242(x78931),x78933),f784(f784(f293(x78931),x78934),x78932)))
% 11.41/11.19 [7894]~P61(x78941)+~P85(f784(f784(f243(x78941),x78942),f2(x78941)))+P85(f784(f784(f243(x78941),f2(x78941)),x78942))+~P85(f784(f784(f243(x78941),x78944),f784(f784(f90(x78941),x78943),x78942)))+P85(f784(f784(f243(x78941),x78943),f784(f784(f293(x78941),x78944),x78942)))
% 11.41/11.19 [7895]~P61(x78951)+~P85(f784(f784(f243(x78951),x78952),f2(x78951)))+P85(f784(f784(f243(x78951),f2(x78951)),x78952))+~P85(f784(f784(f243(x78951),x78954),f784(f784(f293(x78951),x78953),x78952)))+P85(f784(f784(f243(x78951),x78953),f784(f784(f90(x78951),x78954),x78952)))
% 11.41/11.19 [7896]~P61(x78961)+~P85(f784(f784(f243(x78961),x78962),f2(x78961)))+P85(f784(f784(f243(x78961),f2(x78961)),x78962))+~P85(f784(f784(f242(x78961),x78964),f784(f784(f90(x78961),x78963),x78962)))+P85(f784(f784(f242(x78961),x78963),f784(f784(f293(x78961),x78964),x78962)))
% 11.41/11.19 [7897]~P61(x78971)+~P85(f784(f784(f243(x78971),x78972),f2(x78971)))+P85(f784(f784(f243(x78971),f2(x78971)),x78972))+~P85(f784(f784(f242(x78971),x78974),f784(f784(f293(x78971),x78973),x78972)))+P85(f784(f784(f242(x78971),x78973),f784(f784(f90(x78971),x78974),x78972)))
% 11.41/11.19 [8020]~P4(x80201)+~P85(f784(f784(f289(x80201),x80203),x80204))+~P85(f784(f784(f289(x80201),x80203),x80202))+~P85(f784(f784(f289(x80201),x80202),x80204))+P85(f784(f784(f289(x80201),f784(f784(f51(x80201),x80202),x80203)),f784(f784(f51(x80201),x80204),x80203)))
% 11.41/11.19 [8034]~P101(x80341)+~P15(x80341,x80342)+~P85(f784(f784(f242(a859),x80343),x80344))+P85(f784(f784(f242(x80341),f784(f784(f155(x80341),x80342),x80343)),f784(f784(f155(x80341),x80342),x80344)))+~P85(f784(f784(f243(a859),x80344),f784(f188(f860(x80341)),x80342)))
% 11.41/11.19 [8035]~P101(x80351)+~P15(x80351,x80352)+~P85(f784(f784(f242(a859),x80353),x80354))+P85(f784(f784(f242(x80351),f784(f784(f155(x80351),x80352),x80353)),f784(f784(f155(x80351),x80352),x80354)))+~P85(f784(f784(f243(a859),x80354),f784(f188(f860(x80351)),x80352)))
% 11.41/11.19 [8085]~P120(x80851)+~P85(f784(f784(f243(x80851),x80852),f87(x80851)))+~P85(f784(f784(f243(x80851),f2(x80851)),x80852))+~P85(f784(f784(f243(a859),x80854),x80853))+P85(f784(f784(f243(x80851),f784(f784(f252(x80851),x80852),x80853)),f784(f784(f252(x80851),x80852),x80854)))
% 11.41/11.19 [8086]~P120(x80861)+~P85(f784(f784(f242(x80861),x80862),f87(x80861)))+~P85(f784(f784(f242(x80861),f2(x80861)),x80862))+~P85(f784(f784(f242(a859),x80864),x80863))+P85(f784(f784(f242(x80861),f784(f784(f252(x80861),x80862),x80863)),f784(f784(f252(x80861),x80862),x80864)))
% 11.41/11.19 [8087]~P120(x80871)+~P85(f784(f784(f242(x80871),f2(x80871)),x80872))+~P85(f784(f784(f243(a859),f2(a859)),x80873))+~P85(f784(f784(f243(x80871),x80872),x80874))+P85(f784(f784(f243(x80871),f784(f784(f252(x80871),x80872),x80873)),f784(f784(f252(x80871),x80874),x80873)))
% 11.41/11.19 [8105]~P101(x81051)+~P15(x81051,f784(f162(x81051),x81052))+~P85(f784(f784(f242(a859),x81054),x81053))+P85(f784(f784(f242(x81051),f784(f784(f155(x81051),x81052),x81053)),f784(f784(f155(x81051),x81052),x81054)))+~P85(f784(f784(f243(a859),x81053),f784(f188(f860(x81051)),x81052)))
% 11.41/11.19 [8332]~P4(x83321)+P85(f784(f784(f289(x83321),x83322),x83323))+~P85(f784(f784(f289(x83321),x83324),x83323))+~P85(f784(f784(f289(x83321),x83324),x83322))+~P85(f784(f784(f289(x83321),f784(f784(f51(x83321),x83322),x83324)),f784(f784(f51(x83321),x83323),x83324)))
% 11.41/11.19 [8349]~P62(x83491)+~P85(f784(f784(f243(x83491),x83492),f2(x83491)))+~P85(f784(f784(f243(x83491),x83493),x83494))+~P85(f784(f784(f243(x83491),f2(x83491)),f784(f784(f90(x83491),x83493),x83494)))+P85(f784(f784(f243(x83491),f784(f784(f293(x83491),x83492),x83493)),f784(f784(f293(x83491),x83492),x83494)))
% 11.41/11.19 [8350]~P61(x83501)+~P85(f784(f784(f242(x83501),x83502),f2(x83501)))+~P85(f784(f784(f242(x83501),x83503),x83504))+~P85(f784(f784(f243(x83501),f2(x83501)),f784(f784(f90(x83501),x83503),x83504)))+P85(f784(f784(f242(x83501),f784(f784(f293(x83501),x83502),x83503)),f784(f784(f293(x83501),x83502),x83504)))
% 11.41/11.19 [8360]~P62(x83601)+~P85(f784(f784(f243(x83601),x83604),x83603))+~P85(f784(f784(f243(x83601),f2(x83601)),x83602))+~P85(f784(f784(f243(x83601),f2(x83601)),f784(f784(f90(x83601),x83603),x83604)))+P85(f784(f784(f243(x83601),f784(f784(f293(x83601),x83602),x83603)),f784(f784(f293(x83601),x83602),x83604)))
% 11.41/11.19 [8361]~P62(x83611)+~P85(f784(f784(f242(x83611),x83614),x83613))+~P85(f784(f784(f242(x83611),f2(x83611)),x83612))+~P85(f784(f784(f243(x83611),f2(x83611)),f784(f784(f90(x83611),x83613),x83614)))+P85(f784(f784(f242(x83611),f784(f784(f293(x83611),x83612),x83613)),f784(f784(f293(x83611),x83612),x83614)))
% 11.41/11.19 [8467]P85(f784(x84671,x84672))+~P85(f784(f71(x84674),x84672))+P85(f784(x84671,f498(x84671,x84673,x84672,x84674)))+~P85(f784(x84671,f187(f869(x84674,a852))))+~P85(f784(f784(f242(f869(x84674,a852)),x84672),x84673))
% 11.41/11.19 [8475]P85(f784(x84751,x84752))+P85(f784(f71(x84753),f498(x84751,x84754,x84752,x84753)))+~P85(f784(f71(x84753),x84752))+~P85(f784(x84751,f187(f869(x84753,a852))))+~P85(f784(f784(f242(f869(x84753,a852)),x84752),x84754))
% 11.41/11.19 [8704]E(f784(f784(f89(a1),f448(x87041,x87042,x87043,x87044)),f449(x87041,x87042,x87043,x87044)),x87044)+~P85(f784(f784(f243(a1),f2(a1)),x87043))+~P85(f784(f784(f243(a1),x87042),x87044))+~P85(f784(f784(f347(a1),x87042),x87041))+P85(f784(f784(f243(a1),x87042),f784(f784(f3(a1),x87044),x87043)))
% 11.41/11.19 [8892]~P85(f784(f784(f243(a1),f2(a1)),x88923))+~P85(f784(f784(f243(a1),x88922),x88924))+~P85(f784(f784(f347(a1),x88922),x88921))+P85(f784(f784(f347(a1),f448(x88921,x88922,x88923,x88924)),x88921))+P85(f784(f784(f243(a1),x88922),f784(f784(f3(a1),x88924),x88923)))
% 11.41/11.19 [8905]P85(f784(x89051,x89052))+~P85(f784(f71(x89053),x89052))+P85(f784(f784(f347(x89053),f499(x89051,x89054,x89052,x89053)),x89054))+~P85(f784(x89051,f187(f869(x89053,a852))))+~P85(f784(f784(f242(f869(x89053,a852)),x89052),x89054))
% 11.41/11.19 [8922]E(f784(f784(f89(a1),f436(x89221,x89222,x89223,x89224)),f437(x89221,x89222,x89223,x89224)),x89224)+~P85(f784(f784(f243(a1),f2(a1)),x89223))+~P85(f784(f784(f242(a1),x89222),x89224))+P85(f784(f784(f242(a1),x89222),f784(f784(f3(a1),x89224),x89223)))+~P85(f784(f784(f347(a1),f784(f784(f3(a1),x89222),f87(a1))),x89221))
% 11.41/11.19 [8968]~P85(f784(f784(f243(a1),f2(a1)),x89683))+~P85(f784(f784(f243(a1),x89681),x89682))+~P85(f784(f784(f347(a1),x89681),x89684))+P85(f784(f784(f347(a1),f449(x89684,x89681,x89683,x89682)),f305(a1,f87(a1),x89683)))+P85(f784(f784(f243(a1),x89681),f784(f784(f3(a1),x89682),x89683)))
% 11.41/11.19 [9063]~P85(f784(f784(f243(a1),f2(a1)),x90633))+~P85(f784(f784(f242(a1),x90632),x90634))+P85(f784(f784(f347(a1),f436(x90631,x90632,x90633,x90634)),x90631))+P85(f784(f784(f242(a1),x90632),f784(f784(f3(a1),x90634),x90633)))+~P85(f784(f784(f347(a1),f784(f784(f3(a1),x90632),f87(a1))),x90631))
% 11.41/11.19 [9102]~P85(f784(f784(f243(a1),f2(a1)),x91023))+~P85(f784(f784(f242(a1),x91021),x91022))+P85(f784(f784(f347(a1),f437(x91024,x91021,x91023,x91022)),f305(a1,f87(a1),x91023)))+P85(f784(f784(f242(a1),x91021),f784(f784(f3(a1),x91022),x91023)))+~P85(f784(f784(f347(a1),f784(f784(f3(a1),x91021),f87(a1))),x91024))
% 11.41/11.19 [9312]P85(f784(x93121,x93122))+~P85(f784(f784(f347(x93123),f499(x93121,x93124,x93122,x93123)),f498(x93121,x93124,x93122,x93123)))+~P85(f784(f71(x93123),x93122))+~P85(f784(x93121,f187(f869(x93123,a852))))+~P85(f784(f784(f242(f869(x93123,a852)),x93122),x93124))
% 11.41/11.19 [9516]P85(f784(x95161,x95162))+~P85(f784(f71(x95163),x95162))+~P85(f784(x95161,f784(f784(f312(x95163),f499(x95161,x95164,x95162,x95163)),f498(x95161,x95164,x95162,x95163))))+~P85(f784(x95161,f187(f869(x95163,a852))))+~P85(f784(f784(f242(f869(x95163,a852)),x95162),x95164))
% 11.41/11.19 [9845]~P100(x98453)+~P51(a859,x98453,f784(f784(f20(a859,f869(a859,a852),f869(a859,a852)),f784(f784(f10(f869(a859,f869(a852,a852)),f869(f869(a859,a852),f869(a859,a852)),a859),f20(a859,a852,a852)),f784(f784(f10(f869(a859,a852),f869(a859,f869(a852,a852)),a859),f784(f10(a852,f869(a852,a852),a859),a344)),f289(a859)))),f784(f784(f10(f869(a859,a852),f869(a859,a852),a859),f784(f10(a852,a852,a859),a341)),f784(f9(a859,a859,a852),f289(a859)))),x98454)+P85(f784(f784(f243(x98453),f784(x98454,x98452)),f784(x98454,x98451)))+~P85(f784(f784(f289(a859),x98452),x98451))+P85(f784(f784(f289(a859),x98451),x98452))
% 11.41/11.19 [7665]~P61(x76651)+P85(f784(f784(f243(x76651),x76652),f2(x76651)))+P85(f784(f784(f243(x76651),f2(x76651)),x76652))+~P85(f784(f784(f243(x76651),f2(x76651)),x76654))+P85(f784(f784(f243(x76651),f784(f784(f293(x76651),x76653),x76652)),x76654))
% 11.41/11.19 [7666]~P61(x76661)+P85(f784(f784(f243(x76661),x76662),f2(x76661)))+~P85(f784(f784(f242(x76661),f2(x76661)),x76664))+P85(f784(f784(f243(x76661),f2(x76661)),x76662))+P85(f784(f784(f242(x76661),f784(f784(f293(x76661),x76663),x76662)),x76664))
% 11.41/11.19 [7947]~P85(f784(f784(f242(a1),x79474),f2(a1)))+~E(x79472,f784(f784(f89(a1),f784(f784(f90(a1),x79471),x79473)),x79474))+P85(f784(f784(f243(a1),f2(a1)),x79471))+~P85(f784(f784(f243(a1),x79471),x79474))+P85(f784(f64(x79472,x79471),f784(f784(f251(a1,a1),x79473),x79474)))
% 11.41/11.19 [7984]~P85(f784(x79841,x79844))+P85(f784(x79841,f815(x79842,x79841,x79843)))+~P85(f784(f784(f243(a1),f2(a1)),x79843))+~P85(f784(f784(f242(a1),f2(a1)),x79842))+P85(f784(x79841,f784(f784(f89(a1),x79844),f784(f784(f90(a1),x79842),x79843))))
% 11.41/11.19 [7985]~P85(f784(x79851,x79854))+P85(f784(x79851,f820(x79852,x79851,x79853)))+~P85(f784(f784(f243(a1),f2(a1)),x79853))+~P85(f784(f784(f242(a1),f2(a1)),x79852))+P85(f784(x79851,f784(f784(f3(a1),x79854),f784(f784(f90(a1),x79852),x79853))))
% 11.41/11.19 [7986]~P61(x79861)+P85(f784(f784(f243(x79861),x79862),f2(x79861)))+P85(f784(f784(f243(x79861),f2(x79861)),x79862))+P85(f784(f784(f243(x79861),f2(x79861)),x79863))+~P85(f784(f784(f243(x79861),f784(f784(f293(x79861),x79864),x79862)),x79863))
% 11.41/11.19 [7987]~P61(x79871)+P85(f784(f784(f243(x79871),x79872),f2(x79871)))+P85(f784(f784(f243(x79871),f2(x79871)),x79872))+P85(f784(f784(f242(x79871),f2(x79871)),x79873))+~P85(f784(f784(f242(x79871),f784(f784(f293(x79871),x79874),x79872)),x79873))
% 11.41/11.19 [8030]~E(x80301,f784(f784(f89(a1),f784(f784(f90(a1),x80302),x80303)),x80304))+~P85(f784(f784(f243(a1),f2(a1)),x80302))+~P85(f784(f784(f242(a1),f2(a1)),x80304))+~P85(f784(f784(f243(a1),x80304),x80302))+P85(f784(f64(x80301,x80302),f784(f784(f251(a1,a1),x80303),x80304)))
% 11.41/11.19 [8145]~P61(x81451)+P85(f784(f784(f243(x81451),x81452),f2(x81451)))+~P85(f784(f784(f243(x81451),f2(x81451)),x81454))+~P85(f784(f784(f243(x81451),x81453),f784(f784(f90(x81451),x81454),x81452)))+P85(f784(f784(f243(x81451),f784(f784(f293(x81451),x81453),x81452)),x81454))
% 11.41/11.19 [8146]~P61(x81461)+P85(f784(f784(f243(x81461),x81462),f2(x81461)))+~P85(f784(f784(f242(x81461),f2(x81461)),x81464))+~P85(f784(f784(f242(x81461),x81463),f784(f784(f90(x81461),x81464),x81462)))+P85(f784(f784(f242(x81461),f784(f784(f293(x81461),x81463),x81462)),x81464))
% 11.41/11.19 [8224]~P61(x82241)+P85(f784(f784(f243(x82241),x82242),f2(x82241)))+~P85(f784(f784(f243(x82241),x82243),f2(x82241)))+P85(f784(f784(f243(x82241),x82243),f784(f784(f293(x82241),x82244),x82242)))+~P85(f784(f784(f243(x82241),f784(f784(f90(x82241),x82243),x82242)),x82244))
% 11.41/11.19 [8225]~P61(x82251)+P85(f784(f784(f243(x82251),x82252),f2(x82251)))+~P85(f784(f784(f242(x82251),x82253),f2(x82251)))+P85(f784(f784(f242(x82251),x82253),f784(f784(f293(x82251),x82254),x82252)))+~P85(f784(f784(f242(x82251),f784(f784(f90(x82251),x82253),x82252)),x82254))
% 11.41/11.19 [8385]~P61(x83851)+~P85(f784(f784(f243(x83851),x83852),f2(x83851)))+P85(f784(f784(f243(x83851),f2(x83851)),x83852))+~P85(f784(f784(f243(x83851),f784(f784(f293(x83851),x83854),x83852)),x83853))+P85(f784(f784(f243(x83851),f784(f784(f90(x83851),x83853),x83852)),x83854))
% 11.41/11.19 [8386]~P61(x83861)+~P85(f784(f784(f243(x83861),x83862),f2(x83861)))+P85(f784(f784(f243(x83861),f2(x83861)),x83862))+~P85(f784(f784(f243(x83861),f784(f784(f90(x83861),x83864),x83862)),x83863))+P85(f784(f784(f243(x83861),f784(f784(f293(x83861),x83863),x83862)),x83864))
% 11.41/11.19 [8387]~P61(x83871)+~P85(f784(f784(f243(x83871),x83872),f2(x83871)))+P85(f784(f784(f243(x83871),f2(x83871)),x83872))+~P85(f784(f784(f242(x83871),f784(f784(f293(x83871),x83874),x83872)),x83873))+P85(f784(f784(f242(x83871),f784(f784(f90(x83871),x83873),x83872)),x83874))
% 11.41/11.19 [8388]~P61(x83881)+~P85(f784(f784(f243(x83881),x83882),f2(x83881)))+P85(f784(f784(f243(x83881),f2(x83881)),x83882))+~P85(f784(f784(f242(x83881),f784(f784(f90(x83881),x83884),x83882)),x83883))+P85(f784(f784(f242(x83881),f784(f784(f293(x83881),x83883),x83882)),x83884))
% 11.41/11.19 [8407]~P61(x84071)+~P85(f784(f784(f243(x84071),f2(x84071)),x84074))+P85(f784(f784(f243(x84071),f2(x84071)),x84072))+~P85(f784(f784(f243(x84071),f784(f784(f90(x84071),x84074),x84072)),x84073))+P85(f784(f784(f243(x84071),f784(f784(f293(x84071),x84073),x84072)),x84074))
% 11.41/11.19 [8408]~P61(x84081)+~P85(f784(f784(f242(x84081),f2(x84081)),x84084))+P85(f784(f784(f243(x84081),f2(x84081)),x84082))+~P85(f784(f784(f242(x84081),f784(f784(f90(x84081),x84084),x84082)),x84083))+P85(f784(f784(f242(x84081),f784(f784(f293(x84081),x84083),x84082)),x84084))
% 11.41/11.19 [8459]~P61(x84591)+~P90(x84591)+~P85(f784(f784(f243(x84591),f2(x84591)),x84594))+~P85(f784(f784(f243(x84591),f784(f784(f293(x84591),x84592),x84594)),f784(f113(x84591),x84593)))+P85(f784(f784(f243(x84591),x84592),f784(f784(f90(x84591),f784(f113(x84591),x84593)),x84594)))
% 11.41/11.19 [8460]~P61(x84601)+~P90(x84601)+~P85(f784(f784(f243(x84601),f2(x84601)),x84604))+~P85(f784(f784(f242(x84601),f784(f784(f293(x84601),x84602),x84604)),f784(f113(x84601),x84603)))+P85(f784(f784(f242(x84601),x84602),f784(f784(f90(x84601),f784(f113(x84601),x84603)),x84604)))
% 11.41/11.19 [8468]~P61(x84681)+~P90(x84681)+~P85(f784(f784(f243(x84681),f2(x84681)),x84683))+P85(f784(f784(f243(x84681),f784(f784(f293(x84681),x84682),x84683)),f784(f113(x84681),x84684)))+~P85(f784(f784(f243(x84681),x84682),f784(f784(f90(x84681),f784(f113(x84681),x84684)),x84683)))
% 11.41/11.19 [8469]~P61(x84691)+~P90(x84691)+~P85(f784(f784(f243(x84691),f2(x84691)),x84693))+P85(f784(f784(f242(x84691),f784(f784(f293(x84691),x84692),x84693)),f784(f113(x84691),x84694)))+~P85(f784(f784(f242(x84691),x84692),f784(f784(f90(x84691),f784(f113(x84691),x84694)),x84693)))
% 11.41/11.19 [8483]~P61(x84831)+~P85(f784(f784(f243(x84831),x84834),f2(x84831)))+~P85(f784(f784(f243(x84831),x84833),f784(f784(f90(x84831),x84832),x84834)))+P85(f784(f784(f243(x84831),x84832),f784(f784(f293(x84831),x84833),x84834)))+~P85(f784(f784(f243(x84831),f784(f784(f90(x84831),x84832),x84834)),x84833))
% 11.41/11.19 [8484]~P61(x84841)+~P85(f784(f784(f243(x84841),x84842),f2(x84841)))+~P85(f784(f784(f243(x84841),x84843),f784(f784(f90(x84841),x84842),x84844)))+P85(f784(f784(f243(x84841),x84842),f784(f784(f293(x84841),x84843),x84844)))+~P85(f784(f784(f243(x84841),f784(f784(f90(x84841),x84842),x84844)),x84843))
% 11.41/11.19 [8485]~P61(x84851)+~P85(f784(f784(f243(x84851),x84854),f2(x84851)))+~P85(f784(f784(f242(x84851),x84853),f784(f784(f90(x84851),x84852),x84854)))+P85(f784(f784(f242(x84851),x84852),f784(f784(f293(x84851),x84853),x84854)))+~P85(f784(f784(f242(x84851),f784(f784(f90(x84851),x84852),x84854)),x84853))
% 11.41/11.19 [8486]~P61(x84861)+~P85(f784(f784(f242(x84861),x84862),f2(x84861)))+~P85(f784(f784(f242(x84861),x84863),f784(f784(f90(x84861),x84862),x84864)))+P85(f784(f784(f242(x84861),x84862),f784(f784(f293(x84861),x84863),x84864)))+~P85(f784(f784(f242(x84861),f784(f784(f90(x84861),x84862),x84864)),x84863))
% 11.41/11.19 [8531]~P61(x85311)+~P90(x85311)+~P85(f784(f784(f243(x85311),f2(x85311)),f784(f113(x85311),x85313)))+~P85(f784(f784(f243(x85311),x85312),f784(f784(f293(x85311),x85314),f784(f113(x85311),x85313))))+P85(f784(f784(f243(x85311),f784(f784(f90(x85311),x85312),f784(f113(x85311),x85313))),x85314))
% 11.41/11.19 [8532]~P61(x85321)+~P90(x85321)+~P85(f784(f784(f243(x85321),f2(x85321)),f784(f113(x85321),x85323)))+~P85(f784(f784(f243(x85321),x85322),f784(f784(f90(x85321),x85324),f784(f113(x85321),x85323))))+P85(f784(f784(f243(x85321),f784(f784(f293(x85321),x85322),f784(f113(x85321),x85323))),x85324))
% 11.41/11.19 [8533]~P61(x85331)+~P90(x85331)+~P85(f784(f784(f243(x85331),f2(x85331)),f784(f113(x85331),x85333)))+~P85(f784(f784(f242(x85331),x85332),f784(f784(f293(x85331),x85334),f784(f113(x85331),x85333))))+P85(f784(f784(f242(x85331),f784(f784(f90(x85331),x85332),f784(f113(x85331),x85333))),x85334))
% 11.41/11.19 [8534]~P61(x85341)+~P90(x85341)+~P85(f784(f784(f243(x85341),f2(x85341)),f784(f113(x85341),x85343)))+~P85(f784(f784(f242(x85341),x85342),f784(f784(f90(x85341),x85344),f784(f113(x85341),x85343))))+P85(f784(f784(f242(x85341),f784(f784(f293(x85341),x85342),f784(f113(x85341),x85343))),x85344))
% 11.41/11.19 [8586]~P61(x85861)+~P85(f784(f784(f243(x85861),x85863),f2(x85861)))+~P85(f784(f784(f243(x85861),x85862),f784(f784(f90(x85861),x85864),x85863)))+~P85(f784(f784(f243(x85861),f784(f784(f90(x85861),x85864),x85863)),x85862))+P85(f784(f784(f243(x85861),f784(f784(f293(x85861),x85862),x85863)),x85864))
% 11.41/11.19 [8587]~P61(x85871)+~P85(f784(f784(f243(x85871),x85873),f2(x85871)))+~P85(f784(f784(f242(x85871),x85872),f784(f784(f90(x85871),x85874),x85873)))+~P85(f784(f784(f242(x85871),f784(f784(f90(x85871),x85874),x85873)),x85872))+P85(f784(f784(f242(x85871),f784(f784(f293(x85871),x85872),x85873)),x85874))
% 11.41/11.19 [8601]~P61(x86011)+~P85(f784(f784(f243(x86011),f2(x86011)),x86014))+~P85(f784(f784(f243(x86011),x86012),f784(f784(f90(x86011),x86014),x86013)))+~P85(f784(f784(f243(x86011),f784(f784(f90(x86011),x86014),x86013)),x86012))+P85(f784(f784(f243(x86011),f784(f784(f293(x86011),x86012),x86013)),x86014))
% 11.41/11.19 [8602]~P61(x86021)+~P85(f784(f784(f242(x86021),f2(x86021)),x86024))+~P85(f784(f784(f242(x86021),x86022),f784(f784(f90(x86021),x86024),x86023)))+~P85(f784(f784(f242(x86021),f784(f784(f90(x86021),x86024),x86023)),x86022))+P85(f784(f784(f242(x86021),f784(f784(f293(x86021),x86022),x86023)),x86024))
% 11.41/11.19 [8632]~P61(x86321)+~P90(x86321)+~P85(f784(f784(f243(x86321),f2(x86321)),f784(f113(x86321),x86324)))+P85(f784(f784(f243(x86321),x86322),f784(f784(f90(x86321),x86323),f784(f113(x86321),x86324))))+~P85(f784(f784(f243(x86321),f784(f784(f293(x86321),x86322),f784(f113(x86321),x86324))),x86323))
% 11.41/11.19 [8633]~P61(x86331)+~P90(x86331)+~P85(f784(f784(f243(x86331),f2(x86331)),f784(f113(x86331),x86334)))+P85(f784(f784(f243(x86331),x86332),f784(f784(f293(x86331),x86333),f784(f113(x86331),x86334))))+~P85(f784(f784(f243(x86331),f784(f784(f90(x86331),x86332),f784(f113(x86331),x86334))),x86333))
% 11.41/11.19 [8634]~P61(x86341)+~P90(x86341)+~P85(f784(f784(f243(x86341),f2(x86341)),f784(f113(x86341),x86344)))+P85(f784(f784(f242(x86341),x86342),f784(f784(f90(x86341),x86343),f784(f113(x86341),x86344))))+~P85(f784(f784(f242(x86341),f784(f784(f293(x86341),x86342),f784(f113(x86341),x86344))),x86343))
% 11.41/11.19 [8635]~P61(x86351)+~P90(x86351)+~P85(f784(f784(f243(x86351),f2(x86351)),f784(f113(x86351),x86354)))+P85(f784(f784(f242(x86351),x86352),f784(f784(f293(x86351),x86353),f784(f113(x86351),x86354))))+~P85(f784(f784(f242(x86351),f784(f784(f90(x86351),x86352),f784(f113(x86351),x86354))),x86353))
% 11.41/11.19 [8759]E(f784(f784(f3(a1),f445(x87591,x87592,x87593,x87594)),f446(x87591,x87592,x87593,x87594)),x87594)+~P85(f784(f784(f243(a1),f2(a1)),x87593))+~P85(f784(f784(f243(a1),x87594),x87592))+~P85(f784(f784(f347(a1),x87592),x87591))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x87594),x87593)),x87592))
% 11.41/11.19 [8823]~P85(f784(x88231,x88232))+~P85(f784(f784(f243(a1),f2(a1)),x88234))+~P85(f784(f784(f242(a1),f2(a1)),x88233))+~P85(f784(x88231,f784(f784(f89(a1),f815(x88233,x88231,x88234)),x88234)))+P85(f784(x88231,f784(f784(f89(a1),x88232),f784(f784(f90(a1),x88233),x88234))))
% 11.41/11.19 [8824]~P85(f784(x88241,x88242))+~P85(f784(f784(f243(a1),f2(a1)),x88244))+~P85(f784(f784(f242(a1),f2(a1)),x88243))+~P85(f784(x88241,f784(f784(f3(a1),f820(x88243,x88241,x88244)),x88244)))+P85(f784(x88241,f784(f784(f3(a1),x88242),f784(f784(f90(a1),x88243),x88244))))
% 11.41/11.19 [8961]~P85(f784(f784(f243(a1),f2(a1)),x89613))+~P85(f784(f784(f243(a1),x89614),x89612))+~P85(f784(f784(f347(a1),x89612),x89611))+P85(f784(f784(f347(a1),f445(x89611,x89612,x89613,x89614)),x89611))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x89614),x89613)),x89612))
% 11.41/11.19 [8981]E(f784(f784(f3(a1),f438(x89811,x89812,x89813,x89814)),f439(x89811,x89812,x89813,x89814)),x89814)+~P85(f784(f784(f243(a1),f2(a1)),x89813))+~P85(f784(f784(f242(a1),x89814),x89812))+~P85(f784(f784(f347(a1),f784(f784(f89(a1),x89812),f87(a1))),x89811))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x89814),x89813)),x89812))
% 11.41/11.19 [9013]~P85(f784(f784(f243(a1),f2(a1)),x90132))+~P85(f784(f784(f243(a1),x90131),x90133))+~P85(f784(f784(f347(a1),x90133),x90134))+P85(f784(f784(f347(a1),f446(x90134,x90133,x90132,x90131)),f305(a1,f87(a1),x90132)))+P85(f784(f784(f243(a1),f784(f784(f89(a1),x90131),x90132)),x90133))
% 11.41/11.19 [9095]~P85(f784(f784(f243(a1),f2(a1)),x90953))+~P85(f784(f784(f242(a1),x90954),x90952))+P85(f784(f784(f347(a1),f438(x90951,x90952,x90953,x90954)),x90951))+~P85(f784(f784(f347(a1),f784(f784(f89(a1),x90952),f87(a1))),x90951))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x90954),x90953)),x90952))
% 11.41/11.19 [9133]~P85(f784(f784(f243(a1),f2(a1)),x91332))+~P85(f784(f784(f242(a1),x91331),x91333))+P85(f784(f784(f347(a1),f439(x91334,x91333,x91332,x91331)),f305(a1,f87(a1),x91332)))+~P85(f784(f784(f347(a1),f784(f784(f89(a1),x91333),f87(a1))),x91334))+P85(f784(f784(f242(a1),f784(f784(f89(a1),x91331),x91332)),x91333))
% 11.41/11.19 [9397]~P35(x93971,x93973)+~P27(x93971,x93974)+P35(x93971,f784(f784(f110(f869(f868(x93971,x93971),a852)),x93972),x93973))+~P85(f784(f784(f242(f869(f868(x93971,x93971),a852)),x93972),f784(f250(f869(f868(x93971,x93971),a852),f869(f868(x93971,x93971),a852)),x93974)))+~P85(f784(f784(f242(f869(f868(x93971,x93971),a852)),x93973),f784(f260(f869(f868(x93971,x93971),a852),f869(f868(x93971,x93971),a852)),x93974)))
% 11.41/11.19 [9674]~E(f784(f720(x96741,x96744,x96743,x96742),f723(x96741,x96744,x96743,x96742)),f190(f860(a851)))+P85(f784(f784(f243(a1),f722(x96741,x96744,x96743,x96742)),f723(x96741,x96744,x96743,x96742)))+P85(f784(f784(f784(x96741,x96742),x96743),x96744))+P85(f784(f784(f784(x96741,f720(x96741,x96744,x96743,x96742)),f722(x96741,x96744,x96743,x96742)),f784(f784(f89(a1),f723(x96741,x96744,x96743,x96742)),f87(a1))))+~P85(f784(f334(f868(f869(a1,f864(f860(a851))),f868(a1,a1)),a321),f784(f784(f251(f869(a1,f864(f860(a851))),f868(a1,a1)),x96742),f784(f784(f251(a1,a1),x96743),x96744))))
% 11.41/11.19 [9775]~P19(x97752,x97754,x97753)+E(x97751,f187(f869(x97752,a852)))+~P85(f784(f71(x97752),x97751))+P85(f784(f784(f347(x97752),f784(x97753,x97751)),x97751))+~P85(f784(f784(f347(x97752),f784(f784(x97754,f473(x97751,x97753,x97754,x97752)),f474(x97751,x97753,x97754,x97752))),f784(f784(f312(x97752),f473(x97751,x97753,x97754,x97752)),f784(f784(f312(x97752),f474(x97751,x97753,x97754,x97752)),f187(f869(x97752,a852))))))
% 11.41/11.19 [8622]~P61(x86221)+~P90(x86221)+~P85(f784(f784(f243(x86221),f2(x86221)),x86223))+~P85(f784(f784(f243(x86221),f784(f113(x86221),x86222)),f784(f784(f293(x86221),x86224),x86223)))+P85(f784(f784(f243(x86221),f784(f784(f90(x86221),f784(f113(x86221),x86222)),x86223)),x86224))
% 11.41/11.19 [8623]~P61(x86231)+~P90(x86231)+~P85(f784(f784(f243(x86231),f2(x86231)),x86233))+~P85(f784(f784(f242(x86231),f784(f113(x86231),x86232)),f784(f784(f293(x86231),x86234),x86233)))+P85(f784(f784(f242(x86231),f784(f784(f90(x86231),f784(f113(x86231),x86232)),x86233)),x86234))
% 11.41/11.19 [8762]~P61(x87621)+~P90(x87621)+~P85(f784(f784(f243(x87621),f2(x87621)),x87624))+P85(f784(f784(f243(x87621),f784(f113(x87621),x87622)),f784(f784(f293(x87621),x87623),x87624)))+~P85(f784(f784(f243(x87621),f784(f784(f90(x87621),f784(f113(x87621),x87622)),x87624)),x87623))
% 11.41/11.19 [8763]~P61(x87631)+~P90(x87631)+~P85(f784(f784(f243(x87631),f2(x87631)),x87634))+P85(f784(f784(f242(x87631),f784(f113(x87631),x87632)),f784(f784(f293(x87631),x87633),x87634)))+~P85(f784(f784(f242(x87631),f784(f784(f90(x87631),f784(f113(x87631),x87632)),x87634)),x87633))
% 11.41/11.19 [9318]~P52(x93181,x93181,x93184)+P85(f784(f784(f347(f868(x93181,x93181)),f784(f784(f251(x93181,x93181),x93182),x93183)),f310(x93181,x93184)))+P85(f784(f784(f347(f868(x93181,x93181)),f784(f784(f251(x93181,x93181),x93183),x93182)),f310(x93181,x93184)))+~P85(f784(f784(f347(f868(x93181,x93181)),f784(f784(f251(x93181,x93181),x93185),x93182)),f310(x93181,x93184)))+~P85(f784(f784(f347(f868(x93181,x93181)),f784(f784(f251(x93181,x93181),x93185),x93183)),f310(x93181,x93184)))
% 11.41/11.19 [5513]E(x55131,f2(a859))+~E(f784(f50(x55132),x55135),x55131)+E(f784(f50(x55132),x55133),f784(a160,x55131))+~E(x55133,f784(f784(f312(x55132),x55134),x55135))+P85(f784(f784(f347(x55132),x55134),x55135))
% 11.41/11.19 [5635]~P60(x56352)+E(x56351,f2(x56352))+E(x56353,f2(x56352))+~E(f784(f784(f293(x56352),x56354),x56353),f784(f784(f293(x56352),x56355),x56351))+E(f784(f784(f90(x56352),x56354),x56351),f784(f784(f90(x56352),x56355),x56353))
% 11.41/11.19 [5636]~P60(x56362)+E(x56361,f2(x56362))+E(x56363,f2(x56362))+~E(f784(f784(f90(x56362),x56364),x56363),f784(f784(f90(x56362),x56365),x56361))+E(f784(f784(f293(x56362),x56364),x56361),f784(f784(f293(x56362),x56365),x56363))
% 11.41/11.19 [5709]~E(f784(f50(x57091),x57095),x57093)+~E(x57095,f187(f869(x57091,a852)))+E(f784(f50(x57091),x57092),f784(a160,x57093))+~E(x57092,f784(f784(f312(x57091),x57094),x57095))+P85(f784(f784(f347(x57091),x57094),x57095))
% 11.41/11.19 [5935]~P86(x59352)+~E(f784(x59353,x59355),f2(x59352))+E(f784(f784(f11(x59351,x59352),x59353),x59354),f2(x59352))+~P85(f784(f71(x59351),x59354))+~P85(f784(f784(f347(x59351),x59355),x59354))
% 11.41/11.19 [6314]~P101(x63143)+E(x63141,x63142)+~E(f784(f304(x63143,x63144),x63141),f784(f304(x63143,x63145),x63142))+~P85(f784(f784(f243(x63143),x63145),x63142))+~P85(f784(f784(f243(x63143),x63144),x63141))
% 11.41/11.19 [6315]~P101(x63153)+E(x63151,x63152)+~E(f784(f304(x63153,x63151),x63154),f784(f304(x63153,x63152),x63155))+~P85(f784(f784(f243(x63153),x63152),x63155))+~P85(f784(f784(f243(x63153),x63151),x63154))
% 11.41/11.19 [6316]~P101(x63163)+E(x63161,x63162)+~E(f784(f304(x63163,x63164),x63161),f784(f304(x63163,x63165),x63162))+~P85(f784(f784(f243(x63163),x63165),x63162))+~P85(f784(f784(f243(x63163),x63164),x63161))
% 11.41/11.19 [6317]~P101(x63173)+E(x63171,x63172)+~E(f784(f304(x63173,x63171),x63174),f784(f304(x63173,x63172),x63175))+~P85(f784(f784(f243(x63173),x63172),x63175))+~P85(f784(f784(f243(x63173),x63171),x63174))
% 11.41/11.19 [7421]~P101(x74211)+~P15(x74211,f784(f784(f130(x74211),x74214),x74215))+~P85(f784(f784(f347(x74211),x74213),f784(f164(x74211),x74215)))+~P85(f784(f784(f347(x74211),x74212),f784(f164(x74211),x74214)))+P85(f784(f784(f242(x74211),x74212),x74213))
% 11.41/11.19 [8517]~P100(x85171)+~P85(f784(f784(f243(f869(x85171,a852)),f305(x85171,x85175,x85172)),f305(x85171,x85174,x85173)))+~P85(f784(f784(f242(x85171),x85175),x85172))+P85(f784(f784(f243(x85171),x85172),x85173))+P85(f784(f784(f243(x85171),x85174),x85175))
% 11.41/11.19 [9819]~P18(x98192,x98195,x98193)+E(x98191,f187(f869(x98192,a852)))+~E(f784(f784(x98195,f784(x98194,f580(x98191,x98194,x98193,x98195,x98192))),f784(x98194,f581(x98191,x98194,x98193,x98195,x98192))),f784(x98194,f784(f784(x98195,f580(x98191,x98194,x98193,x98195,x98192)),f581(x98191,x98194,x98193,x98195,x98192))))+E(f784(x98193,f784(f313(x98192,x98192,x98194),x98191)),f784(x98194,f784(x98193,x98191)))+~P85(f784(f71(x98192),x98191))
% 11.41/11.19 [6313]~P19(x63132,x63135,x63133)+E(x63131,f187(f869(x63132,a852)))+~P85(f784(f71(x63132),x63131))+E(f784(x63133,f784(f784(f312(x63132),x63134),x63131)),f784(f784(x63135,x63134),f784(x63133,x63131)))+P85(f784(f784(f347(x63132),x63134),x63131))
% 11.41/11.19 [7158]~P18(x71582,x71583,x71584)+E(f784(f784(x71583,f784(x71584,x71581)),f784(x71584,x71585)),f784(x71584,x71585))+E(x71581,f187(f869(x71582,a852)))+~P85(f784(f71(x71582),x71585))+~P85(f784(f784(f242(f869(x71582,a852)),x71581),x71585))
% 11.41/11.19 [7561]~P19(x75614,x75615,x75611)+E(f784(x75611,x75612),x75613)+~P85(f784(f71(x75614),x75612))+~E(f784(f784(f3(f869(x75614,a852)),x75612),f784(f784(f312(x75614),x75613),f187(f869(x75614,a852)))),f187(f869(x75614,a852)))+~P85(f784(f784(f347(x75614),x75613),x75612))
% 11.41/11.19 [7707]E(x77071,x77072)+~E(f784(f188(f860(x77073)),x77072),f784(f188(f860(x77074)),x77075))+~E(f784(f188(f860(x77073)),x77071),f784(f188(f860(x77074)),x77075))+~E(f172(x77074,x77073,f784(f784(f173(x77074,x77073),x77075),x77071)),f172(x77074,x77073,f784(f784(f173(x77074,x77073),x77075),x77072)))+~P85(f784(f132(x77074),x77075))
% 11.41/11.19 [8441]~P71(x84411)+~P115(x84411)+~P85(f784(f71(x84412),x84415))+P85(f784(f784(f289(x84411),f784(f784(f11(x84412,x84411),x84413),x84414)),f784(f784(f11(x84412,x84411),x84413),x84415)))+~P85(f784(f784(f242(f869(x84412,a852)),x84414),x84415))
% 11.41/11.19 [8490]E(x84901,x84902)+~P9(x84903,x84904,x84905)+E(f784(f784(f111(f869(x84903,a852)),x84901),x84902),f187(f869(x84903,a852)))+~P85(f784(f784(f347(f869(x84903,a852)),x84902),f784(f784(f69(x84903),x84904),x84905)))+~P85(f784(f784(f347(f869(x84903,a852)),x84901),f784(f784(f69(x84903),x84904),x84905)))
% 11.41/11.19 [8894]~P26(x88941,x88943,x88945,x88942)+~P85(f784(f71(x88943),x88944))+~P85(f784(f71(x88941),x88942))+P85(f784(f784(f242(a859),f784(f50(x88941),x88942)),f784(f50(x88943),x88944)))+~P85(f784(f784(f242(f869(x88943,a852)),f784(f313(x88941,x88943,x88945),x88942)),x88944))
% 11.41/11.19 [9196]~P68(x91962)+~E(f784(x91963,f492(x91963,x91964,x91965,x91961,x91962)),f2(x91962))+E(f784(f784(f8(x91961,x91962),x91963),x91964),f784(f784(f8(x91961,x91962),x91963),x91965))+~P85(f784(f71(x91961),x91965))+~P85(f784(f784(f242(f869(x91961,a852)),x91964),x91965))
% 11.41/11.19 [9197]~P68(x91972)+~E(f784(x91973,f497(x91973,x91974,x91975,x91971,x91972)),f2(x91972))+E(f784(f784(f8(x91971,x91972),x91973),x91974),f784(f784(f8(x91971,x91972),x91973),x91975))+~P85(f784(f71(x91971),x91975))+~P85(f784(f784(f242(f869(x91971,a852)),x91974),x91975))
% 11.41/11.19 [9198]~P71(x91982)+~E(f784(x91983,f493(x91983,x91984,x91985,x91981,x91982)),f87(x91982))+E(f784(f784(f11(x91981,x91982),x91983),x91984),f784(f784(f11(x91981,x91982),x91983),x91985))+~P85(f784(f71(x91981),x91985))+~P85(f784(f784(f242(f869(x91981,a852)),x91984),x91985))
% 11.41/11.19 [9199]~P71(x91992)+~E(f784(x91993,f494(x91993,x91994,x91995,x91991,x91992)),f87(x91992))+E(f784(f784(f11(x91991,x91992),x91993),x91994),f784(f784(f11(x91991,x91992),x91993),x91995))+~P85(f784(f71(x91991),x91995))+~P85(f784(f784(f242(f869(x91991,a852)),x91994),x91995))
% 11.41/11.19 [9658]~P81(x96581)+~P85(f784(f71(x96582),x96585))+~P85(f784(f784(f242(x96581),f2(x96581)),f784(x96583,f451(x96583,x96584,x96585,x96582,x96581))))+P85(f784(f784(f242(x96581),f784(f784(f8(x96582,x96581),x96583),x96584)),f784(f784(f8(x96582,x96581),x96583),x96585)))+~P85(f784(f784(f242(f869(x96582,a852)),x96584),x96585))
% 11.41/11.19 [7418]E(x74181,f2(a859))+P85(f784(x74182,x74183))+~E(x74184,f784(f784(f89(a859),f784(f784(f90(a859),x74181),x74183)),x74185))+~P85(f784(f784(f243(a859),x74185),x74181))+~P85(f784(x74182,f784(f784(f51(a859),x74184),x74181)))
% 11.41/11.19 [7500]E(x75001,f2(a859))+P85(f784(x75002,x75003))+~P85(f784(x75002,f60(a859,x75004,x75001)))+~E(x75004,f784(f784(f89(a859),f784(f784(f90(a859),x75001),x75005)),x75003))+~P85(f784(f784(f243(a859),x75003),x75001))
% 11.41/11.19 [7795]~P60(x77953)+E(f784(x77951,x77952),f2(x77953))+~P85(f784(f71(x77954),x77955))+E(f784(f784(f11(x77954,x77953),x77951),f784(f784(f3(f869(x77954,a852)),x77955),f784(f784(f312(x77954),x77952),f187(f869(x77954,a852))))),f784(f784(f11(x77954,x77953),x77951),x77955))+P85(f784(f784(f347(x77954),x77952),x77955))
% 11.41/11.19 [8185]~P68(x81851)+~P85(f784(f71(x81852),x81855))+~P85(f784(f71(x81852),x81854))+~E(f784(f784(f111(f869(x81852,a852)),x81854),x81855),f187(f869(x81852,a852)))+E(f784(f784(f89(x81851),f784(f784(f8(x81852,x81851),x81853),x81854)),f784(f784(f8(x81852,x81851),x81853),x81855)),f784(f784(f8(x81852,x81851),x81853),f784(f784(f110(f869(x81852,a852)),x81854),x81855)))
% 11.41/11.19 [8186]~P71(x81861)+~P85(f784(f71(x81862),x81865))+~P85(f784(f71(x81862),x81864))+~E(f784(f784(f111(f869(x81862,a852)),x81864),x81865),f187(f869(x81862,a852)))+E(f784(f784(f90(x81861),f784(f784(f11(x81862,x81861),x81863),x81864)),f784(f784(f11(x81862,x81861),x81863),x81865)),f784(f784(f11(x81862,x81861),x81863),f784(f784(f110(f869(x81862,a852)),x81864),x81865)))
% 11.41/11.19 [8187]~P71(x81871)+~P85(f784(f71(x81872),x81875))+~P85(f784(f71(x81872),x81874))+~E(f784(f784(f111(f869(x81872,a852)),x81874),x81875),f187(f869(x81872,a852)))+E(f784(f784(f90(x81871),f784(f784(f11(x81872,x81871),x81873),x81874)),f784(f784(f11(x81872,x81871),x81873),x81875)),f784(f784(f11(x81872,x81871),x81873),f784(f784(f110(f869(x81872,a852)),x81874),x81875)))
% 11.41/11.19 [8278]~P60(x82783)+E(f784(x82781,x82782),f2(x82783))+~P85(f784(f71(x82784),x82785))+E(f784(f784(f11(x82784,x82783),x82781),f784(f784(f3(f869(x82784,a852)),x82785),f784(f784(f312(x82784),x82782),f187(f869(x82784,a852))))),f784(f784(f293(x82783),f784(f784(f11(x82784,x82783),x82781),x82785)),f784(x82781,x82782)))+~P85(f784(f784(f347(x82784),x82782),x82785))
% 11.41/11.19 [8774]~P9(x87741,x87745,x87744)+~E(f784(f287(x87741,x87741,x87744),f784(f784(f312(x87741),x87742),f187(f869(x87741,a852)))),f784(f287(x87741,x87741,x87744),f784(f784(f312(x87741),x87743),f187(f869(x87741,a852)))))+~P85(f784(f784(f347(x87741),x87743),x87745))+~P85(f784(f784(f347(x87741),x87742),x87745))+P85(f784(f784(f347(f868(x87741,x87741)),f784(f784(f251(x87741,x87741),x87742),x87743)),x87744))
% 11.41/11.19 [8775]~P9(x87751,x87755,x87754)+~E(f784(f287(x87751,x87751,x87754),f784(f784(f312(x87751),x87752),f187(f869(x87751,a852)))),f784(f287(x87751,x87751,x87754),f784(f784(f312(x87751),x87753),f187(f869(x87751,a852)))))+~P85(f784(f784(f347(x87751),x87753),x87755))+~P85(f784(f784(f347(x87751),x87752),x87755))+P85(f784(f784(f347(f868(x87751,x87751)),f784(f784(f251(x87751,x87751),x87752),x87753)),x87754))
% 11.41/11.19 [8855]~P9(x88551,x88555,x88552)+E(f784(f287(x88551,x88551,x88552),f784(f784(f312(x88551),x88553),f187(f869(x88551,a852)))),f784(f287(x88551,x88551,x88552),f784(f784(f312(x88551),x88554),f187(f869(x88551,a852)))))+~P85(f784(f784(f347(x88551),x88554),x88555))+~P85(f784(f784(f347(x88551),x88553),x88555))+~P85(f784(f784(f347(f868(x88551,x88551)),f784(f784(f251(x88551,x88551),x88553),x88554)),x88552))
% 11.41/11.19 [8944]~P9(x89441,x89445,x89444)+~E(f784(f784(f69(x89441),f784(f784(f312(x89441),x89442),f187(f869(x89441,a852)))),x89444),f784(f784(f69(x89441),f784(f784(f312(x89441),x89443),f187(f869(x89441,a852)))),x89444))+~P85(f784(f784(f347(x89441),x89443),x89445))+~P85(f784(f784(f347(x89441),x89442),x89445))+P85(f784(f784(f347(f868(x89441,x89441)),f784(f784(f251(x89441,x89441),x89442),x89443)),x89444))
% 11.41/11.19 [8960]~P9(x89601,x89605,x89603)+E(f784(f784(f69(x89601),f784(f784(f312(x89601),x89602),f187(f869(x89601,a852)))),x89603),f784(f784(f69(x89601),f784(f784(f312(x89601),x89604),f187(f869(x89601,a852)))),x89603))+~P85(f784(f784(f347(x89601),x89604),x89605))+~P85(f784(f784(f347(x89601),x89602),x89605))+~P85(f784(f784(f347(f868(x89601,x89601)),f784(f784(f251(x89601,x89601),x89602),x89604)),x89603))
% 11.41/11.19 [9223]~P71(x92231)+~P85(f784(f71(x92232),x92235))+~P85(f784(f71(x92232),x92234))+~E(f784(f784(f111(f869(x92232,a852)),x92234),x92235),f187(f869(x92232,a852)))+E(f784(f784(f90(x92231),f784(f784(f784(f75(x92231,x92232,f90(x92231)),x92233),f87(x92231)),x92234)),f784(f784(f784(f75(x92231,x92232,f90(x92231)),x92233),f87(x92231)),x92235)),f784(f784(f784(f75(x92231,x92232,f90(x92231)),x92233),f87(x92231)),f784(f784(f110(f869(x92232,a852)),x92234),x92235)))
% 11.41/11.19 [9233]~P68(x92331)+~E(f784(x92333,f520(x92333,x92335,x92334,x92332,x92331)),f2(x92331))+~P85(f784(f71(x92332),x92334))+~P85(f784(f71(x92332),x92335))+E(f784(f784(f89(x92331),f784(f784(f8(x92332,x92331),x92333),x92334)),f784(f784(f8(x92332,x92331),x92333),x92335)),f784(f784(f8(x92332,x92331),x92333),f784(f784(f110(f869(x92332,a852)),x92334),x92335)))
% 11.41/11.19 [9234]~P68(x92341)+~E(f784(x92343,f524(x92343,x92345,x92344,x92342,x92341)),f2(x92341))+~P85(f784(f71(x92342),x92344))+~P85(f784(f71(x92342),x92345))+E(f784(f784(f89(x92341),f784(f784(f8(x92342,x92341),x92343),x92344)),f784(f784(f8(x92342,x92341),x92343),x92345)),f784(f784(f8(x92342,x92341),x92343),f784(f784(f110(f869(x92342,a852)),x92344),x92345)))
% 11.41/11.19 [9235]~P71(x92351)+~E(f784(x92353,f521(x92353,x92355,x92354,x92352,x92351)),f87(x92351))+~P85(f784(f71(x92352),x92354))+~P85(f784(f71(x92352),x92355))+E(f784(f784(f90(x92351),f784(f784(f11(x92352,x92351),x92353),x92354)),f784(f784(f11(x92352,x92351),x92353),x92355)),f784(f784(f11(x92352,x92351),x92353),f784(f784(f110(f869(x92352,a852)),x92354),x92355)))
% 11.41/11.19 [9236]~P71(x92361)+~E(f784(x92363,f523(x92363,x92365,x92364,x92362,x92361)),f87(x92361))+~P85(f784(f71(x92362),x92364))+~P85(f784(f71(x92362),x92365))+E(f784(f784(f90(x92361),f784(f784(f11(x92362,x92361),x92363),x92364)),f784(f784(f11(x92362,x92361),x92363),x92365)),f784(f784(f11(x92362,x92361),x92363),f784(f784(f110(f869(x92362,a852)),x92364),x92365)))
% 11.41/11.19 [9438]~P71(x94381)+~E(f784(x94383,f541(x94383,x94385,x94384,x94382,x94381)),f87(x94381))+~P85(f784(f71(x94382),x94384))+~P85(f784(f71(x94382),x94385))+E(f784(f784(f90(x94381),f784(f784(f784(f75(x94381,x94382,f90(x94381)),x94383),f87(x94381)),x94384)),f784(f784(f784(f75(x94381,x94382,f90(x94381)),x94383),f87(x94381)),x94385)),f784(f784(f784(f75(x94381,x94382,f90(x94381)),x94383),f87(x94381)),f784(f784(f110(f869(x94382,a852)),x94384),x94385)))
% 11.41/11.19 [9543]~P68(x95432)+E(f784(f784(f8(x95431,x95432),x95433),x95434),f784(f784(f8(x95431,x95432),x95433),x95435))+~P85(f784(f71(x95431),x95435))+~P85(f784(f784(f242(f869(x95431,a852)),x95434),x95435))+P85(f784(f784(f347(x95431),f492(x95433,x95434,x95435,x95431,x95432)),f784(f784(f3(f869(x95431,a852)),x95435),x95434)))
% 11.41/11.19 [9544]~P68(x95442)+E(f784(f784(f8(x95441,x95442),x95443),x95444),f784(f784(f8(x95441,x95442),x95443),x95445))+~P85(f784(f71(x95441),x95445))+~P85(f784(f784(f242(f869(x95441,a852)),x95444),x95445))+P85(f784(f784(f347(x95441),f497(x95443,x95444,x95445,x95441,x95442)),f784(f784(f3(f869(x95441,a852)),x95445),x95444)))
% 11.41/11.19 [9545]~P71(x95452)+E(f784(f784(f11(x95451,x95452),x95453),x95454),f784(f784(f11(x95451,x95452),x95453),x95455))+~P85(f784(f71(x95451),x95455))+~P85(f784(f784(f242(f869(x95451,a852)),x95454),x95455))+P85(f784(f784(f347(x95451),f493(x95453,x95454,x95455,x95451,x95452)),f784(f784(f3(f869(x95451,a852)),x95455),x95454)))
% 11.41/11.19 [9546]~P71(x95462)+E(f784(f784(f11(x95461,x95462),x95463),x95464),f784(f784(f11(x95461,x95462),x95463),x95465))+~P85(f784(f71(x95461),x95465))+~P85(f784(f784(f242(f869(x95461,a852)),x95464),x95465))+P85(f784(f784(f347(x95461),f494(x95463,x95464,x95465,x95461,x95462)),f784(f784(f3(f869(x95461,a852)),x95465),x95464)))
% 11.41/11.19 [9561]~P68(x95611)+~P85(f784(f71(x95612),x95614))+~P85(f784(f71(x95612),x95615))+E(f784(f784(f89(x95611),f784(f784(f8(x95612,x95611),x95613),x95614)),f784(f784(f8(x95612,x95611),x95613),x95615)),f784(f784(f8(x95612,x95611),x95613),f784(f784(f110(f869(x95612,a852)),x95614),x95615)))+P85(f784(f784(f347(x95612),f520(x95613,x95615,x95614,x95612,x95611)),f784(f784(f111(f869(x95612,a852)),x95614),x95615)))
% 11.41/11.19 [9562]~P68(x95621)+~P85(f784(f71(x95622),x95624))+~P85(f784(f71(x95622),x95625))+E(f784(f784(f89(x95621),f784(f784(f8(x95622,x95621),x95623),x95624)),f784(f784(f8(x95622,x95621),x95623),x95625)),f784(f784(f8(x95622,x95621),x95623),f784(f784(f110(f869(x95622,a852)),x95624),x95625)))+P85(f784(f784(f347(x95622),f524(x95623,x95625,x95624,x95622,x95621)),f784(f784(f111(f869(x95622,a852)),x95624),x95625)))
% 11.41/11.19 [9563]~P71(x95631)+~P85(f784(f71(x95632),x95634))+~P85(f784(f71(x95632),x95635))+E(f784(f784(f90(x95631),f784(f784(f11(x95632,x95631),x95633),x95634)),f784(f784(f11(x95632,x95631),x95633),x95635)),f784(f784(f11(x95632,x95631),x95633),f784(f784(f110(f869(x95632,a852)),x95634),x95635)))+P85(f784(f784(f347(x95632),f521(x95633,x95635,x95634,x95632,x95631)),f784(f784(f111(f869(x95632,a852)),x95634),x95635)))
% 11.41/11.19 [9564]~P71(x95641)+~P85(f784(f71(x95642),x95644))+~P85(f784(f71(x95642),x95645))+E(f784(f784(f90(x95641),f784(f784(f11(x95642,x95641),x95643),x95644)),f784(f784(f11(x95642,x95641),x95643),x95645)),f784(f784(f11(x95642,x95641),x95643),f784(f784(f110(f869(x95642,a852)),x95644),x95645)))+P85(f784(f784(f347(x95642),f523(x95643,x95645,x95644,x95642,x95641)),f784(f784(f111(f869(x95642,a852)),x95644),x95645)))
% 11.41/11.19 [9577]~P81(x95775)+~P85(f784(f71(x95771),x95774))+P85(f784(f784(f242(x95775),f784(f784(f8(x95771,x95775),x95772),x95773)),f784(f784(f8(x95771,x95775),x95772),x95774)))+~P85(f784(f784(f242(f869(x95771,a852)),x95773),x95774))+P85(f784(f784(f347(x95771),f451(x95772,x95773,x95774,x95771,x95775)),f784(f784(f3(f869(x95771,a852)),x95774),x95773)))
% 11.41/11.19 [9624]~P71(x96241)+~P85(f784(f71(x96242),x96244))+~P85(f784(f71(x96242),x96245))+E(f784(f784(f90(x96241),f784(f784(f784(f75(x96241,x96242,f90(x96241)),x96243),f87(x96241)),x96244)),f784(f784(f784(f75(x96241,x96242,f90(x96241)),x96243),f87(x96241)),x96245)),f784(f784(f784(f75(x96241,x96242,f90(x96241)),x96243),f87(x96241)),f784(f784(f110(f869(x96242,a852)),x96244),x96245)))+P85(f784(f784(f347(x96242),f541(x96243,x96245,x96244,x96242,x96241)),f784(f784(f111(f869(x96242,a852)),x96244),x96245)))
% 11.41/11.19 [8668]~P19(x86681,x86684,x86685)+~P85(f784(f71(x86681),x86682))+E(f784(f784(f3(f869(x86681,a852)),x86682),f784(f784(f312(x86681),x86683),f187(f869(x86681,a852)))),f187(f869(x86681,a852)))+~P85(f784(f784(f347(x86681),x86683),x86682))+E(f784(f784(x86684,x86683),f784(x86685,f784(f784(f3(f869(x86681,a852)),x86682),f784(f784(f312(x86681),x86683),f187(f869(x86681,a852)))))),f784(x86685,x86682))
% 11.41/11.19 [8735]~P19(x87351,x87354,x87355)+~P85(f784(f71(x87351),x87353))+~P85(f784(f71(x87351),x87352))+E(f784(f784(f111(f869(x87351,a852)),x87352),x87353),f187(f869(x87351,a852)))+E(f784(f784(x87354,f784(x87355,f784(f784(f110(f869(x87351,a852)),x87352),x87353))),f784(x87355,f784(f784(f111(f869(x87351,a852)),x87352),x87353))),f784(f784(x87354,f784(x87355,x87352)),f784(x87355,x87353)))
% 11.41/11.19 [9238]~P85(f784(f784(f242(a1),x92384),f2(a1)))+~P85(f784(f784(f243(a1),x92383),x92385))+P85(f784(f784(f242(a1),x92381),x92382))+~P85(f784(f784(f243(a1),x92383),x92384))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),f784(f784(f90(a1),x92383),x92382)),x92385)),f784(f784(f89(a1),f784(f784(f90(a1),x92383),x92381)),x92384)))
% 11.41/11.19 [9240]~P85(f784(f784(f242(a1),f2(a1)),x92405))+P85(f784(f784(f242(a1),x92401),x92402))+~P85(f784(f784(f243(a1),x92403),x92404))+~P85(f784(f784(f243(a1),x92405),x92404))+~P85(f784(f784(f242(a1),f784(f784(f89(a1),f784(f784(f90(a1),x92404),x92401)),x92405)),f784(f784(f89(a1),f784(f784(f90(a1),x92404),x92402)),x92403)))
% 11.41/11.19 [9353]~P60(x93535)+E(f784(x93531,f522(x93531,x93532,x93533,x93534,x93535)),f2(x93535))+~P85(f784(f71(x93534),x93533))+~P85(f784(f71(x93534),x93532))+E(f784(f784(f293(x93535),f784(f784(f90(x93535),f784(f784(f11(x93534,x93535),x93531),x93533)),f784(f784(f11(x93534,x93535),x93531),x93532))),f784(f784(f11(x93534,x93535),x93531),f784(f784(f111(f869(x93534,a852)),x93533),x93532))),f784(f784(f11(x93534,x93535),x93531),f784(f784(f110(f869(x93534,a852)),x93533),x93532)))
% 11.41/11.19 [9618]~P60(x96181)+~P85(f784(f71(x96182),x96184))+~P85(f784(f71(x96182),x96185))+E(f784(f784(f293(x96181),f784(f784(f90(x96181),f784(f784(f11(x96182,x96181),x96183),x96184)),f784(f784(f11(x96182,x96181),x96183),x96185))),f784(f784(f11(x96182,x96181),x96183),f784(f784(f111(f869(x96182,a852)),x96184),x96185))),f784(f784(f11(x96182,x96181),x96183),f784(f784(f110(f869(x96182,a852)),x96184),x96185)))+P85(f784(f784(f347(x96182),f522(x96183,x96185,x96184,x96182,x96181)),f784(f784(f111(f869(x96182,a852)),x96184),x96185)))
% 11.41/11.19 [8980]E(f784(f784(f130(x89801),x89802),x89803),f784(f784(f130(x89801),x89804),x89805))+~E(f784(f784(f165(x89801),f784(f188(f860(x89801)),x89804)),x89802),x89804)+~E(f784(f784(f165(x89801),f784(f188(f860(x89801)),x89802)),x89804),x89802)+~E(x89805,f784(f784(f130(x89801),f784(f784(f133(x89801),f784(f188(f860(x89801)),x89804)),x89802)),x89803))+~E(f784(f784(f130(x89801),f784(f784(f133(x89801),f784(f188(f860(x89801)),x89802)),x89804)),x89805),x89803)
% 11.41/11.19 [9351]~P101(x93512)+E(f784(f784(f142(x93511,x93512,x93513),x93514),f154(x93511,x93514,x93515)),x93515)+~P15(x93512,f784(f784(f146(x93511,x93512),x93513),x93515))+~P85(f784(f784(f347(x93511),x93514),f784(f164(x93511),x93515)))+~E(f784(f135(x93511),f784(f131(x93511,f784(f784(f10(x93512,a852,x93511),f784(a343,f784(x93513,x93514))),x93513)),x93515)),x93514)
% 11.41/11.19 [9672]~P65(x96721)+~P85(f784(f76(x96721,x96721,f90(x96721),x96722,x96723),x96725))+~P85(f784(f784(f347(x96721),x96724),x96723))+P85(f784(f784(f347(x96721),x96722),x96723))+P85(f784(f76(x96721,x96721,f90(x96721),x96724,f784(f784(f312(x96721),x96722),f784(f784(f3(f869(x96721,a852)),x96723),f784(f784(f312(x96721),x96724),f187(f869(x96721,a852)))))),x96725))
% 11.41/11.19 [7162]E(x71621,x71622)+~P26(x71624,x71625,x71623,x71626)+~E(f784(x71623,x71621),f784(x71623,x71622))+~P85(f784(f784(f347(x71624),x71622),x71626))+~P85(f784(f784(f347(x71624),x71621),x71626))
% 11.41/11.19 [7163]E(x71631,x71632)+~P26(x71634,x71635,x71633,x71636)+~E(f784(x71633,x71631),f784(x71633,x71632))+~P85(f784(f784(f347(x71634),x71632),x71636))+~P85(f784(f784(f347(x71634),x71631),x71636))
% 11.41/11.19 [7164]E(x71641,x71642)+~P26(x71644,x71645,x71643,x71646)+~E(f784(x71643,x71641),f784(x71643,x71642))+~P85(f784(f784(f347(x71644),x71642),x71646))+~P85(f784(f784(f347(x71644),x71641),x71646))
% 11.41/11.19 [7165]E(x71651,x71652)+~P26(x71654,x71655,x71653,x71656)+~E(f784(x71653,x71651),f784(x71653,x71652))+~P85(f784(f784(f347(x71654),x71652),x71656))+~P85(f784(f784(f347(x71654),x71651),x71656))
% 11.41/11.19 [6411]~P111(x64114)+E(x64111,x64112)+~E(x64115,x64116)+E(x64113,f2(x64114))+~E(f784(f784(f89(x64114),x64115),f784(f784(f90(x64114),x64113),x64111)),f784(f784(f89(x64114),x64116),f784(f784(f90(x64114),x64113),x64112)))
% 11.41/11.19 [7480]~P101(x74801)+~P6(x74801)+~P85(f784(f784(f243(x74801),x74802),f784(x74805,x74806)))+~P85(f784(f784(f347(x74803),x74806),x74804))+P85(f784(f784(f243(x74801),x74802),f784(f784(f54(x74803,x74801),x74804),x74805)))
% 11.41/11.19 [9836]~P86(x98366)+~P85(f784(f71(x98361),x98365))+P85(f784(f784(f347(x98361),f642(x98362,x98363,x98364,x98365,x98361,x98366)),x98364))+P85(f784(f784(f289(x98366),f784(f784(f11(x98361,x98366),x98363),x98364)),f784(f784(f11(x98361,x98366),x98362),x98365)))+~P85(f784(f784(f242(f869(x98361,a852)),x98364),x98365))
% 11.41/11.19 [9957]~P86(x99571)+~P85(f784(f71(x99572),x99576))+~P85(f784(f784(f289(x99571),f784(x99573,f642(x99575,x99573,x99574,x99576,x99572,x99571))),f784(x99575,f642(x99575,x99573,x99574,x99576,x99572,x99571))))+P85(f784(f784(f289(x99571),f784(f784(f11(x99572,x99571),x99573),x99574)),f784(f784(f11(x99572,x99571),x99575),x99576)))+~P85(f784(f784(f242(f869(x99572,a852)),x99574),x99576))
% 11.41/11.19 [8156]~P101(x81561)+~P6(x81561)+~P85(f784(f784(f243(x81561),f784(x81564,x81566)),x81565))+~P85(f784(f784(f347(x81562),x81566),x81563))+P85(f784(f784(f243(x81561),f784(f784(f55(x81562,x81561),x81563),x81564)),x81565))
% 11.41/11.19 [8414]~P20(x84142,x84145,x84146,x84141)+~P85(f784(f71(x84142),x84144))+~P85(f784(f71(x84142),x84143))+~E(f784(f784(f111(f869(x84142,a852)),x84143),x84144),f187(f869(x84142,a852)))+E(f784(x84141,f784(f784(f110(f869(x84142,a852)),x84143),x84144)),f784(f82(x84145,x84145,x84145,f784(x84141,x84143)),f784(x84141,x84144)))
% 11.41/11.19 [9068]~P115(x90681)+~P109(x90681)+~P85(f784(f784(f289(x90681),x90682),x90685))+~P85(f784(f784(f289(x90681),x90682),f784(f784(f89(x90681),x90683),x90686)))+P85(f784(f784(f289(x90681),x90682),f784(f784(f89(x90681),f784(f784(f3(x90681),x90683),f784(f784(f90(x90681),x90684),x90685))),x90686)))
% 11.41/11.19 [9069]~P115(x90691)+~P109(x90691)+~P85(f784(f784(f289(x90691),x90692),x90695))+~P85(f784(f784(f289(x90691),x90692),f784(f784(f89(x90691),x90693),x90696)))+P85(f784(f784(f289(x90691),x90692),f784(f784(f89(x90691),f784(f784(f3(x90691),x90693),f784(f784(f90(x90691),x90694),x90695))),x90696)))
% 11.41/11.19 [9227]~P115(x92271)+~P109(x92271)+~P85(f784(f784(f289(x92271),x92272),x92275))+P85(f784(f784(f289(x92271),x92272),f784(f784(f89(x92271),x92273),x92274)))+~P85(f784(f784(f289(x92271),x92272),f784(f784(f89(x92271),f784(f784(f3(x92271),x92273),f784(f784(f90(x92271),x92276),x92275))),x92274)))
% 11.41/11.19 [9228]~P115(x92281)+~P109(x92281)+~P85(f784(f784(f289(x92281),x92282),x92285))+P85(f784(f784(f289(x92281),x92282),f784(f784(f89(x92281),x92283),x92284)))+~P85(f784(f784(f289(x92281),x92282),f784(f784(f89(x92281),f784(f784(f3(x92281),x92283),f784(f784(f90(x92281),x92286),x92285))),x92284)))
% 11.41/11.19 [8706]E(x87061,x87062)+~P54(x87064,x87065,x87066,x87063,x87067)+~E(f784(x87063,x87061),f784(x87063,x87062))+~P85(f784(f784(f347(x87065),x87062),x87067))+~P85(f784(f784(f347(x87065),x87061),x87067))
% 11.41/11.19 [9966]~P9(x99661,x99667,x99666)+~P13(x99661,f869(x99665,a852),x99666,x99664)+P85(f784(f784(f347(x99661),f513(x99662,x99663,x99664,x99665,x99666,x99667,x99661)),x99667))+~P85(f784(f784(f347(f869(x99661,a852)),x99663),f784(f784(f69(x99661),x99667),x99666)))+P85(f784(f784(f347(f869(x99665,a852)),f784(f784(f54(x99661,f869(x99665,a852)),x99663),x99664)),x99662))
% 11.41/11.19 [10013]~P9(x100132,x100136,x100137)+~P13(x100132,f869(x100131,a852),x100137,x100134)+~P85(f784(f784(f347(f869(x100132,a852)),x100133),f784(f784(f69(x100132),x100136),x100137)))+~P85(f784(f784(f347(f869(x100131,a852)),f784(x100134,f513(x100135,x100133,x100134,x100131,x100137,x100136,x100132))),x100135))+P85(f784(f784(f347(f869(x100131,a852)),f784(f784(f54(x100132,f869(x100131,a852)),x100133),x100134)),x100135))
% 11.41/11.19 [8324]~P71(x83242)+~P26(x83241,x83245,x83248,x83244)+~E(x83243,f784(f82(x83245,x83242,x83241,x83246),x83248))+~E(x83247,f784(f313(x83241,x83245,x83248),x83244))+E(f784(f784(f11(x83241,x83242),x83243),x83244),f784(f784(f11(x83245,x83242),x83246),x83247))
% 11.41/11.19 [10016]~P71(x100162)+~P26(x100165,x100161,x100168,x100167)+~E(f784(x100166,f543(x100163,x100166,x100164,x100167,x100168,x100161,x100165,x100162)),f784(f784(f82(x100161,x100162,x100165,x100163),x100168),f543(x100163,x100166,x100164,x100167,x100168,x100161,x100165,x100162)))+~E(x100164,f784(f313(x100165,x100161,x100168),x100167))+E(f784(f784(f11(x100161,x100162),x100163),x100164),f784(f784(f11(x100165,x100162),x100166),x100167))
% 11.41/11.19 [10019]~P68(x100192)+~P26(x100191,x100195,x100198,x100194)+~E(x100197,f784(f313(x100191,x100195,x100198),x100194))+E(f784(f784(f8(x100191,x100192),x100193),x100194),f784(f784(f8(x100195,x100192),x100196),x100197))+P85(f784(f784(f347(x100191),f647(x100196,x100193,x100197,x100194,x100198,x100195,x100191,x100192)),x100194))
% 11.41/11.19 [10020]~P71(x100202)+~P26(x100201,x100205,x100208,x100204)+~E(x100207,f784(f313(x100201,x100205,x100208),x100204))+E(f784(f784(f11(x100201,x100202),x100203),x100204),f784(f784(f11(x100205,x100202),x100206),x100207))+P85(f784(f784(f347(x100201),f543(x100206,x100203,x100207,x100204,x100208,x100205,x100201,x100202)),x100204))
% 11.41/11.19 [10024]~P68(x100242)+~P26(x100245,x100241,x100248,x100247)+~E(x100244,f784(f313(x100245,x100241,x100248),x100247))+~E(f784(x100246,f647(x100243,x100246,x100244,x100247,x100248,x100241,x100245,x100242)),f784(x100243,f784(x100248,f647(x100243,x100246,x100244,x100247,x100248,x100241,x100245,x100242))))+E(f784(f784(f8(x100241,x100242),x100243),x100244),f784(f784(f8(x100245,x100242),x100246),x100247))
% 11.41/11.19 [9416]~E(f784(f188(f860(x94162)),x94165),f784(f188(f860(x94161)),x94163))+~E(f784(f188(f860(x94162)),x94164),f784(f188(f860(x94161)),x94163))+~E(f784(f784(f784(f81(x94161,f864(x94162)),f172(x94161,x94162,f784(f784(f173(x94161,x94162),x94163),x94164))),x94166),f784(f237(x94162),x94167)),f784(f784(f784(f81(x94161,f864(x94162)),f172(x94161,x94162,f784(f784(f173(x94161,x94162),x94163),x94165))),x94166),f784(f237(x94162),x94168)))+E(f172(x94161,x94162,f784(f784(f173(x94161,x94162),x94163),x94164)),f172(x94161,x94162,f784(f784(f173(x94161,x94162),x94163),x94165)))+P85(f784(f784(f347(x94161),x94166),f784(f164(x94161),x94163)))
% 11.41/11.19 [9512]~P24(x95126,x95122,x95125,x95127,x95128,x95121)+~P85(f784(f71(x95122),x95124))+~P85(f784(f71(x95122),x95123))+~E(f784(f784(f111(f869(x95122,a852)),x95123),x95124),f187(f869(x95122,a852)))+E(f784(x95121,f784(f784(f110(f869(x95122,a852)),x95123),x95124)),f784(f784(x95125,f784(x95121,x95123)),f784(x95121,x95124)))
% 11.41/11.19 [9911]~P24(x99118,x99112,x99115,x99117,x99116,x99111)+~E(f784(x99116,f583(x99114,x99113,x99111,x99116,x99117,x99115,x99112)),x99117)+~P85(f784(f71(x99112),x99113))+~P85(f784(f71(x99112),x99114))+E(f784(x99111,f784(f784(f110(f869(x99112,a852)),x99113),x99114)),f784(f784(x99115,f784(x99111,x99113)),f784(x99111,x99114)))
% 11.41/11.19 [9972]~P24(x99728,x99722,x99725,x99727,x99726,x99721)+~P85(f784(f71(x99722),x99723))+~P85(f784(f71(x99722),x99724))+E(f784(x99721,f784(f784(f110(f869(x99722,a852)),x99723),x99724)),f784(f784(x99725,f784(x99721,x99723)),f784(x99721,x99724)))+P85(f784(f784(f347(x99722),f583(x99724,x99723,x99721,x99726,x99727,x99725,x99722)),f784(f784(f111(f869(x99722,a852)),x99723),x99724)))
% 11.41/11.19 [9663]~P9(x96634,x96638,x96635)+~P9(x96631,x96639,x96633)+~P14(x96631,x96634,f869(x96632,a852),x96633,x96635,x96637)+P13(x96631,f869(x96632,a852),x96633,f784(f784(f10(f869(x96634,f869(x96632,a852)),f869(x96632,a852),x96631),f784(f54(x96634,f869(x96632,a852)),f784(f287(x96634,x96634,x96635),f784(f784(f312(x96634),x96636),f187(f869(x96634,a852)))))),x96637))+~P85(f784(f784(f347(x96634),x96636),x96638))
% 11.41/11.19 [4957]~P124(x49572)+~P129(x49572)+~P140(x49572)+~P106(x49572)+E(x49571,f2(x49572))+~E(f784(f784(f252(x49572),x49571),x49573),f2(x49572))
% 11.41/11.19 [4958]~P124(x49582)+~P129(x49582)+~P140(x49582)+~P106(x49582)+~E(x49581,f2(a859))+~E(f784(f784(f252(x49582),x49583),x49581),f2(x49582))
% 11.41/11.19 [6391]~P81(x63911)+~E(x63913,f2(x63911))+~E(x63912,f2(x63911))+E(f784(f784(f89(x63911),x63912),x63913),f2(x63911))+~P85(f784(f784(f242(x63911),f2(x63911)),x63913))+~P85(f784(f784(f242(x63911),f2(x63911)),x63912))
% 11.41/11.19 [8752]E(x87521,f2(a859))+~E(x87522,f784(f784(f89(a859),f784(f784(f90(a859),f784(f250(a859,a859),x87523)),x87521)),f784(f260(a859,a859),x87523)))+P85(f784(f63(x87522,x87521),x87523))+~P85(f784(f784(f242(a859),f784(f260(a859,a859),x87523)),f2(a859)))+P85(f784(f784(f243(a859),f2(a859)),x87521))+~P85(f784(f784(f243(a859),x87521),f784(f260(a859,a859),x87523)))
% 11.41/11.19 [8764]~E(f784(f250(a859,a859),x87643),f2(a859))+~E(x87641,f784(f784(f89(a859),f784(f784(f90(a859),f784(f250(a859,a859),x87643)),x87642)),f784(f260(a859,a859),x87643)))+P85(f784(f63(x87641,x87642),x87643))+~P85(f784(f784(f242(a859),f784(f260(a859,a859),x87643)),f2(a859)))+P85(f784(f784(f243(a859),f2(a859)),x87642))+~P85(f784(f784(f243(a859),x87642),f784(f260(a859,a859),x87643)))
% 11.41/11.19 [8771]E(x87711,f2(a859))+~E(x87712,f784(f784(f89(a859),f784(f784(f90(a859),f784(f250(a859,a859),x87713)),x87711)),f784(f260(a859,a859),x87713)))+P85(f784(f63(x87712,x87711),x87713))+~P85(f784(f784(f243(a859),f2(a859)),x87711))+~P85(f784(f784(f242(a859),f2(a859)),f784(f260(a859,a859),x87713)))+~P85(f784(f784(f243(a859),f784(f260(a859,a859),x87713)),x87711))
% 11.41/11.19 [8785]~E(f784(f250(a859,a859),x87853),f2(a859))+~E(x87851,f784(f784(f89(a859),f784(f784(f90(a859),f784(f250(a859,a859),x87853)),x87852)),f784(f260(a859,a859),x87853)))+P85(f784(f63(x87851,x87852),x87853))+~P85(f784(f784(f243(a859),f2(a859)),x87852))+~P85(f784(f784(f242(a859),f2(a859)),f784(f260(a859,a859),x87853)))+~P85(f784(f784(f243(a859),f784(f260(a859,a859),x87853)),x87852))
% 11.41/11.19 [6789]~P93(x67892)+E(x67891,f187(f869(x67892,a852)))+E(x67893,f187(f869(x67892,a852)))+~P85(f784(f71(x67892),x67891))+~P85(f784(f71(x67892),x67893))+E(f15(x67892,f784(f784(f110(f869(x67892,a852)),x67893),x67891)),f784(f784(f110(x67892),f15(x67892,x67893)),f15(x67892,x67891)))
% 11.41/11.19 [6790]~P101(x67902)+E(x67901,f187(f869(x67902,a852)))+E(x67903,f187(f869(x67902,a852)))+~P85(f784(f71(x67902),x67901))+~P85(f784(f71(x67902),x67903))+E(f16(x67902,f784(f784(f110(f869(x67902,a852)),x67903),x67901)),f784(f784(f186(x67902),f16(x67902,x67903)),f16(x67902,x67901)))
% 11.41/11.19 [6791]~P101(x67912)+E(x67911,f187(f869(x67912,a852)))+E(x67913,f187(f869(x67912,a852)))+~P85(f784(f71(x67912),x67911))+~P85(f784(f71(x67912),x67913))+E(f17(x67912,f784(f784(f110(f869(x67912,a852)),x67913),x67911)),f784(f784(f246(x67912),f17(x67912,x67913)),f17(x67912,x67911)))
% 11.41/11.19 [6792]~P93(x67922)+E(x67921,f187(f869(x67922,a852)))+E(x67923,f187(f869(x67922,a852)))+~P85(f784(f71(x67922),x67921))+~P85(f784(f71(x67922),x67923))+E(f12(x67922,f784(f784(f110(f869(x67922,a852)),x67923),x67921)),f784(f784(f111(x67922),f12(x67922,x67923)),f12(x67922,x67921)))
% 11.41/11.19 [7452]~P92(x74522)+E(x74521,f187(f869(x74522,a852)))+E(x74523,f187(f869(x74522,a852)))+~P85(f784(f71(x74522),x74521))+~P85(f784(f71(x74522),x74523))+E(f784(f784(f90(x74522),f784(f73(x74522,f90(x74522)),x74523)),f784(f73(x74522,f90(x74522)),x74521)),f784(f73(x74522,f90(x74522)),f784(f784(f110(f869(x74522,a852)),x74523),x74521)))
% 11.41/11.19 [7617]~P101(x76172)+E(x76171,f187(f869(x76172,a852)))+E(x76173,f187(f869(x76172,a852)))+~P85(f784(f71(x76172),x76171))+~P85(f784(f71(x76172),x76173))+E(f784(f784(f186(x76172),f13(x76172,f186(x76172),x76173)),f13(x76172,f186(x76172),x76171)),f13(x76172,f186(x76172),f784(f784(f110(f869(x76172,a852)),x76173),x76171)))
% 11.41/11.19 [7618]~P101(x76182)+E(x76181,f187(f869(x76182,a852)))+E(x76183,f187(f869(x76182,a852)))+~P85(f784(f71(x76182),x76181))+~P85(f784(f71(x76182),x76183))+E(f784(f784(f246(x76182),f14(x76182,f246(x76182),x76183)),f14(x76182,f246(x76182),x76181)),f14(x76182,f246(x76182),f784(f784(f110(f869(x76182,a852)),x76183),x76181)))
% 11.41/11.19 [8621]~P85(f784(x86211,x86213))+P85(f784(x86211,f366(x86211,x86212)))+P85(f784(x86211,f358(x86211,x86212)))+~P85(f784(f784(f243(a1),f2(a1)),x86212))+~P85(f784(f784(f347(a1),x86213),f305(a1,f87(a1),x86212)))+P85(f784(x86211,f784(f784(f3(a1),f358(x86211,x86212)),f784(f784(f90(a1),f364(x86211,x86212)),x86212))))
% 11.41/11.19 [8885]~P85(f784(x88851,x88853))+~P85(f784(x88851,f358(x88851,x88852)))+P85(f784(x88851,f366(x88851,x88852)))+~P85(f784(f784(f243(a1),f2(a1)),x88852))+~P85(f784(f784(f347(a1),x88853),f305(a1,f87(a1),x88852)))+~P85(f784(x88851,f784(f784(f3(a1),f358(x88851,x88852)),f784(f784(f90(a1),f364(x88851,x88852)),x88852))))
% 11.41/11.19 [10044]~P97(x100442)+E(x100441,f187(f869(x100442,a852)))+E(x100443,f187(f869(x100442,a852)))+~P85(f784(f71(x100442),x100441))+~P85(f784(f71(x100442),x100443))+E(f12(x100442,f784(f266(x100442),f784(f784(f10(f869(x100442,a852),a852,x100442),f96(x100442)),f784(f784(f10(f869(x100442,f869(x100442,a852)),f869(x100442,a852),x100442),f784(f10(f869(x100442,a852),a852,x100442),f96(x100442))),f784(f784(f9(x100442,f869(x100442,f869(x100442,a852)),f869(x100442,f869(x100442,a852))),f784(f784(f10(f869(x100442,f869(f869(x100442,a852),f869(x100442,a852))),f869(f869(x100442,f869(x100442,a852)),f869(x100442,f869(x100442,a852))),x100442),f20(x100442,f869(x100442,a852),f869(x100442,a852))),f784(f784(f10(f869(x100442,f869(x100442,f869(a852,a852))),f869(x100442,f869(f869(x100442,a852),f869(x100442,a852))),x100442),f784(f10(f869(x100442,f869(a852,a852)),f869(f869(x100442,a852),f869(x100442,a852)),x100442),f20(x100442,a852,a852))),f784(f784(f10(f869(x100442,f869(x100442,a852)),f869(x100442,f869(x100442,f869(a852,a852))),x100442),f784(f10(f869(x100442,a852),f869(x100442,f869(a852,a852)),x100442),f784(f10(a852,f869(a852,a852),x100442),a344))),f784(f784(f9(x100442,f869(x100442,f869(x100442,x100442)),f869(x100442,f869(x100442,a852))),f784(f784(f10(f869(f869(x100442,x100442),f869(x100442,a852)),f869(f869(x100442,f869(x100442,x100442)),f869(x100442,f869(x100442,a852))),x100442),f10(f869(x100442,x100442),f869(x100442,a852),x100442)),f784(f784(f10(f869(x100442,a852),f869(f869(x100442,x100442),f869(x100442,a852)),x100442),f10(x100442,a852,x100442)),a343))),f110(x100442)))))),f784(f784(f9(x100442,f869(x100442,a852),f869(x100442,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x100442,a852),f869(x100442,a852)),x100442),f10(a852,a852,x100442)),f784(f784(f10(a852,f869(a852,a852),x100442),a344),f784(f784(f9(x100442,f869(x100442,a852),a852),f347(x100442)),x100443)))),f784(f784(f9(x100442,f869(x100442,a852),a852),f347(x100442)),x100441))))))),f784(f784(f110(x100442),f12(x100442,x100443)),f12(x100442,x100441)))
% 11.41/11.19 [10045]~P97(x100452)+E(x100451,f187(f869(x100452,a852)))+E(x100453,f187(f869(x100452,a852)))+~P85(f784(f71(x100452),x100451))+~P85(f784(f71(x100452),x100453))+E(f15(x100452,f784(f266(x100452),f784(f784(f10(f869(x100452,a852),a852,x100452),f96(x100452)),f784(f784(f10(f869(x100452,f869(x100452,a852)),f869(x100452,a852),x100452),f784(f10(f869(x100452,a852),a852,x100452),f96(x100452))),f784(f784(f9(x100452,f869(x100452,f869(x100452,a852)),f869(x100452,f869(x100452,a852))),f784(f784(f10(f869(x100452,f869(f869(x100452,a852),f869(x100452,a852))),f869(f869(x100452,f869(x100452,a852)),f869(x100452,f869(x100452,a852))),x100452),f20(x100452,f869(x100452,a852),f869(x100452,a852))),f784(f784(f10(f869(x100452,f869(x100452,f869(a852,a852))),f869(x100452,f869(f869(x100452,a852),f869(x100452,a852))),x100452),f784(f10(f869(x100452,f869(a852,a852)),f869(f869(x100452,a852),f869(x100452,a852)),x100452),f20(x100452,a852,a852))),f784(f784(f10(f869(x100452,f869(x100452,a852)),f869(x100452,f869(x100452,f869(a852,a852))),x100452),f784(f10(f869(x100452,a852),f869(x100452,f869(a852,a852)),x100452),f784(f10(a852,f869(a852,a852),x100452),a344))),f784(f784(f9(x100452,f869(x100452,f869(x100452,x100452)),f869(x100452,f869(x100452,a852))),f784(f784(f10(f869(f869(x100452,x100452),f869(x100452,a852)),f869(f869(x100452,f869(x100452,x100452)),f869(x100452,f869(x100452,a852))),x100452),f10(f869(x100452,x100452),f869(x100452,a852),x100452)),f784(f784(f10(f869(x100452,a852),f869(f869(x100452,x100452),f869(x100452,a852)),x100452),f10(x100452,a852,x100452)),a343))),f111(x100452)))))),f784(f784(f9(x100452,f869(x100452,a852),f869(x100452,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x100452,a852),f869(x100452,a852)),x100452),f10(a852,a852,x100452)),f784(f784(f10(a852,f869(a852,a852),x100452),a344),f784(f784(f9(x100452,f869(x100452,a852),a852),f347(x100452)),x100453)))),f784(f784(f9(x100452,f869(x100452,a852),a852),f347(x100452)),x100451))))))),f784(f784(f111(x100452),f15(x100452,x100453)),f15(x100452,x100451)))
% 11.41/11.19 [10046]~P101(x100462)+E(x100461,f187(f869(x100462,a852)))+E(x100463,f187(f869(x100462,a852)))+~P85(f784(f71(x100462),x100461))+~P85(f784(f71(x100462),x100463))+E(f13(x100462,f186(x100462),f784(f266(x100462),f784(f784(f10(f869(x100462,a852),a852,x100462),f96(x100462)),f784(f784(f10(f869(x100462,f869(x100462,a852)),f869(x100462,a852),x100462),f784(f10(f869(x100462,a852),a852,x100462),f96(x100462))),f784(f784(f9(x100462,f869(x100462,f869(x100462,a852)),f869(x100462,f869(x100462,a852))),f784(f784(f10(f869(x100462,f869(f869(x100462,a852),f869(x100462,a852))),f869(f869(x100462,f869(x100462,a852)),f869(x100462,f869(x100462,a852))),x100462),f20(x100462,f869(x100462,a852),f869(x100462,a852))),f784(f784(f10(f869(x100462,f869(x100462,f869(a852,a852))),f869(x100462,f869(f869(x100462,a852),f869(x100462,a852))),x100462),f784(f10(f869(x100462,f869(a852,a852)),f869(f869(x100462,a852),f869(x100462,a852)),x100462),f20(x100462,a852,a852))),f784(f784(f10(f869(x100462,f869(x100462,a852)),f869(x100462,f869(x100462,f869(a852,a852))),x100462),f784(f10(f869(x100462,a852),f869(x100462,f869(a852,a852)),x100462),f784(f10(a852,f869(a852,a852),x100462),a344))),f784(f784(f9(x100462,f869(x100462,f869(x100462,x100462)),f869(x100462,f869(x100462,a852))),f784(f784(f10(f869(f869(x100462,x100462),f869(x100462,a852)),f869(f869(x100462,f869(x100462,x100462)),f869(x100462,f869(x100462,a852))),x100462),f10(f869(x100462,x100462),f869(x100462,a852),x100462)),f784(f784(f10(f869(x100462,a852),f869(f869(x100462,x100462),f869(x100462,a852)),x100462),f10(x100462,a852,x100462)),a343))),f246(x100462)))))),f784(f784(f9(x100462,f869(x100462,a852),f869(x100462,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x100462,a852),f869(x100462,a852)),x100462),f10(a852,a852,x100462)),f784(f784(f10(a852,f869(a852,a852),x100462),a344),f784(f784(f9(x100462,f869(x100462,a852),a852),f347(x100462)),x100463)))),f784(f784(f9(x100462,f869(x100462,a852),a852),f347(x100462)),x100461))))))),f784(f784(f246(x100462),f13(x100462,f186(x100462),x100463)),f13(x100462,f186(x100462),x100461)))
% 11.41/11.19 [10047]~P101(x100472)+E(x100471,f187(f869(x100472,a852)))+E(x100473,f187(f869(x100472,a852)))+~P85(f784(f71(x100472),x100471))+~P85(f784(f71(x100472),x100473))+E(f14(x100472,f246(x100472),f784(f266(x100472),f784(f784(f10(f869(x100472,a852),a852,x100472),f96(x100472)),f784(f784(f10(f869(x100472,f869(x100472,a852)),f869(x100472,a852),x100472),f784(f10(f869(x100472,a852),a852,x100472),f96(x100472))),f784(f784(f9(x100472,f869(x100472,f869(x100472,a852)),f869(x100472,f869(x100472,a852))),f784(f784(f10(f869(x100472,f869(f869(x100472,a852),f869(x100472,a852))),f869(f869(x100472,f869(x100472,a852)),f869(x100472,f869(x100472,a852))),x100472),f20(x100472,f869(x100472,a852),f869(x100472,a852))),f784(f784(f10(f869(x100472,f869(x100472,f869(a852,a852))),f869(x100472,f869(f869(x100472,a852),f869(x100472,a852))),x100472),f784(f10(f869(x100472,f869(a852,a852)),f869(f869(x100472,a852),f869(x100472,a852)),x100472),f20(x100472,a852,a852))),f784(f784(f10(f869(x100472,f869(x100472,a852)),f869(x100472,f869(x100472,f869(a852,a852))),x100472),f784(f10(f869(x100472,a852),f869(x100472,f869(a852,a852)),x100472),f784(f10(a852,f869(a852,a852),x100472),a344))),f784(f784(f9(x100472,f869(x100472,f869(x100472,x100472)),f869(x100472,f869(x100472,a852))),f784(f784(f10(f869(f869(x100472,x100472),f869(x100472,a852)),f869(f869(x100472,f869(x100472,x100472)),f869(x100472,f869(x100472,a852))),x100472),f10(f869(x100472,x100472),f869(x100472,a852),x100472)),f784(f784(f10(f869(x100472,a852),f869(f869(x100472,x100472),f869(x100472,a852)),x100472),f10(x100472,a852,x100472)),a343))),f186(x100472)))))),f784(f784(f9(x100472,f869(x100472,a852),f869(x100472,a852)),f784(f784(f10(f869(a852,a852),f869(f869(x100472,a852),f869(x100472,a852)),x100472),f10(a852,a852,x100472)),f784(f784(f10(a852,f869(a852,a852),x100472),a344),f784(f784(f9(x100472,f869(x100472,a852),a852),f347(x100472)),x100473)))),f784(f784(f9(x100472,f869(x100472,a852),a852),f347(x100472)),x100471))))))),f784(f784(f186(x100472),f14(x100472,f246(x100472),x100473)),f14(x100472,f246(x100472),x100471)))
% 11.41/11.19 [7118]~P120(x71183)+E(x71181,x71182)+~E(f784(f784(f252(x71183),x71181),x71184),f784(f784(f252(x71183),x71182),x71184))+~P85(f784(f784(f242(x71183),f2(x71183)),x71182))+~P85(f784(f784(f242(x71183),f2(x71183)),x71181))+~P85(f784(f784(f243(a859),f2(a859)),x71184))
% 11.41/11.19 [7970]~P61(x79701)+~P90(x79701)+P85(f784(f784(f243(x79701),x79702),f2(x79701)))+P85(f784(f784(f243(x79701),f2(x79701)),x79702))+P85(f784(f784(f243(x79701),f784(f784(f293(x79701),x79703),x79702)),f784(f113(x79701),x79704)))+~P85(f784(f784(f243(x79701),f2(x79701)),f784(f113(x79701),x79704)))
% 11.41/11.19 [7971]~P61(x79711)+~P90(x79711)+P85(f784(f784(f243(x79711),x79712),f2(x79711)))+P85(f784(f784(f243(x79711),f2(x79711)),x79712))+P85(f784(f784(f242(x79711),f784(f784(f293(x79711),x79713),x79712)),f784(f113(x79711),x79714)))+~P85(f784(f784(f242(x79711),f2(x79711)),f784(f113(x79711),x79714)))
% 11.41/11.19 [8202]~P61(x82021)+~P90(x82021)+P85(f784(f784(f243(x82021),x82022),f2(x82021)))+P85(f784(f784(f243(x82021),f2(x82021)),x82022))+~P85(f784(f784(f243(x82021),f784(f784(f293(x82021),x82024),x82022)),f784(f113(x82021),x82023)))+P85(f784(f784(f243(x82021),f2(x82021)),f784(f113(x82021),x82023)))
% 11.41/11.19 [8203]~P61(x82031)+~P90(x82031)+P85(f784(f784(f243(x82031),x82032),f2(x82031)))+P85(f784(f784(f243(x82031),f2(x82031)),x82032))+~P85(f784(f784(f242(x82031),f784(f784(f293(x82031),x82034),x82032)),f784(f113(x82031),x82033)))+P85(f784(f784(f242(x82031),f2(x82031)),f784(f113(x82031),x82033)))
% 11.41/11.19 [7413]~P101(x74132)+E(x74131,f187(f869(x74132,a852)))+~P85(f784(f71(x74132),x74131))+~P85(f784(f784(f347(x74132),x74134),x74131))+P85(f784(f784(f243(x74132),x74133),x74134))+~P85(f784(f784(f243(x74132),x74133),f784(f73(x74132,f246(x74132)),x74131)))
% 11.41/11.19 [7414]~P101(x74142)+E(x74141,f187(f869(x74142,a852)))+~P85(f784(f71(x74142),x74141))+~P85(f784(f784(f347(x74142),x74144),x74141))+P85(f784(f784(f242(x74142),x74143),x74144))+~P85(f784(f784(f242(x74142),x74143),f784(f73(x74142,f246(x74142)),x74141)))
% 11.41/11.19 [7415]~P99(x74152)+E(x74151,f187(f869(x74152,a852)))+~P85(f784(f71(x74152),x74151))+~P85(f784(f784(f347(x74152),x74154),x74151))+P85(f784(f784(f242(x74152),x74153),x74154))+~P85(f784(f784(f242(x74152),x74153),f784(f73(x74152,f111(x74152)),x74151)))
% 11.41/11.19 [7920]~P61(x79201)+~P90(x79201)+P85(f784(f784(f243(x79201),f784(f113(x79201),x79202)),f2(x79201)))+~P85(f784(f784(f243(x79201),x79203),f2(x79201)))+P85(f784(f784(f243(x79201),f2(x79201)),f784(f113(x79201),x79202)))+P85(f784(f784(f243(x79201),x79203),f784(f784(f293(x79201),x79204),f784(f113(x79201),x79202))))
% 11.41/11.19 [7921]~P61(x79211)+~P90(x79211)+P85(f784(f784(f243(x79211),f784(f113(x79211),x79212)),f2(x79211)))+~P85(f784(f784(f242(x79211),x79213),f2(x79211)))+P85(f784(f784(f243(x79211),f2(x79211)),f784(f113(x79211),x79212)))+P85(f784(f784(f242(x79211),x79213),f784(f784(f293(x79211),x79214),f784(f113(x79211),x79212))))
% 11.41/11.19 [7931]~P61(x79311)+~P90(x79311)+P85(f784(f784(f243(x79311),x79312),f2(x79311)))+~P85(f784(f784(f243(x79311),f784(f113(x79311),x79313)),f2(x79311)))+P85(f784(f784(f243(x79311),f2(x79311)),x79312))+P85(f784(f784(f243(x79311),f784(f113(x79311),x79313)),f784(f784(f293(x79311),x79314),x79312)))
% 11.41/11.19 [7932]~P61(x79321)+~P90(x79321)+P85(f784(f784(f243(x79321),x79322),f2(x79321)))+~P85(f784(f784(f242(x79321),f784(f113(x79321),x79323)),f2(x79321)))+P85(f784(f784(f243(x79321),f2(x79321)),x79322))+P85(f784(f784(f242(x79321),f784(f113(x79321),x79323)),f784(f784(f293(x79321),x79324),x79322)))
% 11.41/11.19 [8078]~P61(x80781)+~P90(x80781)+P85(f784(f784(f243(x80781),x80782),f2(x80781)))+P85(f784(f784(f243(x80781),f784(f113(x80781),x80783)),f2(x80781)))+P85(f784(f784(f243(x80781),f2(x80781)),x80782))+~P85(f784(f784(f243(x80781),f784(f113(x80781),x80783)),f784(f784(f293(x80781),x80784),x80782)))
% 11.41/11.19 [8079]~P61(x80791)+~P90(x80791)+P85(f784(f784(f243(x80791),x80792),f2(x80791)))+P85(f784(f784(f242(x80791),f784(f113(x80791),x80793)),f2(x80791)))+P85(f784(f784(f243(x80791),f2(x80791)),x80792))+~P85(f784(f784(f242(x80791),f784(f113(x80791),x80793)),f784(f784(f293(x80791),x80794),x80792)))
% 11.41/11.19 [8150]~P61(x81501)+~P90(x81501)+P85(f784(f784(f243(x81501),x81502),f2(x81501)))+P85(f784(f784(f243(x81501),f784(f113(x81501),x81503)),f2(x81501)))+P85(f784(f784(f243(x81501),f2(x81501)),f784(f113(x81501),x81503)))+~P85(f784(f784(f243(x81501),x81502),f784(f784(f293(x81501),x81504),f784(f113(x81501),x81503))))
% 11.41/11.19 [8151]~P61(x81511)+~P90(x81511)+P85(f784(f784(f242(x81511),x81512),f2(x81511)))+P85(f784(f784(f243(x81511),f784(f113(x81511),x81513)),f2(x81511)))+P85(f784(f784(f243(x81511),f2(x81511)),f784(f113(x81511),x81513)))+~P85(f784(f784(f242(x81511),x81512),f784(f784(f293(x81511),x81514),f784(f113(x81511),x81513))))
% 11.41/11.19 [8343]~P61(x83431)+~P90(x83431)+~P85(f784(f784(f243(x83431),x83433),f2(x83431)))+P85(f784(f784(f243(x83431),f2(x83431)),f784(f113(x83431),x83432)))+~P85(f784(f784(f243(x83431),x83434),f784(f784(f90(x83431),x83433),f784(f113(x83431),x83432))))+P85(f784(f784(f243(x83431),x83433),f784(f784(f293(x83431),x83434),f784(f113(x83431),x83432))))
% 11.41/11.19 [8344]~P61(x83441)+~P90(x83441)+~P85(f784(f784(f242(x83441),x83443),f2(x83441)))+P85(f784(f784(f243(x83441),f2(x83441)),f784(f113(x83441),x83442)))+~P85(f784(f784(f242(x83441),x83444),f784(f784(f90(x83441),x83443),f784(f113(x83441),x83442))))+P85(f784(f784(f242(x83441),x83443),f784(f784(f293(x83441),x83444),f784(f113(x83441),x83442))))
% 11.41/11.19 [8511]~P61(x85111)+~P90(x85111)+~P85(f784(f784(f243(x85111),f784(f113(x85111),x85112)),f2(x85111)))+P85(f784(f784(f243(x85111),f2(x85111)),f784(f113(x85111),x85112)))+~P85(f784(f784(f243(x85111),x85114),f784(f784(f90(x85111),x85113),f784(f113(x85111),x85112))))+P85(f784(f784(f243(x85111),x85113),f784(f784(f293(x85111),x85114),f784(f113(x85111),x85112))))
% 11.41/11.19 [8512]~P61(x85121)+~P90(x85121)+~P85(f784(f784(f243(x85121),f784(f113(x85121),x85122)),f2(x85121)))+P85(f784(f784(f243(x85121),f2(x85121)),f784(f113(x85121),x85122)))+~P85(f784(f784(f243(x85121),x85124),f784(f784(f293(x85121),x85123),f784(f113(x85121),x85122))))+P85(f784(f784(f243(x85121),x85123),f784(f784(f90(x85121),x85124),f784(f113(x85121),x85122))))
% 11.41/11.19 [8513]~P61(x85131)+~P90(x85131)+~P85(f784(f784(f243(x85131),f784(f113(x85131),x85132)),f2(x85131)))+P85(f784(f784(f243(x85131),f2(x85131)),f784(f113(x85131),x85132)))+~P85(f784(f784(f242(x85131),x85134),f784(f784(f90(x85131),x85133),f784(f113(x85131),x85132))))+P85(f784(f784(f242(x85131),x85133),f784(f784(f293(x85131),x85134),f784(f113(x85131),x85132))))
% 11.41/11.19 [8514]~P61(x85141)+~P90(x85141)+~P85(f784(f784(f243(x85141),f784(f113(x85141),x85142)),f2(x85141)))+P85(f784(f784(f243(x85141),f2(x85141)),f784(f113(x85141),x85142)))+~P85(f784(f784(f242(x85141),x85144),f784(f784(f293(x85141),x85143),f784(f113(x85141),x85142))))+P85(f784(f784(f242(x85141),x85143),f784(f784(f90(x85141),x85144),f784(f113(x85141),x85142))))
% 11.41/11.19 [7309]E(x73091,f2(a1))+E(f784(f784(f51(a1),x73092),x73091),x73093)+~P85(f784(f784(f242(a1),x73094),f2(a1)))+~E(x73092,f784(f784(f89(a1),f784(f784(f90(a1),x73091),x73093)),x73094))+P85(f784(f784(f243(a1),f2(a1)),x73091))+~P85(f784(f784(f243(a1),x73091),x73094))
% 11.41/11.19 [7325]E(f60(a1,x73252,x73251),x73253)+E(x73251,f2(a1))+~P85(f784(f784(f242(a1),x73253),f2(a1)))+~E(x73252,f784(f784(f89(a1),f784(f784(f90(a1),x73251),x73254)),x73253))+P85(f784(f784(f243(a1),f2(a1)),x73251))+~P85(f784(f784(f243(a1),x73251),x73253))
% 11.41/11.19 [7451]E(x74511,f2(a1))+E(f784(f784(f51(a1),x74512),x74511),x74513)+~E(x74512,f784(f784(f89(a1),f784(f784(f90(a1),x74511),x74513)),x74514))+~P85(f784(f784(f243(a1),f2(a1)),x74511))+~P85(f784(f784(f242(a1),f2(a1)),x74514))+~P85(f784(f784(f243(a1),x74514),x74511))
% 11.41/11.19 [7476]E(f60(a1,x74762,x74761),x74763)+E(x74761,f2(a1))+~E(x74762,f784(f784(f89(a1),f784(f784(f90(a1),x74761),x74764)),x74763))+~P85(f784(f784(f243(a1),f2(a1)),x74761))+~P85(f784(f784(f242(a1),f2(a1)),x74763))+~P85(f784(f784(f243(a1),x74763),x74761))
% 11.41/11.19 [7621]~P101(x76212)+E(x76211,f187(f869(x76212,a852)))+~P85(f784(f71(x76212),x76211))+~P85(f784(f784(f347(x76212),x76214),x76211))+~P85(f784(f784(f243(x76212),x76214),x76213))+P85(f784(f784(f243(x76212),f784(f73(x76212,f246(x76212)),x76211)),x76213))
% 11.41/11.19 [7622]~P101(x76222)+E(x76221,f187(f869(x76222,a852)))+~P85(f784(f71(x76222),x76221))+~P85(f784(f784(f347(x76222),x76224),x76221))+~P85(f784(f784(f242(x76222),x76224),x76223))+P85(f784(f784(f242(x76222),f784(f73(x76222,f246(x76222)),x76221)),x76223))
% 11.41/11.19 [8180]~P85(f784(f784(f242(a1),x81804),f2(a1)))+~E(x81801,f784(f784(f89(a1),f784(f784(f90(a1),x81802),x81803)),x81804))+~P85(f784(f784(f242(a1),f2(a1)),x81804))+~P85(f784(f784(f243(a1),x81804),x81802))+~P85(f784(f784(f243(a1),x81802),x81804))+P85(f784(f64(x81801,x81802),f784(f784(f251(a1,a1),x81803),x81804)))
% 11.41/11.19 [8300]~P61(x83001)+~P90(x83001)+P85(f784(f784(f243(x83001),f784(f113(x83001),x83002)),f2(x83001)))+~P85(f784(f784(f243(x83001),f2(x83001)),x83004))+P85(f784(f784(f243(x83001),f2(x83001)),f784(f113(x83001),x83002)))+P85(f784(f784(f243(x83001),f784(f784(f293(x83001),x83003),f784(f113(x83001),x83002))),x83004))
% 11.41/11.19 [8301]~P61(x83011)+~P90(x83011)+P85(f784(f784(f243(x83011),f784(f113(x83011),x83012)),f2(x83011)))+~P85(f784(f784(f242(x83011),f2(x83011)),x83014))+P85(f784(f784(f243(x83011),f2(x83011)),f784(f113(x83011),x83012)))+P85(f784(f784(f242(x83011),f784(f784(f293(x83011),x83013),f784(f113(x83011),x83012))),x83014))
% 11.41/11.19 [8417]~P61(x84171)+~P90(x84171)+~P85(f784(f784(f243(x84171),x84172),f2(x84171)))+P85(f784(f784(f243(x84171),f2(x84171)),x84172))+~P85(f784(f784(f243(x84171),f784(f113(x84171),x84174)),f784(f784(f293(x84171),x84173),x84172)))+P85(f784(f784(f243(x84171),x84173),f784(f784(f90(x84171),f784(f113(x84171),x84174)),x84172)))
% 11.41/11.19 [8418]~P61(x84181)+~P90(x84181)+~P85(f784(f784(f243(x84181),x84182),f2(x84181)))+P85(f784(f784(f243(x84181),f2(x84181)),x84182))+~P85(f784(f784(f242(x84181),f784(f113(x84181),x84184)),f784(f784(f293(x84181),x84183),x84182)))+P85(f784(f784(f242(x84181),x84183),f784(f784(f90(x84181),f784(f113(x84181),x84184)),x84182)))
% 11.41/11.19 [8457]~P61(x84571)+~P90(x84571)+~P85(f784(f784(f243(x84571),x84572),f2(x84571)))+P85(f784(f784(f243(x84571),f2(x84571)),x84572))+P85(f784(f784(f243(x84571),f784(f113(x84571),x84573)),f784(f784(f293(x84571),x84574),x84572)))+~P85(f784(f784(f243(x84571),x84574),f784(f784(f90(x84571),f784(f113(x84571),x84573)),x84572)))
% 11.41/11.19 [8458]~P61(x84581)+~P90(x84581)+~P85(f784(f784(f243(x84581),x84582),f2(x84581)))+P85(f784(f784(f243(x84581),f2(x84581)),x84582))+P85(f784(f784(f242(x84581),f784(f113(x84581),x84583)),f784(f784(f293(x84581),x84584),x84582)))+~P85(f784(f784(f242(x84581),x84584),f784(f784(f90(x84581),f784(f113(x84581),x84583)),x84582)))
% 11.41/11.19 [8542]~P61(x85421)+~P90(x85421)+P85(f784(f784(f243(x85421),f784(f113(x85421),x85423)),f2(x85421)))+P85(f784(f784(f243(x85421),f2(x85421)),x85422))+P85(f784(f784(f243(x85421),f2(x85421)),f784(f113(x85421),x85423)))+~P85(f784(f784(f243(x85421),f784(f784(f293(x85421),x85424),f784(f113(x85421),x85423))),x85422))
% 11.41/11.19 [8543]~P61(x85431)+~P90(x85431)+P85(f784(f784(f243(x85431),f784(f113(x85431),x85433)),f2(x85431)))+P85(f784(f784(f242(x85431),f2(x85431)),x85432))+P85(f784(f784(f243(x85431),f2(x85431)),f784(f113(x85431),x85433)))+~P85(f784(f784(f242(x85431),f784(f784(f293(x85431),x85434),f784(f113(x85431),x85433))),x85432))
% 11.41/11.19 [8583]~P61(x85831)+~P90(x85831)+~P85(f784(f784(f243(x85831),f784(f113(x85831),x85833)),f2(x85831)))+P85(f784(f784(f243(x85831),f2(x85831)),x85832))+P85(f784(f784(f243(x85831),f784(f113(x85831),x85833)),f784(f784(f293(x85831),x85834),x85832)))+~P85(f784(f784(f243(x85831),x85834),f784(f784(f90(x85831),f784(f113(x85831),x85833)),x85832)))
% 11.41/11.19 [8584]~P61(x85841)+~P90(x85841)+~P85(f784(f784(f242(x85841),f784(f113(x85841),x85843)),f2(x85841)))+P85(f784(f784(f243(x85841),f2(x85841)),x85842))+P85(f784(f784(f242(x85841),f784(f113(x85841),x85843)),f784(f784(f293(x85841),x85844),x85842)))+~P85(f784(f784(f242(x85841),x85844),f784(f784(f90(x85841),f784(f113(x85841),x85843)),x85842)))
% 11.41/11.19 [8591]~P61(x85911)+~P90(x85911)+P85(f784(f784(f243(x85911),x85912),f2(x85911)))+P85(f784(f784(f243(x85911),f784(f784(f293(x85911),x85913),x85912)),f784(f113(x85911),x85914)))+~P85(f784(f784(f243(x85911),f2(x85911)),f784(f113(x85911),x85914)))+~P85(f784(f784(f243(x85911),x85913),f784(f784(f90(x85911),f784(f113(x85911),x85914)),x85912)))
% 11.41/11.19 [8592]~P61(x85921)+~P90(x85921)+P85(f784(f784(f243(x85921),x85922),f2(x85921)))+P85(f784(f784(f242(x85921),f784(f784(f293(x85921),x85923),x85922)),f784(f113(x85921),x85924)))+~P85(f784(f784(f242(x85921),f2(x85921)),f784(f113(x85921),x85924)))+~P85(f784(f784(f242(x85921),x85923),f784(f784(f90(x85921),f784(f113(x85921),x85924)),x85922)))
% 11.41/11.19 [8609]~P61(x86091)+~P90(x86091)+P85(f784(f784(f243(x86091),f784(f113(x86091),x86092)),f2(x86091)))+~P85(f784(f784(f243(x86091),f2(x86091)),x86094))+~P85(f784(f784(f243(x86091),x86093),f784(f784(f90(x86091),x86094),f784(f113(x86091),x86092))))+P85(f784(f784(f243(x86091),f784(f784(f293(x86091),x86093),f784(f113(x86091),x86092))),x86094))
% 11.41/11.19 [8610]~P61(x86101)+~P90(x86101)+P85(f784(f784(f243(x86101),f784(f113(x86101),x86102)),f2(x86101)))+~P85(f784(f784(f242(x86101),f2(x86101)),x86104))+~P85(f784(f784(f242(x86101),x86103),f784(f784(f90(x86101),x86104),f784(f113(x86101),x86102))))+P85(f784(f784(f242(x86101),f784(f784(f293(x86101),x86103),f784(f113(x86101),x86102))),x86104))
% 11.41/11.19 [8691]~P61(x86911)+~P90(x86911)+P85(f784(f784(f243(x86911),f784(f113(x86911),x86912)),f2(x86911)))+~P85(f784(f784(f243(x86911),x86913),f2(x86911)))+P85(f784(f784(f243(x86911),x86913),f784(f784(f293(x86911),x86914),f784(f113(x86911),x86912))))+~P85(f784(f784(f243(x86911),f784(f784(f90(x86911),x86913),f784(f113(x86911),x86912))),x86914))
% 11.41/11.19 [8692]~P61(x86921)+~P90(x86921)+P85(f784(f784(f243(x86921),f784(f113(x86921),x86922)),f2(x86921)))+~P85(f784(f784(f242(x86921),x86923),f2(x86921)))+P85(f784(f784(f242(x86921),x86923),f784(f784(f293(x86921),x86924),f784(f113(x86921),x86922))))+~P85(f784(f784(f242(x86921),f784(f784(f90(x86921),x86923),f784(f113(x86921),x86922))),x86924))
% 11.41/11.19 [8789]~P61(x87891)+~P90(x87891)+~P85(f784(f784(f243(x87891),f2(x87891)),x87894))+P85(f784(f784(f243(x87891),f2(x87891)),f784(f113(x87891),x87892)))+~P85(f784(f784(f243(x87891),f784(f784(f90(x87891),x87894),f784(f113(x87891),x87892))),x87893))+P85(f784(f784(f243(x87891),f784(f784(f293(x87891),x87893),f784(f113(x87891),x87892))),x87894))
% 11.41/11.19 [8790]~P61(x87901)+~P90(x87901)+~P85(f784(f784(f242(x87901),f2(x87901)),x87904))+P85(f784(f784(f243(x87901),f2(x87901)),f784(f113(x87901),x87902)))+~P85(f784(f784(f242(x87901),f784(f784(f90(x87901),x87904),f784(f113(x87901),x87902))),x87903))+P85(f784(f784(f242(x87901),f784(f784(f293(x87901),x87903),f784(f113(x87901),x87902))),x87904))
% 11.41/11.19 [8841]~P61(x88411)+~P90(x88411)+~P85(f784(f784(f243(x88411),x88412),f2(x88411)))+P85(f784(f784(f243(x88411),x88412),f784(f784(f293(x88411),x88413),f784(f113(x88411),x88414))))+~P85(f784(f784(f243(x88411),x88413),f784(f784(f90(x88411),x88412),f784(f113(x88411),x88414))))+~P85(f784(f784(f243(x88411),f784(f784(f90(x88411),x88412),f784(f113(x88411),x88414))),x88413))
% 11.41/11.19 [8842]~P61(x88421)+~P90(x88421)+~P85(f784(f784(f242(x88421),x88422),f2(x88421)))+P85(f784(f784(f242(x88421),x88422),f784(f784(f293(x88421),x88423),f784(f113(x88421),x88424))))+~P85(f784(f784(f242(x88421),x88423),f784(f784(f90(x88421),x88422),f784(f113(x88421),x88424))))+~P85(f784(f784(f242(x88421),f784(f784(f90(x88421),x88422),f784(f113(x88421),x88424))),x88423))
% 11.41/11.19 [8865]~P61(x88651)+~P90(x88651)+~P85(f784(f784(f243(x88651),f784(f113(x88651),x88652)),f2(x88651)))+P85(f784(f784(f243(x88651),f2(x88651)),f784(f113(x88651),x88652)))+~P85(f784(f784(f243(x88651),f784(f784(f293(x88651),x88654),f784(f113(x88651),x88652))),x88653))+P85(f784(f784(f243(x88651),f784(f784(f90(x88651),x88653),f784(f113(x88651),x88652))),x88654))
% 11.41/11.19 [8866]~P61(x88661)+~P90(x88661)+~P85(f784(f784(f243(x88661),f784(f113(x88661),x88662)),f2(x88661)))+P85(f784(f784(f243(x88661),f2(x88661)),f784(f113(x88661),x88662)))+~P85(f784(f784(f243(x88661),f784(f784(f90(x88661),x88664),f784(f113(x88661),x88662))),x88663))+P85(f784(f784(f243(x88661),f784(f784(f293(x88661),x88663),f784(f113(x88661),x88662))),x88664))
% 11.41/11.19 [8867]~P61(x88671)+~P90(x88671)+~P85(f784(f784(f243(x88671),f784(f113(x88671),x88672)),f2(x88671)))+P85(f784(f784(f243(x88671),f2(x88671)),f784(f113(x88671),x88672)))+~P85(f784(f784(f242(x88671),f784(f784(f293(x88671),x88674),f784(f113(x88671),x88672))),x88673))+P85(f784(f784(f242(x88671),f784(f784(f90(x88671),x88673),f784(f113(x88671),x88672))),x88674))
% 11.41/11.19 [8868]~P61(x88681)+~P90(x88681)+~P85(f784(f784(f243(x88681),f784(f113(x88681),x88682)),f2(x88681)))+P85(f784(f784(f243(x88681),f2(x88681)),f784(f113(x88681),x88682)))+~P85(f784(f784(f242(x88681),f784(f784(f90(x88681),x88684),f784(f113(x88681),x88682))),x88683))+P85(f784(f784(f242(x88681),f784(f784(f293(x88681),x88683),f784(f113(x88681),x88682))),x88684))
% 11.41/11.19 [8945]~P61(x89451)+~P90(x89451)+~P85(f784(f784(f243(x89451),f784(f113(x89451),x89454)),f2(x89451)))+P85(f784(f784(f243(x89451),x89452),f784(f784(f293(x89451),x89453),f784(f113(x89451),x89454))))+~P85(f784(f784(f243(x89451),x89453),f784(f784(f90(x89451),x89452),f784(f113(x89451),x89454))))+~P85(f784(f784(f243(x89451),f784(f784(f90(x89451),x89452),f784(f113(x89451),x89454))),x89453))
% 11.41/11.19 [8946]~P61(x89461)+~P90(x89461)+~P85(f784(f784(f243(x89461),f784(f113(x89461),x89464)),f2(x89461)))+P85(f784(f784(f242(x89461),x89462),f784(f784(f293(x89461),x89463),f784(f113(x89461),x89464))))+~P85(f784(f784(f242(x89461),x89463),f784(f784(f90(x89461),x89462),f784(f113(x89461),x89464))))+~P85(f784(f784(f242(x89461),f784(f784(f90(x89461),x89462),f784(f113(x89461),x89464))),x89463))
% 11.41/11.19 [8984]~P61(x89841)+~P90(x89841)+~P85(f784(f784(f243(x89841),f2(x89841)),x89844))+~P85(f784(f784(f243(x89841),x89842),f784(f784(f90(x89841),x89844),f784(f113(x89841),x89843))))+~P85(f784(f784(f243(x89841),f784(f784(f90(x89841),x89844),f784(f113(x89841),x89843))),x89842))+P85(f784(f784(f243(x89841),f784(f784(f293(x89841),x89842),f784(f113(x89841),x89843))),x89844))
% 11.41/11.19 [8985]~P61(x89851)+~P90(x89851)+~P85(f784(f784(f242(x89851),f2(x89851)),x89854))+~P85(f784(f784(f242(x89851),x89852),f784(f784(f90(x89851),x89854),f784(f113(x89851),x89853))))+~P85(f784(f784(f242(x89851),f784(f784(f90(x89851),x89854),f784(f113(x89851),x89853))),x89852))+P85(f784(f784(f242(x89851),f784(f784(f293(x89851),x89852),f784(f113(x89851),x89853))),x89854))
% 11.41/11.19 [9022]~P61(x90221)+~P90(x90221)+~P85(f784(f784(f243(x90221),f784(f113(x90221),x90223)),f2(x90221)))+~P85(f784(f784(f243(x90221),x90222),f784(f784(f90(x90221),x90224),f784(f113(x90221),x90223))))+~P85(f784(f784(f243(x90221),f784(f784(f90(x90221),x90224),f784(f113(x90221),x90223))),x90222))+P85(f784(f784(f243(x90221),f784(f784(f293(x90221),x90222),f784(f113(x90221),x90223))),x90224))
% 11.41/11.19 [9023]~P61(x90231)+~P90(x90231)+~P85(f784(f784(f243(x90231),f784(f113(x90231),x90233)),f2(x90231)))+~P85(f784(f784(f242(x90231),x90232),f784(f784(f90(x90231),x90234),f784(f113(x90231),x90233))))+~P85(f784(f784(f242(x90231),f784(f784(f90(x90231),x90234),f784(f113(x90231),x90233))),x90232))+P85(f784(f784(f242(x90231),f784(f784(f293(x90231),x90232),f784(f113(x90231),x90233))),x90234))
% 11.41/11.19 [8748]~P61(x87481)+~P90(x87481)+~P85(f784(f784(f243(x87481),x87482),f2(x87481)))+~P85(f784(f784(f243(x87481),f784(f784(f293(x87481),x87484),x87482)),f784(f113(x87481),x87483)))+P85(f784(f784(f243(x87481),f2(x87481)),x87482))+P85(f784(f784(f243(x87481),f784(f784(f90(x87481),f784(f113(x87481),x87483)),x87482)),x87484))
% 11.41/11.19 [8749]~P61(x87491)+~P90(x87491)+~P85(f784(f784(f243(x87491),x87492),f2(x87491)))+~P85(f784(f784(f242(x87491),f784(f784(f293(x87491),x87494),x87492)),f784(f113(x87491),x87493)))+P85(f784(f784(f243(x87491),f2(x87491)),x87492))+P85(f784(f784(f242(x87491),f784(f784(f90(x87491),f784(f113(x87491),x87493)),x87492)),x87494))
% 11.41/11.19 [8843]~P61(x88431)+~P90(x88431)+~P85(f784(f784(f243(x88431),x88432),f2(x88431)))+P85(f784(f784(f243(x88431),f2(x88431)),x88432))+P85(f784(f784(f243(x88431),f784(f784(f293(x88431),x88433),x88432)),f784(f113(x88431),x88434)))+~P85(f784(f784(f243(x88431),f784(f784(f90(x88431),f784(f113(x88431),x88434)),x88432)),x88433))
% 11.41/11.19 [8844]~P61(x88441)+~P90(x88441)+~P85(f784(f784(f243(x88441),x88442),f2(x88441)))+P85(f784(f784(f243(x88441),f2(x88441)),x88442))+P85(f784(f784(f242(x88441),f784(f784(f293(x88441),x88443),x88442)),f784(f113(x88441),x88444)))+~P85(f784(f784(f242(x88441),f784(f784(f90(x88441),f784(f113(x88441),x88444)),x88442)),x88443))
% 11.41/11.19 [8882]~P61(x88821)+~P90(x88821)+P85(f784(f784(f243(x88821),x88822),f2(x88821)))+~P85(f784(f784(f243(x88821),f784(f113(x88821),x88823)),f2(x88821)))+P85(f784(f784(f243(x88821),f784(f113(x88821),x88823)),f784(f784(f293(x88821),x88824),x88822)))+~P85(f784(f784(f243(x88821),f784(f784(f90(x88821),f784(f113(x88821),x88823)),x88822)),x88824))
% 11.41/11.19 [8883]~P61(x88831)+~P90(x88831)+P85(f784(f784(f243(x88831),x88832),f2(x88831)))+~P85(f784(f784(f242(x88831),f784(f113(x88831),x88833)),f2(x88831)))+P85(f784(f784(f242(x88831),f784(f113(x88831),x88833)),f784(f784(f293(x88831),x88834),x88832)))+~P85(f784(f784(f242(x88831),f784(f784(f90(x88831),f784(f113(x88831),x88833)),x88832)),x88834))
% 11.41/11.19 [8899]~P61(x88991)+~P90(x88991)+P85(f784(f784(f243(x88991),f2(x88991)),x88992))+P85(f784(f784(f243(x88991),f784(f784(f293(x88991),x88993),x88992)),f784(f113(x88991),x88994)))+~P85(f784(f784(f243(x88991),f2(x88991)),f784(f113(x88991),x88994)))+~P85(f784(f784(f243(x88991),f784(f784(f90(x88991),f784(f113(x88991),x88994)),x88992)),x88993))
% 11.41/11.19 [8900]~P61(x89001)+~P90(x89001)+P85(f784(f784(f243(x89001),f2(x89001)),x89002))+P85(f784(f784(f242(x89001),f784(f784(f293(x89001),x89003),x89002)),f784(f113(x89001),x89004)))+~P85(f784(f784(f242(x89001),f2(x89001)),f784(f113(x89001),x89004)))+~P85(f784(f784(f242(x89001),f784(f784(f90(x89001),f784(f113(x89001),x89004)),x89002)),x89003))
% 11.41/11.19 [9054]~P61(x90541)+~P90(x90541)+~P85(f784(f784(f243(x90541),x90544),f2(x90541)))+P85(f784(f784(f243(x90541),f784(f113(x90541),x90542)),f784(f784(f293(x90541),x90543),x90544)))+~P85(f784(f784(f243(x90541),x90543),f784(f784(f90(x90541),f784(f113(x90541),x90542)),x90544)))+~P85(f784(f784(f243(x90541),f784(f784(f90(x90541),f784(f113(x90541),x90542)),x90544)),x90543))
% 11.41/11.19 [9055]~P61(x90551)+~P90(x90551)+~P85(f784(f784(f243(x90551),x90554),f2(x90551)))+P85(f784(f784(f242(x90551),f784(f113(x90551),x90552)),f784(f784(f293(x90551),x90553),x90554)))+~P85(f784(f784(f242(x90551),x90553),f784(f784(f90(x90551),f784(f113(x90551),x90552)),x90554)))+~P85(f784(f784(f242(x90551),f784(f784(f90(x90551),f784(f113(x90551),x90552)),x90554)),x90553))
% 11.41/11.19 [9085]~P61(x90851)+~P90(x90851)+~P85(f784(f784(f243(x90851),x90853),f2(x90851)))+P85(f784(f784(f243(x90851),f784(f784(f293(x90851),x90852),x90853)),f784(f113(x90851),x90854)))+~P85(f784(f784(f243(x90851),x90852),f784(f784(f90(x90851),f784(f113(x90851),x90854)),x90853)))+~P85(f784(f784(f243(x90851),f784(f784(f90(x90851),f784(f113(x90851),x90854)),x90853)),x90852))
% 11.41/11.19 [9086]~P61(x90861)+~P90(x90861)+~P85(f784(f784(f243(x90861),x90863),f2(x90861)))+P85(f784(f784(f242(x90861),f784(f784(f293(x90861),x90862),x90863)),f784(f113(x90861),x90864)))+~P85(f784(f784(f242(x90861),x90862),f784(f784(f90(x90861),f784(f113(x90861),x90864)),x90863)))+~P85(f784(f784(f242(x90861),f784(f784(f90(x90861),f784(f113(x90861),x90864)),x90863)),x90862))
% 11.41/11.19 [9104]~P61(x91041)+~P90(x91041)+~P85(f784(f784(f243(x91041),f784(f113(x91041),x91042)),f2(x91041)))+P85(f784(f784(f243(x91041),f784(f113(x91041),x91042)),f784(f784(f293(x91041),x91043),x91044)))+~P85(f784(f784(f243(x91041),x91043),f784(f784(f90(x91041),f784(f113(x91041),x91042)),x91044)))+~P85(f784(f784(f243(x91041),f784(f784(f90(x91041),f784(f113(x91041),x91042)),x91044)),x91043))
% 11.41/11.19 [9105]~P61(x91051)+~P90(x91051)+~P85(f784(f784(f242(x91051),f784(f113(x91051),x91052)),f2(x91051)))+P85(f784(f784(f242(x91051),f784(f113(x91051),x91052)),f784(f784(f293(x91051),x91053),x91054)))+~P85(f784(f784(f242(x91051),x91053),f784(f784(f90(x91051),f784(f113(x91051),x91052)),x91054)))+~P85(f784(f784(f242(x91051),f784(f784(f90(x91051),f784(f113(x91051),x91052)),x91054)),x91053))
% 11.41/11.19 [9109]~P61(x91091)+~P90(x91091)+P85(f784(f784(f243(x91091),f784(f784(f293(x91091),x91092),x91093)),f784(f113(x91091),x91094)))+~P85(f784(f784(f243(x91091),f2(x91091)),f784(f113(x91091),x91094)))+~P85(f784(f784(f243(x91091),x91092),f784(f784(f90(x91091),f784(f113(x91091),x91094)),x91093)))+~P85(f784(f784(f243(x91091),f784(f784(f90(x91091),f784(f113(x91091),x91094)),x91093)),x91092))
% 11.41/11.19 [9110]~P61(x91101)+~P90(x91101)+P85(f784(f784(f242(x91101),f784(f784(f293(x91101),x91102),x91103)),f784(f113(x91101),x91104)))+~P85(f784(f784(f242(x91101),f2(x91101)),f784(f113(x91101),x91104)))+~P85(f784(f784(f242(x91101),x91102),f784(f784(f90(x91101),f784(f113(x91101),x91104)),x91103)))+~P85(f784(f784(f242(x91101),f784(f784(f90(x91101),f784(f113(x91101),x91104)),x91103)),x91102))
% 11.41/11.19 [5958]~P86(x59582)+~P129(x59582)+~E(f784(x59583,x59585),f2(x59582))+E(f784(f784(f11(x59581,x59582),x59583),x59584),f2(x59582))+~P85(f784(f71(x59581),x59584))+~P85(f784(f784(f347(x59581),x59585),x59584))
% 11.41/11.19 [8347]~P100(x83471)+P85(f784(f784(f243(f869(x83471,a852)),f305(x83471,x83472,x83473)),f305(x83471,x83474,x83475)))+~P85(f784(f784(f243(x83471),x83473),x83475))+~P85(f784(f784(f242(x83471),x83474),x83472))+~P85(f784(f784(f242(x83471),x83474),x83475))+~P85(f784(f784(f242(x83471),x83473),x83475))
% 11.41/11.19 [8348]~P100(x83481)+P85(f784(f784(f243(f869(x83481,a852)),f305(x83481,x83482,x83483)),f305(x83481,x83484,x83485)))+~P85(f784(f784(f243(x83481),x83484),x83482))+~P85(f784(f784(f242(x83481),x83483),x83485))+~P85(f784(f784(f242(x83481),x83484),x83485))+~P85(f784(f784(f242(x83481),x83484),x83482))
% 11.41/11.19 [9132]P56(x91322,x91323,x91324,x91321)+E(x91321,f187(f869(x91322,a852)))+~P85(f784(f71(x91322),x91324))+~P85(f784(f71(x91322),x91321))+~P85(f784(f784(x91323,f545(x91321,x91324,x91323,x91322)),x91325))+~P85(f784(f784(f347(x91322),x91325),x91321))
% 11.41/11.19 [9256]~E(x92563,x92565)+~P68(x92561)+~P71(x92561)+~P37(x92563)+E(f784(f784(f8(a1,x92561),x92562),x92563),f784(f784(f8(a1,x92561),x92564),x92565))+P85(f784(f784(f242(a1),f2(a1)),f394(x92562,x92564,x92563,x92565,x92561)))
% 11.41/11.19 [9257]~E(x92573,x92575)+~P68(x92571)+~P71(x92571)+~P37(x92573)+E(f784(f784(f11(a1,x92571),x92572),x92573),f784(f784(f11(a1,x92571),x92574),x92575))+P85(f784(f784(f242(a1),f2(a1)),f500(x92572,x92574,x92573,x92575,x92571)))
% 11.41/11.19 [9423]~E(x94235,x94233)+~P68(x94231)+~P71(x94231)+~P37(x94235)+~E(f784(x94232,f394(x94234,x94232,x94235,x94233,x94231)),f784(x94234,f394(x94234,x94232,x94235,x94233,x94231)))+E(f784(f784(f8(a1,x94231),x94232),x94233),f784(f784(f8(a1,x94231),x94234),x94235))
% 11.41/11.19 [9424]~E(x94245,x94243)+~P68(x94241)+~P71(x94241)+~P37(x94245)+~E(f784(x94242,f500(x94244,x94242,x94245,x94243,x94241)),f784(x94244,f500(x94244,x94242,x94245,x94243,x94241)))+E(f784(f784(f11(a1,x94241),x94242),x94243),f784(f784(f11(a1,x94241),x94244),x94245))
% 11.41/11.19 [9509]~P77(x95093)+E(f784(x95091,x95092),f2(x95093))+~E(f784(f784(f8(x95094,x95093),x95091),x95095),f2(x95093))+~P85(f784(f71(x95094),x95095))+P85(f784(f784(f347(x95094),f481(x95092,x95091,x95095,x95094,x95093)),x95095))+~P85(f784(f784(f347(x95094),x95092),x95095))
% 11.41/11.19 [9639]~P77(x96393)+E(f784(x96391,x96392),f2(x96393))+~E(f784(f784(f8(x96394,x96393),x96391),x96395),f2(x96393))+~P85(f784(f71(x96394),x96395))+~P85(f784(f784(f347(x96394),x96392),x96395))+~P85(f784(f784(f242(x96393),f2(x96393)),f784(x96391,f481(x96392,x96391,x96395,x96394,x96393))))
% 11.41/11.19 [8260]~P125(x82601)+~P85(f784(f784(f242(x82601),f2(x82601)),x82603))+~P85(f784(f784(f243(x82601),x82603),x82605))+~P85(f784(f784(f243(x82601),x82602),x82604))+~P85(f784(f784(f243(x82601),f2(x82601)),x82604))+P85(f784(f784(f243(x82601),f784(f784(f90(x82601),x82602),x82603)),f784(f784(f90(x82601),x82604),x82605)))
% 11.41/11.19 [8261]~P125(x82611)+~P85(f784(f784(f242(x82611),f2(x82611)),x82613))+~P85(f784(f784(f242(x82611),f2(x82611)),x82612))+~P85(f784(f784(f243(x82611),x82613),x82615))+~P85(f784(f784(f243(x82611),x82612),x82614))+P85(f784(f784(f243(x82611),f784(f784(f90(x82611),x82612),x82613)),f784(f784(f90(x82611),x82614),x82615)))
% 11.41/11.19 [8262]~P125(x82621)+~P85(f784(f784(f242(x82621),x82622),x82624))+~P85(f784(f784(f242(x82621),f2(x82621)),x82623))+~P85(f784(f784(f243(x82621),x82623),x82625))+~P85(f784(f784(f243(x82621),f2(x82621)),x82622))+P85(f784(f784(f243(x82621),f784(f784(f90(x82621),x82622),x82623)),f784(f784(f90(x82621),x82624),x82625)))
% 11.41/11.19 [8263]~P125(x82631)+~P85(f784(f784(f242(x82631),x82633),x82635))+~P85(f784(f784(f242(x82631),f2(x82631)),x82632))+~P85(f784(f784(f243(x82631),x82632),x82634))+~P85(f784(f784(f243(x82631),f2(x82631)),x82633))+P85(f784(f784(f243(x82631),f784(f784(f90(x82631),x82632),x82633)),f784(f784(f90(x82631),x82634),x82635)))
% 11.41/11.19 [8264]~P62(x82641)+~P85(f784(f784(f242(x82641),x82642),x82644))+~P85(f784(f784(f243(x82641),x82645),x82643))+~P85(f784(f784(f243(x82641),f2(x82641)),x82645))+~P85(f784(f784(f243(x82641),f2(x82641)),x82642))+P85(f784(f784(f243(x82641),f784(f784(f293(x82641),x82642),x82643)),f784(f784(f293(x82641),x82644),x82645)))
% 11.41/11.19 [8265]~P62(x82651)+~P85(f784(f784(f242(x82651),x82655),x82653))+~P85(f784(f784(f242(x82651),f2(x82651)),x82652))+~P85(f784(f784(f243(x82651),x82652),x82654))+~P85(f784(f784(f243(x82651),f2(x82651)),x82655))+P85(f784(f784(f243(x82651),f784(f784(f293(x82651),x82652),x82653)),f784(f784(f293(x82651),x82654),x82655)))
% 11.41/11.19 [8266]~P133(x82661)+~P85(f784(f784(f242(x82661),x82663),x82665))+~P85(f784(f784(f242(x82661),x82662),x82664))+~P85(f784(f784(f242(x82661),f2(x82661)),x82663))+~P85(f784(f784(f242(x82661),f2(x82661)),x82664))+P85(f784(f784(f242(x82661),f784(f784(f90(x82661),x82662),x82663)),f784(f784(f90(x82661),x82664),x82665)))
% 11.41/11.19 [8267]~P133(x82671)+~P85(f784(f784(f242(x82671),x82673),x82675))+~P85(f784(f784(f242(x82671),x82672),x82674))+~P85(f784(f784(f242(x82671),f2(x82671)),x82673))+~P85(f784(f784(f242(x82671),f2(x82671)),x82672))+P85(f784(f784(f242(x82671),f784(f784(f90(x82671),x82672),x82673)),f784(f784(f90(x82671),x82674),x82675)))
% 11.41/11.19 [8268]~P62(x82681)+~P85(f784(f784(f243(x82681),f2(x82681)),x82685))+~P85(f784(f784(f242(x82681),x82685),x82683))+~P85(f784(f784(f242(x82681),x82682),x82684))+~P85(f784(f784(f242(x82681),f2(x82681)),x82682))+P85(f784(f784(f242(x82681),f784(f784(f293(x82681),x82682),x82683)),f784(f784(f293(x82681),x82684),x82685)))
% 11.41/11.19 [9547]~P68(x95475)+~P80(x95475)+E(x95471,f187(f869(x95472,a852)))+~P85(f784(f71(x95472),x95471))+P85(f784(f784(f347(x95472),f501(x95473,x95474,x95471,x95472,x95475)),x95471))+P85(f784(f784(f243(x95475),f784(f784(f8(x95472,x95475),x95474),x95471)),f784(f784(f8(x95472,x95475),x95473),x95471)))
% 11.41/11.19 [9659]~P68(x96591)+~P78(x96591)+~P85(f784(f71(x96592),x96595))+~P85(f784(f784(f242(x96591),f2(x96591)),f784(x96593,f424(x96593,x96594,x96595,x96592,x96591))))+P85(f784(f784(f242(x96591),f784(f784(f8(x96592,x96591),x96593),x96594)),f784(f784(f8(x96592,x96591),x96593),x96595)))+~P85(f784(f784(f242(f869(x96592,a852)),x96594),x96595))
% 11.41/11.19 [9824]~P68(x98243)+~P80(x98243)+E(x98241,f187(f869(x98242,a852)))+~P85(f784(f71(x98242),x98241))+~P85(f784(f784(f243(x98243),f784(x98244,f501(x98245,x98244,x98241,x98242,x98243))),f784(x98245,f501(x98245,x98244,x98241,x98242,x98243))))+P85(f784(f784(f243(x98243),f784(f784(f8(x98242,x98243),x98244),x98241)),f784(f784(f8(x98242,x98243),x98245),x98241)))
% 11.41/11.19 [6979]~P18(x69792,x69795,x69794)+E(x69791,f187(f869(x69792,a852)))+E(x69793,f187(f869(x69792,a852)))+~P85(f784(f71(x69792),x69791))+~P85(f784(f71(x69792),x69793))+E(f784(x69794,f784(f784(f110(f869(x69792,a852)),x69793),x69791)),f784(f784(x69795,f784(x69794,x69793)),f784(x69794,x69791)))
% 11.41/11.19 [7586]~P143(x75861,x75863,x75864)+P85(f784(x75861,x75862))+~P85(f784(f784(f243(a1),x75864),f2(a1)))+~P85(f784(f784(f242(a1),x75865),f2(a1)))+~E(x75863,f784(f784(f89(a1),f784(f784(f90(a1),x75864),x75862)),x75865))+~P85(f784(f784(f243(a1),x75864),x75865))
% 11.41/11.19 [7587]~P142(x75871,x75873,x75874)+P85(f784(x75871,x75872))+~P85(f784(f784(f243(a1),x75874),f2(a1)))+~P85(f784(f784(f242(a1),x75872),f2(a1)))+~E(x75873,f784(f784(f89(a1),f784(f784(f90(a1),x75874),x75875)),x75872))+~P85(f784(f784(f243(a1),x75874),x75872))
% 11.41/11.19 [7630]~P143(x76301,x76303,x76304)+P85(f784(x76301,x76302))+~E(x76303,f784(f784(f89(a1),f784(f784(f90(a1),x76304),x76302)),x76305))+~P85(f784(f784(f243(a1),f2(a1)),x76304))+~P85(f784(f784(f242(a1),f2(a1)),x76305))+~P85(f784(f784(f243(a1),x76305),x76304))
% 11.41/11.19 [7631]~P142(x76311,x76313,x76314)+P85(f784(x76311,x76312))+~E(x76313,f784(f784(f89(a1),f784(f784(f90(a1),x76314),x76315)),x76312))+~P85(f784(f784(f243(a1),f2(a1)),x76314))+~P85(f784(f784(f242(a1),f2(a1)),x76312))+~P85(f784(f784(f243(a1),x76312),x76314))
% 11.41/11.19 [8550]P85(f784(f784(x85501,x85502),x85503))+~P85(f784(f784(x85501,f784(f784(f51(a1),x85504),x85505)),f60(a1,x85504,x85505)))+~P85(f784(f784(f243(a1),x85505),f2(a1)))+~P85(f784(f784(f242(a1),x85503),f2(a1)))+~E(x85504,f784(f784(f89(a1),f784(f784(f90(a1),x85505),x85502)),x85503))+~P85(f784(f784(f243(a1),x85505),x85503))
% 11.41/11.19 [8557]P85(f784(f784(x85571,x85572),x85573))+~P85(f784(f784(x85571,f784(f784(f51(a1),x85574),x85575)),f60(a1,x85574,x85575)))+~E(x85574,f784(f784(f89(a1),f784(f784(f90(a1),x85575),x85572)),x85573))+~P85(f784(f784(f243(a1),f2(a1)),x85575))+~P85(f784(f784(f242(a1),f2(a1)),x85573))+~P85(f784(f784(f243(a1),x85573),x85575))
% 11.41/11.19 [8777]E(x87771,x87772)+~P53(x87773,x87775,x87774)+~P85(f784(f784(f347(x87773),x87772),x87775))+~P85(f784(f784(f347(x87773),x87771),x87775))+P85(f784(f784(f347(f868(x87773,x87773)),f784(f784(f251(x87773,x87773),x87771),x87772)),x87774))+P85(f784(f784(f347(f868(x87773,x87773)),f784(f784(f251(x87773,x87773),x87772),x87771)),x87774))
% 11.41/11.19 [9578]~P68(x95785)+~P78(x95785)+~P85(f784(f71(x95781),x95784))+P85(f784(f784(f242(x95785),f784(f784(f8(x95781,x95785),x95782),x95783)),f784(f784(f8(x95781,x95785),x95782),x95784)))+~P85(f784(f784(f242(f869(x95781,a852)),x95783),x95784))+P85(f784(f784(f347(x95781),f424(x95782,x95783,x95784,x95781,x95785)),f784(f784(f3(f869(x95781,a852)),x95784),x95783)))
% 11.41/11.19 [9666]E(x96661,f187(f869(x96662,a852)))+~P85(f784(f71(x96662),x96663))+~P85(f784(f71(x96662),x96661))+P85(f784(f784(f347(f868(f869(x96662,a852),f869(x96662,a852))),f784(f784(f251(f869(x96662,a852),f869(x96662,a852)),x96663),x96661)),f338(x96662,x96664)))+~P85(f784(f784(f347(x96662),x96665),x96661))+~P85(f784(f784(f347(f868(x96662,x96662)),f784(f784(f251(x96662,x96662),f547(x96664,x96661,x96663,x96662)),x96665)),x96664))
% 11.41/11.19 [9667]E(x96671,f187(f869(x96672,a852)))+~P85(f784(f71(x96672),x96673))+~P85(f784(f71(x96672),x96671))+P85(f784(f784(f347(f868(f869(x96672,a852),f869(x96672,a852))),f784(f784(f251(f869(x96672,a852),f869(x96672,a852)),x96673),x96671)),f338(x96672,x96674)))+~P85(f784(f784(f347(x96672),x96675),x96671))+~P85(f784(f784(f347(f868(x96672,x96672)),f784(f784(f251(x96672,x96672),f635(x96674,x96671,x96673,x96672)),x96675)),x96674))
% 11.41/11.19 [9827]~P77(x98271)+~E(f784(f784(f8(x98275,x98271),x98272),x98276),x98274)+~P85(f784(f71(x98275),x98276))+P85(f784(f784(f347(x98275),f475(x98273,x98274,x98272,x98276,x98275,x98271)),x98276))+P85(f784(f784(f242(x98271),f784(x98272,x98273)),x98274))+~P85(f784(f784(f347(x98275),x98273),x98276))
% 11.41/11.19 [9883]~P77(x98831)+~E(f784(f784(f8(x98835,x98831),x98832),x98836),x98834)+~P85(f784(f71(x98835),x98836))+~P85(f784(f784(f347(x98835),x98833),x98836))+~P85(f784(f784(f242(x98831),f2(x98831)),f784(x98832,f475(x98833,x98834,x98832,x98836,x98835,x98831))))+P85(f784(f784(f242(x98831),f784(x98832,x98833)),x98834))
% 11.41/11.19 [10000]~E(x100005,x100008)+~E(x100004,x100007)+~P68(x100002)+~P103(x100001)+E(f784(f784(f8(x100001,x100002),x100003),f784(f304(x100001,x100004),x100005)),f784(f784(f8(x100001,x100002),x100006),f784(f304(x100001,x100007),x100008)))+P85(f784(f784(f242(x100001),x100004),f384(x100003,x100006,x100005,x100008,x100004,x100007,x100001,x100002)))
% 11.41/11.19 [10015]~E(x100157,x100154)+~E(x100158,x100155)+~P68(x100152)+~P103(x100151)+~E(f784(x100153,f384(x100156,x100153,x100158,x100155,x100157,x100154,x100151,x100152)),f784(x100156,f384(x100156,x100153,x100158,x100155,x100157,x100154,x100151,x100152)))+E(f784(f784(f8(x100151,x100152),x100153),f784(f304(x100151,x100154),x100155)),f784(f784(f8(x100151,x100152),x100156),f784(f304(x100151,x100157),x100158)))
% 11.41/11.19 [10018]~E(x100184,x100187)+~E(x100185,x100188)+~P68(x100182)+~P103(x100181)+E(f784(f784(f8(x100181,x100182),x100183),f784(f304(x100181,x100184),x100185)),f784(f784(f8(x100181,x100182),x100186),f784(f304(x100181,x100187),x100188)))+P85(f784(f784(f243(x100181),f384(x100183,x100186,x100185,x100188,x100184,x100187,x100181,x100182)),x100185))
% 11.41/11.19 [9671]~P9(x96715,x96719,x96716)+~P9(x96711,x967110,x96713)+~P14(x96711,x96715,f869(x96712,a852),x96713,x96716,x96718)+~P85(f784(f784(f347(x96715),x96717),x96719))+~P85(f784(f784(f347(x96711),x96714),x967110))+E(f784(f784(f54(x96711,f869(x96712,a852)),f784(f287(x96711,x96711,x96713),f784(f784(f312(x96711),x96714),f187(f869(x96711,a852))))),f784(f784(f10(f869(x96715,f869(x96712,a852)),f869(x96712,a852),x96711),f784(f54(x96715,f869(x96712,a852)),f784(f287(x96715,x96715,x96716),f784(f784(f312(x96715),x96717),f187(f869(x96715,a852)))))),x96718)),f784(f784(x96718,x96714),x96717))
% 11.41/11.19 [5485]~P101(x54853)+~P15(x54853,x54852)+~P15(x54853,x54851)+E(x54851,x54852)+~E(f784(f164(x54853),x54851),f784(f164(x54853),x54852))+~P85(f784(f132(x54853),x54852))+~P85(f784(f132(x54853),x54851))
% 11.41/11.19 [4839]~P124(x48392)+~P129(x48392)+~P140(x48392)+~P106(x48392)+~E(x48393,f2(x48392))+E(x48391,f2(a859))+E(f784(f784(f252(x48392),x48393),x48391),f2(x48392))
% 11.41/11.19 [9016]E(x90161,f2(a859))+~E(x90162,f784(f784(f89(a859),f784(f784(f90(a859),f784(f250(a859,a859),x90163)),x90161)),f784(f260(a859,a859),x90163)))+P85(f784(f63(x90162,x90161),x90163))+~P85(f784(f784(f242(a859),f784(f260(a859,a859),x90163)),f2(a859)))+~P85(f784(f784(f242(a859),f2(a859)),f784(f260(a859,a859),x90163)))+~P85(f784(f784(f243(a859),x90161),f784(f260(a859,a859),x90163)))+~P85(f784(f784(f243(a859),f784(f260(a859,a859),x90163)),x90161))
% 11.41/11.19 [9025]~E(f784(f250(a859,a859),x90253),f2(a859))+~E(x90251,f784(f784(f89(a859),f784(f784(f90(a859),f784(f250(a859,a859),x90253)),x90252)),f784(f260(a859,a859),x90253)))+P85(f784(f63(x90251,x90252),x90253))+~P85(f784(f784(f242(a859),f784(f260(a859,a859),x90253)),f2(a859)))+~P85(f784(f784(f242(a859),f2(a859)),f784(f260(a859,a859),x90253)))+~P85(f784(f784(f243(a859),x90252),f784(f260(a859,a859),x90253)))+~P85(f784(f784(f243(a859),f784(f260(a859,a859),x90253)),x90252))
% 11.41/11.19 [7464]~P93(x74642)+E(x74641,f187(f869(x74642,a852)))+E(x74643,f187(f869(x74642,a852)))+~P85(f784(f71(x74642),x74641))+~P85(f784(f71(x74642),x74643))+~E(f784(f784(f111(f869(x74642,a852)),x74643),x74641),f187(f869(x74642,a852)))+E(f15(x74642,f784(f784(f110(f869(x74642,a852)),x74643),x74641)),f784(f784(f110(x74642),f15(x74642,x74643)),f15(x74642,x74641)))
% 11.41/11.19 [7465]~P101(x74652)+E(x74651,f187(f869(x74652,a852)))+E(x74653,f187(f869(x74652,a852)))+~P85(f784(f71(x74652),x74651))+~P85(f784(f71(x74652),x74653))+~E(f784(f784(f111(f869(x74652,a852)),x74653),x74651),f187(f869(x74652,a852)))+E(f16(x74652,f784(f784(f110(f869(x74652,a852)),x74653),x74651)),f784(f784(f186(x74652),f16(x74652,x74653)),f16(x74652,x74651)))
% 11.41/11.19 [7466]~P101(x74662)+E(x74661,f187(f869(x74662,a852)))+E(x74663,f187(f869(x74662,a852)))+~P85(f784(f71(x74662),x74661))+~P85(f784(f71(x74662),x74663))+~E(f784(f784(f111(f869(x74662,a852)),x74663),x74661),f187(f869(x74662,a852)))+E(f17(x74662,f784(f784(f110(f869(x74662,a852)),x74663),x74661)),f784(f784(f246(x74662),f17(x74662,x74663)),f17(x74662,x74661)))
% 11.41/11.19 [7467]~P93(x74672)+E(x74671,f187(f869(x74672,a852)))+E(x74673,f187(f869(x74672,a852)))+~P85(f784(f71(x74672),x74671))+~P85(f784(f71(x74672),x74673))+~E(f784(f784(f111(f869(x74672,a852)),x74673),x74671),f187(f869(x74672,a852)))+E(f12(x74672,f784(f784(f110(f869(x74672,a852)),x74673),x74671)),f784(f784(f111(x74672),f12(x74672,x74673)),f12(x74672,x74671)))
% 11.41/11.19 [7943]~P65(x79432)+E(x79431,f187(f869(x79432,a852)))+E(x79433,f187(f869(x79432,a852)))+~P85(f784(f71(x79432),x79431))+~P85(f784(f71(x79432),x79433))+~E(f784(f784(f111(f869(x79432,a852)),x79433),x79431),f187(f869(x79432,a852)))+E(f784(f784(f90(x79432),f784(f73(x79432,f90(x79432)),x79433)),f784(f73(x79432,f90(x79432)),x79431)),f784(f73(x79432,f90(x79432)),f784(f784(f110(f869(x79432,a852)),x79433),x79431)))
% 11.41/11.19 [8013]~P101(x80132)+E(x80131,f187(f869(x80132,a852)))+E(x80133,f187(f869(x80132,a852)))+~P85(f784(f71(x80132),x80131))+~P85(f784(f71(x80132),x80133))+~E(f784(f784(f111(f869(x80132,a852)),x80133),x80131),f187(f869(x80132,a852)))+E(f784(f784(f186(x80132),f13(x80132,f186(x80132),x80133)),f13(x80132,f186(x80132),x80131)),f13(x80132,f186(x80132),f784(f784(f110(f869(x80132,a852)),x80133),x80131)))
% 11.41/11.19 [8014]~P101(x80142)+E(x80141,f187(f869(x80142,a852)))+E(x80143,f187(f869(x80142,a852)))+~P85(f784(f71(x80142),x80141))+~P85(f784(f71(x80142),x80143))+~E(f784(f784(f111(f869(x80142,a852)),x80143),x80141),f187(f869(x80142,a852)))+E(f784(f784(f246(x80142),f14(x80142,f246(x80142),x80143)),f14(x80142,f246(x80142),x80141)),f14(x80142,f246(x80142),f784(f784(f110(f869(x80142,a852)),x80143),x80141)))
% 11.41/11.19 [7723]E(x77231,f2(a1))+E(f784(f784(f51(a1),x77232),x77231),x77233)+~P85(f784(f784(f242(a1),x77234),f2(a1)))+~E(x77232,f784(f784(f89(a1),f784(f784(f90(a1),x77231),x77233)),x77234))+~P85(f784(f784(f242(a1),f2(a1)),x77234))+~P85(f784(f784(f243(a1),x77234),x77231))+~P85(f784(f784(f243(a1),x77231),x77234))
% 11.41/11.19 [7729]E(f60(a1,x77292,x77291),x77293)+E(x77291,f2(a1))+~P85(f784(f784(f242(a1),x77293),f2(a1)))+~E(x77292,f784(f784(f89(a1),f784(f784(f90(a1),x77291),x77294)),x77293))+~P85(f784(f784(f242(a1),f2(a1)),x77293))+~P85(f784(f784(f243(a1),x77293),x77291))+~P85(f784(f784(f243(a1),x77291),x77293))
% 11.41/11.19 [6755]~P4(x67552)+E(x67551,f2(x67552))+E(x67553,f2(x67552))+~E(f784(f784(f51(x67552),x67554),x67553),f784(f784(f51(x67552),x67555),x67551))+E(f784(f784(f90(x67552),x67554),x67551),f784(f784(f90(x67552),x67553),x67555))+~P85(f784(f784(f289(x67552),x67551),x67555))+~P85(f784(f784(f289(x67552),x67553),x67554))
% 11.41/11.19 [6756]~P4(x67562)+E(x67561,f2(x67562))+E(x67563,f2(x67562))+~E(f784(f784(f90(x67562),x67564),x67563),f784(f784(f90(x67562),x67561),x67565))+E(f784(f784(f51(x67562),x67564),x67561),f784(f784(f51(x67562),x67565),x67563))+~P85(f784(f784(f289(x67562),x67561),x67564))+~P85(f784(f784(f289(x67562),x67563),x67565))
% 11.41/11.19 [7639]~P19(x76392,x76395,x76394)+E(x76391,f187(f869(x76392,a852)))+E(x76393,f187(f869(x76392,a852)))+~P85(f784(f71(x76392),x76391))+~P85(f784(f71(x76392),x76393))+~E(f784(f784(f111(f869(x76392,a852)),x76393),x76391),f187(f869(x76392,a852)))+E(f784(x76394,f784(f784(f110(f869(x76392,a852)),x76393),x76391)),f784(f784(x76395,f784(x76394,x76393)),f784(x76394,x76391)))
% 11.41/11.19 [9229]~P26(x92293,x92291,x92295,x92294)+~P26(x92291,x92293,x92296,x92292)+E(f784(f50(x92291),x92292),f784(f50(x92293),x92294))+~P85(f784(f71(x92293),x92294))+~P85(f784(f71(x92291),x92292))+~P85(f784(f784(f242(f869(x92293,a852)),f784(f313(x92291,x92293,x92296),x92292)),x92294))+~P85(f784(f784(f242(f869(x92291,a852)),f784(f313(x92293,x92291,x92295),x92294)),x92292))
% 11.41/11.19 [9178]~P85(f784(f784(f243(a1),f784(f784(f89(a1),f784(f784(f90(a1),x91785),x91781)),x91786)),f2(a1)))+~E(f784(f784(f89(a1),f784(f784(f90(a1),x91783),x91782)),x91784),f784(f784(f89(a1),f784(f784(f90(a1),x91785),x91781)),x91786))+~P85(f784(f784(f243(a1),f2(a1)),x91785))+~P85(f784(f784(f242(a1),f2(a1)),x91786))+~P85(f784(f784(f243(a1),x91784),x91783))+~P85(f784(f784(f242(a1),x91785),x91783))+P85(f784(f784(f242(a1),x91781),x91782))
% 11.41/11.19 [8967]~E(f784(f784(f89(a1),f784(f784(f90(a1),x89673),x89671)),x89674),f784(f784(f89(a1),f784(f784(f90(a1),x89675),x89672)),x89676))+~P85(f784(f784(f243(a1),f2(a1)),x89675))+~P85(f784(f784(f242(a1),f2(a1)),x89674))+~P85(f784(f784(f243(a1),x89676),x89675))+~P85(f784(f784(f242(a1),x89675),x89673))+P85(f784(f784(f242(a1),x89671),x89672))+~P85(f784(f784(f242(a1),f2(a1)),f784(f784(f89(a1),f784(f784(f90(a1),x89675),x89672)),x89676)))
% 11.41/11.19 [9134]~P126(x91341)+~E(f784(f784(f89(x91341),x91342),x91344),f87(x91341))+~P85(f784(f784(f242(x91341),f2(x91341)),x91344))+~P85(f784(f784(f242(x91341),f2(x91341)),x91342))+~P85(f784(f784(f243(x91341),x91345),x91346))+~P85(f784(f784(f243(x91341),x91343),x91346))+P85(f784(f784(f243(x91341),f784(f784(f89(x91341),f784(f784(f90(x91341),x91342),x91343)),f784(f784(f90(x91341),x91344),x91345))),x91346))
% 11.41/11.19 [9135]~P128(x91351)+~E(f784(f784(f89(x91351),x91352),x91354),f87(x91351))+~P85(f784(f784(f242(x91351),x91355),x91356))+~P85(f784(f784(f242(x91351),x91353),x91356))+~P85(f784(f784(f242(x91351),f2(x91351)),x91354))+~P85(f784(f784(f242(x91351),f2(x91351)),x91352))+P85(f784(f784(f242(x91351),f784(f784(f89(x91351),f784(f784(f90(x91351),x91352),x91353)),f784(f784(f90(x91351),x91354),x91355))),x91356))
% 11.41/11.19 [9923]~P9(x99237,x99236,x99235)+E(x99231,x99232)+~P13(x99237,f869(x99234,a852),x99235,x99233)+E(f784(x99233,f511(x99231,x99232,x99233,x99234,x99235,x99236,x99237)),f784(x99233,f512(x99231,x99232,x99233,x99234,x99235,x99236,x99237)))+~E(f784(f784(f54(x99237,f869(x99234,a852)),x99231),x99233),f784(f784(f54(x99237,f869(x99234,a852)),x99232),x99233))+~P85(f784(f784(f347(f869(x99237,a852)),x99232),f784(f784(f69(x99237),x99236),x99235)))+~P85(f784(f784(f347(f869(x99237,a852)),x99231),f784(f784(f69(x99237),x99236),x99235)))
% 11.41/11.19 [9964]~P9(x99643,x99647,x99646)+E(x99641,x99642)+~P13(x99643,f869(x99645,a852),x99646,x99644)+~E(f784(f784(f54(x99643,f869(x99645,a852)),x99641),x99644),f784(f784(f54(x99643,f869(x99645,a852)),x99642),x99644))+P85(f784(f784(f347(x99643),f512(x99641,x99642,x99644,x99645,x99646,x99647,x99643)),x99647))+~P85(f784(f784(f347(f869(x99643,a852)),x99642),f784(f784(f69(x99643),x99647),x99646)))+~P85(f784(f784(f347(f869(x99643,a852)),x99641),f784(f784(f69(x99643),x99647),x99646)))
% 11.41/11.19 [9965]~P9(x99653,x99657,x99656)+E(x99651,x99652)+~P13(x99653,f869(x99655,a852),x99656,x99654)+~E(f784(f784(f54(x99653,f869(x99655,a852)),x99651),x99654),f784(f784(f54(x99653,f869(x99655,a852)),x99652),x99654))+P85(f784(f784(f347(x99653),f511(x99651,x99652,x99654,x99655,x99656,x99657,x99653)),x99657))+~P85(f784(f784(f347(f869(x99653,a852)),x99652),f784(f784(f69(x99653),x99657),x99656)))+~P85(f784(f784(f347(f869(x99653,a852)),x99651),f784(f784(f69(x99653),x99657),x99656)))
% 11.41/11.19 [10031]E(x100311,x100312)+~P9(x100313,x100316,x100317)+~P13(x100313,f869(x100314,a852),x100317,x100315)+~E(f784(f784(f54(x100313,f869(x100314,a852)),x100311),x100315),f784(f784(f54(x100313,f869(x100314,a852)),x100312),x100315))+~P85(f784(f784(f347(f868(x100313,x100313)),f784(f784(f251(x100313,x100313),f512(x100311,x100312,x100315,x100314,x100317,x100316,x100313)),f511(x100311,x100312,x100315,x100314,x100317,x100316,x100313))),x100317))+~P85(f784(f784(f347(f869(x100313,a852)),x100312),f784(f784(f69(x100313),x100316),x100317)))+~P85(f784(f784(f347(f869(x100313,a852)),x100311),f784(f784(f69(x100313),x100316),x100317)))
% 11.41/11.19 [8966]~P9(x89661,x89667,x89664)+~E(x89665,x89666)+~P85(f784(f784(f347(x89661),x89663),x89666))+~P85(f784(f784(f347(x89661),x89662),x89665))+~P85(f784(f784(f347(f869(x89661,a852)),x89666),f784(f784(f69(x89661),x89667),x89664)))+~P85(f784(f784(f347(f869(x89661,a852)),x89665),f784(f784(f69(x89661),x89667),x89664)))+P85(f784(f784(f347(f868(x89661,x89661)),f784(f784(f251(x89661,x89661),x89662),x89663)),x89664))
% 11.41/11.19 [9099]E(x90991,x90992)+~P9(x90993,x90994,x90995)+~P85(f784(f784(f347(x90993),x90996),x90992))+~P85(f784(f784(f347(x90993),x90997),x90991))+~P85(f784(f784(f347(f869(x90993,a852)),x90992),f784(f784(f69(x90993),x90994),x90995)))+~P85(f784(f784(f347(f869(x90993,a852)),x90991),f784(f784(f69(x90993),x90994),x90995)))+~P85(f784(f784(f347(f868(x90993,x90993)),f784(f784(f251(x90993,x90993),x90997),x90996)),x90995))
% 11.41/11.19 [9100]E(x91001,x91002)+~P9(x91003,x91004,x91005)+~P85(f784(f784(f347(x91003),x91006),x91002))+~P85(f784(f784(f347(x91003),x91007),x91001))+~P85(f784(f784(f347(f869(x91003,a852)),x91002),f784(f784(f69(x91003),x91004),x91005)))+~P85(f784(f784(f347(f869(x91003,a852)),x91001),f784(f784(f69(x91003),x91004),x91005)))+~P85(f784(f784(f347(f868(x91003,x91003)),f784(f784(f251(x91003,x91003),x91007),x91006)),x91005))
% 11.41/11.19 [10049]~P9(x100499,x100498,x100497)+~P9(x100491,x1004911,x1004910)+~P14(x100491,x100499,f869(x100496,a852),x1004910,x100497,x100495)+P85(f784(f784(f347(x100491),f514(x100492,x100493,x100494,x100495,x100496,x100497,x100498,x100499,x1004910,x1004911,x100491)),x1004911))+~P85(f784(f784(f347(f869(x100499,a852)),x100493),f784(f784(f69(x100499),x100498),x100497)))+~P85(f784(f784(f347(f869(x100491,a852)),x100494),f784(f784(f69(x100491),x1004911),x1004910)))+P85(f784(f784(f347(f869(x100496,a852)),f784(f784(f54(x100491,f869(x100496,a852)),x100494),f784(f784(f10(f869(x100499,f869(x100496,a852)),f869(x100496,a852),x100491),f784(f54(x100499,f869(x100496,a852)),x100493)),x100495))),x100492))
% 11.41/11.19 [10050]~P9(x1005011,x1005010,x100509)+~P9(x100501,x100508,x100507)+~P14(x1005011,x100501,f869(x100506,a852),x100509,x100507,x100505)+P85(f784(f784(f347(x100501),f515(x100502,x100503,x100504,x100505,x100506,x100507,x100508,x100501,x100509,x1005010,x1005011)),x100508))+~P85(f784(f784(f347(f869(x1005011,a852)),x100504),f784(f784(f69(x1005011),x1005010),x100509)))+~P85(f784(f784(f347(f869(x100501,a852)),x100503),f784(f784(f69(x100501),x100508),x100507)))+P85(f784(f784(f347(f869(x100506,a852)),f784(f784(f54(x1005011,f869(x100506,a852)),x100504),f784(f784(f10(f869(x100501,f869(x100506,a852)),f869(x100506,a852),x1005011),f784(f54(x100501,f869(x100506,a852)),x100503)),x100505))),x100502))
% 11.41/11.19 [10051]~P9(x100512,x100518,x100519)+~P9(x100514,x1005110,x1005111)+~P14(x100512,x100514,f869(x100511,a852),x100519,x1005111,x100516)+~P85(f784(f784(f347(f869(x100512,a852)),x100513),f784(f784(f69(x100512),x100518),x100519)))+~P85(f784(f784(f347(f869(x100514,a852)),x100515),f784(f784(f69(x100514),x1005110),x1005111)))+~P85(f784(f784(f347(f869(x100511,a852)),f784(f784(x100516,f514(x100517,x100515,x100513,x100516,x100511,x1005111,x1005110,x100514,x100519,x100518,x100512)),f515(x100517,x100515,x100513,x100516,x100511,x1005111,x1005110,x100514,x100519,x100518,x100512))),x100517))+P85(f784(f784(f347(f869(x100511,a852)),f784(f784(f54(x100512,f869(x100511,a852)),x100513),f784(f784(f10(f869(x100514,f869(x100511,a852)),f869(x100511,a852),x100512),f784(f54(x100514,f869(x100511,a852)),x100515)),x100516))),x100517))
% 11.41/11.19 [9009]E(x90091,x90092)+~P101(x90094)+~P26(x90093,x90094,x90095,f784(f784(f110(f869(x90093,a852)),f784(f164(x90093),x90091)),f784(f164(x90093),x90092)))+~E(f784(f164(x90093),x90091),f784(f164(x90093),x90092))+~P15(x90094,f784(f784(f146(x90093,x90094),x90095),x90092))+~P15(x90094,f784(f784(f146(x90093,x90094),x90095),x90091))+~P85(f784(f132(x90094),f784(f784(f146(x90093,x90094),x90095),x90092)))+~P85(f784(f132(x90094),f784(f784(f146(x90093,x90094),x90095),x90091)))
% 11.41/11.19 %EqnAxiom
% 11.41/11.19 [1]E(x11,x11)
% 11.41/11.19 [2]E(x22,x21)+~E(x21,x22)
% 11.41/11.19 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 11.41/11.19 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 11.41/11.19 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 11.41/11.19 [6]~E(x61,x62)+E(f109(x61),f109(x62))
% 11.41/11.19 [7]~E(x71,x72)+E(f36(x71),f36(x72))
% 11.41/11.19 [8]~E(x81,x82)+E(f784(x81,x83),f784(x82,x83))
% 11.41/11.19 [9]~E(x91,x92)+E(f784(x93,x91),f784(x93,x92))
% 11.41/11.19 [10]~E(x101,x102)+E(f93(x101),f93(x102))
% 11.41/11.19 [11]~E(x111,x112)+E(f10(x111,x113,x114),f10(x112,x113,x114))
% 11.41/11.19 [12]~E(x121,x122)+E(f10(x123,x121,x124),f10(x123,x122,x124))
% 11.41/11.19 [13]~E(x131,x132)+E(f10(x133,x134,x131),f10(x133,x134,x132))
% 11.41/11.19 [14]~E(x141,x142)+E(f868(x141,x143),f868(x142,x143))
% 11.41/11.19 [15]~E(x151,x152)+E(f868(x153,x151),f868(x153,x152))
% 11.41/11.19 [16]~E(x161,x162)+E(f869(x161,x163),f869(x162,x163))
% 11.41/11.19 [17]~E(x171,x172)+E(f869(x173,x171),f869(x173,x172))
% 11.41/11.19 [18]~E(x181,x182)+E(f186(x181),f186(x182))
% 11.41/11.19 [19]~E(x191,x192)+E(f110(x191),f110(x192))
% 11.41/11.19 [20]~E(x201,x202)+E(f187(x201),f187(x202))
% 11.41/11.19 [21]~E(x211,x212)+E(f515(x211,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112),f515(x212,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112))
% 11.41/11.19 [22]~E(x221,x222)+E(f515(x223,x221,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f515(x223,x222,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212))
% 11.41/11.19 [23]~E(x231,x232)+E(f515(x233,x234,x231,x235,x236,x237,x238,x239,x2310,x2311,x2312),f515(x233,x234,x232,x235,x236,x237,x238,x239,x2310,x2311,x2312))
% 11.41/11.19 [24]~E(x241,x242)+E(f515(x243,x244,x245,x241,x246,x247,x248,x249,x2410,x2411,x2412),f515(x243,x244,x245,x242,x246,x247,x248,x249,x2410,x2411,x2412))
% 11.41/11.19 [25]~E(x251,x252)+E(f515(x253,x254,x255,x256,x251,x257,x258,x259,x2510,x2511,x2512),f515(x253,x254,x255,x256,x252,x257,x258,x259,x2510,x2511,x2512))
% 11.41/11.19 [26]~E(x261,x262)+E(f515(x263,x264,x265,x266,x267,x261,x268,x269,x2610,x2611,x2612),f515(x263,x264,x265,x266,x267,x262,x268,x269,x2610,x2611,x2612))
% 11.41/11.19 [27]~E(x271,x272)+E(f515(x273,x274,x275,x276,x277,x278,x271,x279,x2710,x2711,x2712),f515(x273,x274,x275,x276,x277,x278,x272,x279,x2710,x2711,x2712))
% 11.41/11.19 [28]~E(x281,x282)+E(f515(x283,x284,x285,x286,x287,x288,x289,x281,x2810,x2811,x2812),f515(x283,x284,x285,x286,x287,x288,x289,x282,x2810,x2811,x2812))
% 11.41/11.19 [29]~E(x291,x292)+E(f515(x293,x294,x295,x296,x297,x298,x299,x2910,x291,x2911,x2912),f515(x293,x294,x295,x296,x297,x298,x299,x2910,x292,x2911,x2912))
% 11.41/11.19 [30]~E(x301,x302)+E(f515(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x301,x3012),f515(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x302,x3012))
% 11.41/11.19 [31]~E(x311,x312)+E(f515(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x311),f515(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x312))
% 11.41/11.19 [32]~E(x321,x322)+E(f246(x321),f246(x322))
% 11.41/11.19 [33]~E(x331,x332)+E(f111(x331),f111(x332))
% 11.41/11.19 [34]~E(x341,x342)+E(f112(x341),f112(x342))
% 11.41/11.19 [35]~E(x351,x352)+E(f41(x351),f41(x352))
% 11.41/11.19 [36]~E(x361,x362)+E(f347(x361),f347(x362))
% 11.41/11.19 [37]~E(x371,x372)+E(f87(x371),f87(x372))
% 11.41/11.19 [38]~E(x381,x382)+E(f120(x381),f120(x382))
% 11.41/11.19 [39]~E(x391,x392)+E(f145(x391),f145(x392))
% 11.41/11.19 [40]~E(x401,x402)+E(f89(x401),f89(x402))
% 11.41/11.19 [41]~E(x411,x412)+E(f514(x411,x413,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112),f514(x412,x413,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112))
% 11.41/11.19 [42]~E(x421,x422)+E(f514(x423,x421,x424,x425,x426,x427,x428,x429,x4210,x4211,x4212),f514(x423,x422,x424,x425,x426,x427,x428,x429,x4210,x4211,x4212))
% 11.41/11.19 [43]~E(x431,x432)+E(f514(x433,x434,x431,x435,x436,x437,x438,x439,x4310,x4311,x4312),f514(x433,x434,x432,x435,x436,x437,x438,x439,x4310,x4311,x4312))
% 11.41/11.19 [44]~E(x441,x442)+E(f514(x443,x444,x445,x441,x446,x447,x448,x449,x4410,x4411,x4412),f514(x443,x444,x445,x442,x446,x447,x448,x449,x4410,x4411,x4412))
% 11.41/11.19 [45]~E(x451,x452)+E(f514(x453,x454,x455,x456,x451,x457,x458,x459,x4510,x4511,x4512),f514(x453,x454,x455,x456,x452,x457,x458,x459,x4510,x4511,x4512))
% 11.41/11.19 [46]~E(x461,x462)+E(f514(x463,x464,x465,x466,x467,x461,x468,x469,x4610,x4611,x4612),f514(x463,x464,x465,x466,x467,x462,x468,x469,x4610,x4611,x4612))
% 11.41/11.19 [47]~E(x471,x472)+E(f514(x473,x474,x475,x476,x477,x478,x471,x479,x4710,x4711,x4712),f514(x473,x474,x475,x476,x477,x478,x472,x479,x4710,x4711,x4712))
% 11.41/11.19 [48]~E(x481,x482)+E(f514(x483,x484,x485,x486,x487,x488,x489,x481,x4810,x4811,x4812),f514(x483,x484,x485,x486,x487,x488,x489,x482,x4810,x4811,x4812))
% 11.41/11.19 [49]~E(x491,x492)+E(f514(x493,x494,x495,x496,x497,x498,x499,x4910,x491,x4911,x4912),f514(x493,x494,x495,x496,x497,x498,x499,x4910,x492,x4911,x4912))
% 11.41/11.19 [50]~E(x501,x502)+E(f514(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x501,x5012),f514(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x502,x5012))
% 11.41/11.19 [51]~E(x511,x512)+E(f514(x513,x514,x515,x516,x517,x518,x519,x5110,x5111,x5112,x511),f514(x513,x514,x515,x516,x517,x518,x519,x5110,x5111,x5112,x512))
% 11.41/11.19 [52]~E(x521,x522)+E(f159(x521),f159(x522))
% 11.41/11.19 [53]~E(x531,x532)+E(f113(x531),f113(x532))
% 11.41/11.19 [54]~E(x541,x542)+E(f795(x541,x543,x544),f795(x542,x543,x544))
% 11.41/11.19 [55]~E(x551,x552)+E(f795(x553,x551,x554),f795(x553,x552,x554))
% 11.41/11.19 [56]~E(x561,x562)+E(f795(x563,x564,x561),f795(x563,x564,x562))
% 11.41/11.19 [57]~E(x571,x572)+E(f6(x571),f6(x572))
% 11.41/11.19 [58]~E(x581,x582)+E(f71(x581),f71(x582))
% 11.41/11.19 [59]~E(x591,x592)+E(f42(x591),f42(x592))
% 11.41/11.19 [60]~E(x601,x602)+E(f44(x601),f44(x602))
% 11.41/11.19 [61]~E(x611,x612)+E(f20(x611,x613,x614),f20(x612,x613,x614))
% 11.41/11.19 [62]~E(x621,x622)+E(f20(x623,x621,x624),f20(x623,x622,x624))
% 11.41/11.19 [63]~E(x631,x632)+E(f20(x633,x634,x631),f20(x633,x634,x632))
% 11.41/11.19 [64]~E(x641,x642)+E(f43(x641),f43(x642))
% 11.41/11.19 [65]~E(x651,x652)+E(f88(x651),f88(x652))
% 11.41/11.19 [66]~E(x661,x662)+E(f793(x661,x663,x664),f793(x662,x663,x664))
% 11.41/11.19 [67]~E(x671,x672)+E(f793(x673,x671,x674),f793(x673,x672,x674))
% 11.41/11.19 [68]~E(x681,x682)+E(f793(x683,x684,x681),f793(x683,x684,x682))
% 11.41/11.19 [69]~E(x691,x692)+E(f250(x691,x693),f250(x692,x693))
% 11.41/11.19 [70]~E(x701,x702)+E(f250(x703,x701),f250(x703,x702))
% 11.41/11.19 [71]~E(x711,x712)+E(f8(x711,x713),f8(x712,x713))
% 11.41/11.19 [72]~E(x721,x722)+E(f8(x723,x721),f8(x723,x722))
% 11.41/11.19 [73]~E(x731,x732)+E(f188(x731),f188(x732))
% 11.41/11.19 [74]~E(x741,x742)+E(f14(x741,x743,x744),f14(x742,x743,x744))
% 11.41/11.19 [75]~E(x751,x752)+E(f14(x753,x751,x754),f14(x753,x752,x754))
% 11.41/11.19 [76]~E(x761,x762)+E(f14(x763,x764,x761),f14(x763,x764,x762))
% 11.41/11.19 [77]~E(x771,x772)+E(f243(x771),f243(x772))
% 11.41/11.19 [78]~E(x781,x782)+E(f9(x781,x783,x784),f9(x782,x783,x784))
% 11.41/11.19 [79]~E(x791,x792)+E(f9(x793,x791,x794),f9(x793,x792,x794))
% 11.41/11.19 [80]~E(x801,x802)+E(f9(x803,x804,x801),f9(x803,x804,x802))
% 11.41/11.19 [81]~E(x811,x812)+E(f69(x811),f69(x812))
% 11.41/11.19 [82]~E(x821,x822)+E(f90(x821),f90(x822))
% 11.41/11.19 [83]~E(x831,x832)+E(f221(x831,x833),f221(x832,x833))
% 11.41/11.19 [84]~E(x841,x842)+E(f221(x843,x841),f221(x843,x842))
% 11.41/11.19 [85]~E(x851,x852)+E(f164(x851),f164(x852))
% 11.41/11.19 [86]~E(x861,x862)+E(f133(x861),f133(x862))
% 11.41/11.19 [87]~E(x871,x872)+E(f442(x871,x873,x874,x875),f442(x872,x873,x874,x875))
% 11.41/11.19 [88]~E(x881,x882)+E(f442(x883,x881,x884,x885),f442(x883,x882,x884,x885))
% 11.41/11.19 [89]~E(x891,x892)+E(f442(x893,x894,x891,x895),f442(x893,x894,x892,x895))
% 11.41/11.19 [90]~E(x901,x902)+E(f442(x903,x904,x905,x901),f442(x903,x904,x905,x902))
% 11.41/11.19 [91]~E(x911,x912)+E(f304(x911,x913),f304(x912,x913))
% 11.41/11.19 [92]~E(x921,x922)+E(f304(x923,x921),f304(x923,x922))
% 11.41/11.19 [93]~E(x931,x932)+E(f39(x931,x933,x934,x935,x936,x937,x938,x939,x9310,x9311),f39(x932,x933,x934,x935,x936,x937,x938,x939,x9310,x9311))
% 11.41/11.19 [94]~E(x941,x942)+E(f39(x943,x941,x944,x945,x946,x947,x948,x949,x9410,x9411),f39(x943,x942,x944,x945,x946,x947,x948,x949,x9410,x9411))
% 11.41/11.19 [95]~E(x951,x952)+E(f39(x953,x954,x951,x955,x956,x957,x958,x959,x9510,x9511),f39(x953,x954,x952,x955,x956,x957,x958,x959,x9510,x9511))
% 11.41/11.19 [96]~E(x961,x962)+E(f39(x963,x964,x965,x961,x966,x967,x968,x969,x9610,x9611),f39(x963,x964,x965,x962,x966,x967,x968,x969,x9610,x9611))
% 11.41/11.19 [97]~E(x971,x972)+E(f39(x973,x974,x975,x976,x971,x977,x978,x979,x9710,x9711),f39(x973,x974,x975,x976,x972,x977,x978,x979,x9710,x9711))
% 11.41/11.19 [98]~E(x981,x982)+E(f39(x983,x984,x985,x986,x987,x981,x988,x989,x9810,x9811),f39(x983,x984,x985,x986,x987,x982,x988,x989,x9810,x9811))
% 11.41/11.19 [99]~E(x991,x992)+E(f39(x993,x994,x995,x996,x997,x998,x991,x999,x9910,x9911),f39(x993,x994,x995,x996,x997,x998,x992,x999,x9910,x9911))
% 11.41/11.19 [100]~E(x1001,x1002)+E(f39(x1003,x1004,x1005,x1006,x1007,x1008,x1009,x1001,x10010,x10011),f39(x1003,x1004,x1005,x1006,x1007,x1008,x1009,x1002,x10010,x10011))
% 11.41/11.19 [101]~E(x1011,x1012)+E(f39(x1013,x1014,x1015,x1016,x1017,x1018,x1019,x10110,x1011,x10111),f39(x1013,x1014,x1015,x1016,x1017,x1018,x1019,x10110,x1012,x10111))
% 11.41/11.19 [102]~E(x1021,x1022)+E(f39(x1023,x1024,x1025,x1026,x1027,x1028,x1029,x10210,x10211,x1021),f39(x1023,x1024,x1025,x1026,x1027,x1028,x1029,x10210,x10211,x1022))
% 11.41/11.19 [103]~E(x1031,x1032)+E(f251(x1031,x1033),f251(x1032,x1033))
% 11.41/11.19 [104]~E(x1041,x1042)+E(f251(x1043,x1041),f251(x1043,x1042))
% 11.41/11.19 [105]~E(x1051,x1052)+E(f289(x1051),f289(x1052))
% 11.41/11.19 [106]~E(x1061,x1062)+E(f790(x1061,x1063,x1064),f790(x1062,x1063,x1064))
% 11.41/11.19 [107]~E(x1071,x1072)+E(f790(x1073,x1071,x1074),f790(x1073,x1072,x1074))
% 11.41/11.19 [108]~E(x1081,x1082)+E(f790(x1083,x1084,x1081),f790(x1083,x1084,x1082))
% 11.41/11.19 [109]~E(x1091,x1092)+E(f60(x1091,x1093,x1094),f60(x1092,x1093,x1094))
% 11.41/11.19 [110]~E(x1101,x1102)+E(f60(x1103,x1101,x1104),f60(x1103,x1102,x1104))
% 11.41/11.19 [111]~E(x1111,x1112)+E(f60(x1113,x1114,x1111),f60(x1113,x1114,x1112))
% 11.41/11.19 [112]~E(x1121,x1122)+E(f50(x1121),f50(x1122))
% 11.41/11.19 [113]~E(x1131,x1132)+E(f84(x1131),f84(x1132))
% 11.41/11.19 [114]~E(x1141,x1142)+E(f242(x1141),f242(x1142))
% 11.41/11.19 [115]~E(x1151,x1152)+E(f134(x1151,x1153),f134(x1152,x1153))
% 11.41/11.19 [116]~E(x1161,x1162)+E(f134(x1163,x1161),f134(x1163,x1162))
% 11.41/11.19 [117]~E(x1171,x1172)+E(f266(x1171),f266(x1172))
% 11.41/11.19 [118]~E(x1181,x1182)+E(f52(x1181,x1183),f52(x1182,x1183))
% 11.41/11.19 [119]~E(x1191,x1192)+E(f52(x1193,x1191),f52(x1193,x1192))
% 11.41/11.19 [120]~E(x1201,x1202)+E(f312(x1201),f312(x1202))
% 11.41/11.19 [121]~E(x1211,x1212)+E(f789(x1211,x1213,x1214),f789(x1212,x1213,x1214))
% 11.41/11.19 [122]~E(x1221,x1222)+E(f789(x1223,x1221,x1224),f789(x1223,x1222,x1224))
% 11.41/11.19 [123]~E(x1231,x1232)+E(f789(x1233,x1234,x1231),f789(x1233,x1234,x1232))
% 11.41/11.19 [124]~E(x1241,x1242)+E(f860(x1241),f860(x1242))
% 11.41/11.19 [125]~E(x1251,x1252)+E(f16(x1251,x1253),f16(x1252,x1253))
% 11.41/11.19 [126]~E(x1261,x1262)+E(f16(x1263,x1261),f16(x1263,x1262))
% 11.41/11.19 [127]~E(x1271,x1272)+E(f293(x1271),f293(x1272))
% 11.41/11.19 [128]~E(x1281,x1282)+E(f55(x1281,x1283),f55(x1282,x1283))
% 11.41/11.19 [129]~E(x1291,x1292)+E(f55(x1293,x1291),f55(x1293,x1292))
% 11.41/11.19 [130]~E(x1301,x1302)+E(f386(x1301,x1303,x1304),f386(x1302,x1303,x1304))
% 11.41/11.19 [131]~E(x1311,x1312)+E(f386(x1313,x1311,x1314),f386(x1313,x1312,x1314))
% 11.41/11.19 [132]~E(x1321,x1322)+E(f386(x1323,x1324,x1321),f386(x1323,x1324,x1322))
% 11.41/11.19 [133]~E(x1331,x1332)+E(f313(x1331,x1333,x1334),f313(x1332,x1333,x1334))
% 11.41/11.19 [134]~E(x1341,x1342)+E(f313(x1343,x1341,x1344),f313(x1343,x1342,x1344))
% 11.41/11.19 [135]~E(x1351,x1352)+E(f313(x1353,x1354,x1351),f313(x1353,x1354,x1352))
% 11.41/11.19 [136]~E(x1361,x1362)+E(f75(x1361,x1363,x1364),f75(x1362,x1363,x1364))
% 11.41/11.19 [137]~E(x1371,x1372)+E(f75(x1373,x1371,x1374),f75(x1373,x1372,x1374))
% 11.41/11.19 [138]~E(x1381,x1382)+E(f75(x1383,x1384,x1381),f75(x1383,x1384,x1382))
% 11.41/11.19 [139]~E(x1391,x1392)+E(f864(x1391),f864(x1392))
% 11.41/11.19 [140]~E(x1401,x1402)+E(f130(x1401),f130(x1402))
% 11.41/11.19 [141]~E(x1411,x1412)+E(f144(x1411),f144(x1412))
% 11.41/11.19 [142]~E(x1421,x1422)+E(f738(x1421,x1423),f738(x1422,x1423))
% 11.41/11.19 [143]~E(x1431,x1432)+E(f738(x1433,x1431),f738(x1433,x1432))
% 11.41/11.19 [144]~E(x1441,x1442)+E(f12(x1441,x1443),f12(x1442,x1443))
% 11.41/11.19 [145]~E(x1451,x1452)+E(f12(x1453,x1451),f12(x1453,x1452))
% 11.41/11.19 [146]~E(x1461,x1462)+E(f74(x1461,x1463,x1464),f74(x1462,x1463,x1464))
% 11.41/11.19 [147]~E(x1471,x1472)+E(f74(x1473,x1471,x1474),f74(x1473,x1472,x1474))
% 11.41/11.19 [148]~E(x1481,x1482)+E(f74(x1483,x1484,x1481),f74(x1483,x1484,x1482))
% 11.41/11.19 [149]~E(x1491,x1492)+E(f493(x1491,x1493,x1494,x1495,x1496),f493(x1492,x1493,x1494,x1495,x1496))
% 11.41/11.19 [150]~E(x1501,x1502)+E(f493(x1503,x1501,x1504,x1505,x1506),f493(x1503,x1502,x1504,x1505,x1506))
% 11.41/11.19 [151]~E(x1511,x1512)+E(f493(x1513,x1514,x1511,x1515,x1516),f493(x1513,x1514,x1512,x1515,x1516))
% 11.41/11.19 [152]~E(x1521,x1522)+E(f493(x1523,x1524,x1525,x1521,x1526),f493(x1523,x1524,x1525,x1522,x1526))
% 11.41/11.19 [153]~E(x1531,x1532)+E(f493(x1533,x1534,x1535,x1536,x1531),f493(x1533,x1534,x1535,x1536,x1532))
% 11.41/11.19 [154]~E(x1541,x1542)+E(f305(x1541,x1543,x1544),f305(x1542,x1543,x1544))
% 11.41/11.19 [155]~E(x1551,x1552)+E(f305(x1553,x1551,x1554),f305(x1553,x1552,x1554))
% 11.41/11.19 [156]~E(x1561,x1562)+E(f305(x1563,x1564,x1561),f305(x1563,x1564,x1562))
% 11.41/11.19 [157]~E(x1571,x1572)+E(f455(x1571,x1573),f455(x1572,x1573))
% 11.41/11.19 [158]~E(x1581,x1582)+E(f455(x1583,x1581),f455(x1583,x1582))
% 11.41/11.19 [159]~E(x1591,x1592)+E(f287(x1591,x1593,x1594),f287(x1592,x1593,x1594))
% 11.41/11.19 [160]~E(x1601,x1602)+E(f287(x1603,x1601,x1604),f287(x1603,x1602,x1604))
% 11.41/11.19 [161]~E(x1611,x1612)+E(f287(x1613,x1614,x1611),f287(x1613,x1614,x1612))
% 11.41/11.19 [162]~E(x1621,x1622)+E(f99(x1621,x1623),f99(x1622,x1623))
% 11.41/11.19 [163]~E(x1631,x1632)+E(f99(x1633,x1631),f99(x1633,x1632))
% 11.41/11.19 [164]~E(x1641,x1642)+E(f310(x1641,x1643),f310(x1642,x1643))
% 11.41/11.19 [165]~E(x1651,x1652)+E(f310(x1653,x1651),f310(x1653,x1652))
% 11.41/11.19 [166]~E(x1661,x1662)+E(f115(x1661),f115(x1662))
% 11.41/11.19 [167]~E(x1671,x1672)+E(f117(x1671),f117(x1672))
% 11.41/11.19 [168]~E(x1681,x1682)+E(f346(x1681),f346(x1682))
% 11.41/11.19 [169]~E(x1691,x1692)+E(f648(x1691,x1693,x1694,x1695,x1696),f648(x1692,x1693,x1694,x1695,x1696))
% 11.41/11.19 [170]~E(x1701,x1702)+E(f648(x1703,x1701,x1704,x1705,x1706),f648(x1703,x1702,x1704,x1705,x1706))
% 11.41/11.19 [171]~E(x1711,x1712)+E(f648(x1713,x1714,x1711,x1715,x1716),f648(x1713,x1714,x1712,x1715,x1716))
% 11.41/11.19 [172]~E(x1721,x1722)+E(f648(x1723,x1724,x1725,x1721,x1726),f648(x1723,x1724,x1725,x1722,x1726))
% 11.41/11.19 [173]~E(x1731,x1732)+E(f648(x1733,x1734,x1735,x1736,x1731),f648(x1733,x1734,x1735,x1736,x1732))
% 11.41/11.19 [174]~E(x1741,x1742)+E(f806(x1741,x1743,x1744),f806(x1742,x1743,x1744))
% 11.41/11.19 [175]~E(x1751,x1752)+E(f806(x1753,x1751,x1754),f806(x1753,x1752,x1754))
% 11.41/11.19 [176]~E(x1761,x1762)+E(f806(x1763,x1764,x1761),f806(x1763,x1764,x1762))
% 11.41/11.19 [177]~E(x1771,x1772)+E(f248(x1771,x1773),f248(x1772,x1773))
% 11.41/11.19 [178]~E(x1781,x1782)+E(f248(x1783,x1781),f248(x1783,x1782))
% 11.41/11.19 [179]~E(x1791,x1792)+E(f249(x1791),f249(x1792))
% 11.41/11.19 [180]~E(x1801,x1802)+E(f155(x1801),f155(x1802))
% 11.41/11.19 [181]~E(x1811,x1812)+E(f180(x1811,x1813),f180(x1812,x1813))
% 11.41/11.19 [182]~E(x1821,x1822)+E(f180(x1823,x1821),f180(x1823,x1822))
% 11.41/11.19 [183]~E(x1831,x1832)+E(f175(x1831,x1833,x1834),f175(x1832,x1833,x1834))
% 11.41/11.19 [184]~E(x1841,x1842)+E(f175(x1843,x1841,x1844),f175(x1843,x1842,x1844))
% 11.41/11.19 [185]~E(x1851,x1852)+E(f175(x1853,x1854,x1851),f175(x1853,x1854,x1852))
% 11.41/11.19 [186]~E(x1861,x1862)+E(f54(x1861,x1863),f54(x1862,x1863))
% 11.41/11.19 [187]~E(x1871,x1872)+E(f54(x1873,x1871),f54(x1873,x1872))
% 11.41/11.19 [188]~E(x1881,x1882)+E(f668(x1881,x1883,x1884,x1885),f668(x1882,x1883,x1884,x1885))
% 11.41/11.19 [189]~E(x1891,x1892)+E(f668(x1893,x1891,x1894,x1895),f668(x1893,x1892,x1894,x1895))
% 11.41/11.19 [190]~E(x1901,x1902)+E(f668(x1903,x1904,x1901,x1905),f668(x1903,x1904,x1902,x1905))
% 11.41/11.19 [191]~E(x1911,x1912)+E(f668(x1913,x1914,x1915,x1911),f668(x1913,x1914,x1915,x1912))
% 11.41/11.19 [192]~E(x1921,x1922)+E(f201(x1921,x1923,x1924,x1925),f201(x1922,x1923,x1924,x1925))
% 11.41/11.19 [193]~E(x1931,x1932)+E(f201(x1933,x1931,x1934,x1935),f201(x1933,x1932,x1934,x1935))
% 11.41/11.19 [194]~E(x1941,x1942)+E(f201(x1943,x1944,x1941,x1945),f201(x1943,x1944,x1942,x1945))
% 11.41/11.19 [195]~E(x1951,x1952)+E(f201(x1953,x1954,x1955,x1951),f201(x1953,x1954,x1955,x1952))
% 11.41/11.19 [196]~E(x1961,x1962)+E(f190(x1961),f190(x1962))
% 11.41/11.19 [197]~E(x1971,x1972)+E(f767(x1971,x1973,x1974),f767(x1972,x1973,x1974))
% 11.41/11.19 [198]~E(x1981,x1982)+E(f767(x1983,x1981,x1984),f767(x1983,x1982,x1984))
% 11.41/11.19 [199]~E(x1991,x1992)+E(f767(x1993,x1994,x1991),f767(x1993,x1994,x1992))
% 11.41/11.19 [200]~E(x2001,x2002)+E(f82(x2001,x2003,x2004,x2005),f82(x2002,x2003,x2004,x2005))
% 11.41/11.19 [201]~E(x2011,x2012)+E(f82(x2013,x2011,x2014,x2015),f82(x2013,x2012,x2014,x2015))
% 11.41/11.19 [202]~E(x2021,x2022)+E(f82(x2023,x2024,x2021,x2025),f82(x2023,x2024,x2022,x2025))
% 11.41/11.19 [203]~E(x2031,x2032)+E(f82(x2033,x2034,x2035,x2031),f82(x2033,x2034,x2035,x2032))
% 11.41/11.19 [204]~E(x2041,x2042)+E(f51(x2041),f51(x2042))
% 11.41/11.19 [205]~E(x2051,x2052)+E(f7(x2051),f7(x2052))
% 11.41/11.19 [206]~E(x2061,x2062)+E(f162(x2061),f162(x2062))
% 11.41/11.19 [207]~E(x2071,x2072)+E(f291(x2071,x2073,x2074),f291(x2072,x2073,x2074))
% 11.41/11.19 [208]~E(x2081,x2082)+E(f291(x2083,x2081,x2084),f291(x2083,x2082,x2084))
% 11.41/11.19 [209]~E(x2091,x2092)+E(f291(x2093,x2094,x2091),f291(x2093,x2094,x2092))
% 11.41/11.19 [210]~E(x2101,x2102)+E(f132(x2101),f132(x2102))
% 11.41/11.19 [211]~E(x2111,x2112)+E(f38(x2111,x2113),f38(x2112,x2113))
% 11.41/11.19 [212]~E(x2121,x2122)+E(f38(x2123,x2121),f38(x2123,x2122))
% 11.41/11.19 [213]~E(x2131,x2132)+E(f286(x2131),f286(x2132))
% 11.41/11.19 [214]~E(x2141,x2142)+E(f456(x2141,x2143),f456(x2142,x2143))
% 11.41/11.19 [215]~E(x2151,x2152)+E(f456(x2153,x2151),f456(x2153,x2152))
% 11.41/11.19 [216]~E(x2161,x2162)+E(f142(x2161,x2163,x2164),f142(x2162,x2163,x2164))
% 11.41/11.19 [217]~E(x2171,x2172)+E(f142(x2173,x2171,x2174),f142(x2173,x2172,x2174))
% 11.41/11.19 [218]~E(x2181,x2182)+E(f142(x2183,x2184,x2181),f142(x2183,x2184,x2182))
% 11.41/11.19 [219]~E(x2191,x2192)+E(f772(x2191,x2193),f772(x2192,x2193))
% 11.41/11.19 [220]~E(x2201,x2202)+E(f772(x2203,x2201),f772(x2203,x2202))
% 11.41/11.19 [221]~E(x2211,x2212)+E(f173(x2211,x2213),f173(x2212,x2213))
% 11.41/11.19 [222]~E(x2221,x2222)+E(f173(x2223,x2221),f173(x2223,x2222))
% 11.41/11.19 [223]~E(x2231,x2232)+E(f131(x2231,x2233),f131(x2232,x2233))
% 11.41/11.19 [224]~E(x2241,x2242)+E(f131(x2243,x2241),f131(x2243,x2242))
% 11.41/11.19 [225]~E(x2251,x2252)+E(f146(x2251,x2253),f146(x2252,x2253))
% 11.41/11.19 [226]~E(x2261,x2262)+E(f146(x2263,x2261),f146(x2263,x2262))
% 11.41/11.19 [227]~E(x2271,x2272)+E(f721(x2271,x2273,x2274,x2275,x2276,x2277),f721(x2272,x2273,x2274,x2275,x2276,x2277))
% 11.41/11.19 [228]~E(x2281,x2282)+E(f721(x2283,x2281,x2284,x2285,x2286,x2287),f721(x2283,x2282,x2284,x2285,x2286,x2287))
% 11.41/11.19 [229]~E(x2291,x2292)+E(f721(x2293,x2294,x2291,x2295,x2296,x2297),f721(x2293,x2294,x2292,x2295,x2296,x2297))
% 11.41/11.19 [230]~E(x2301,x2302)+E(f721(x2303,x2304,x2305,x2301,x2306,x2307),f721(x2303,x2304,x2305,x2302,x2306,x2307))
% 11.41/11.19 [231]~E(x2311,x2312)+E(f721(x2313,x2314,x2315,x2316,x2311,x2317),f721(x2313,x2314,x2315,x2316,x2312,x2317))
% 11.41/11.19 [232]~E(x2321,x2322)+E(f721(x2323,x2324,x2325,x2326,x2327,x2321),f721(x2323,x2324,x2325,x2326,x2327,x2322))
% 11.41/11.19 [233]~E(x2331,x2332)+E(f334(x2331,x2333),f334(x2332,x2333))
% 11.41/11.19 [234]~E(x2341,x2342)+E(f334(x2343,x2341),f334(x2343,x2342))
% 11.41/11.19 [235]~E(x2351,x2352)+E(f718(x2351,x2353,x2354,x2355,x2356,x2357),f718(x2352,x2353,x2354,x2355,x2356,x2357))
% 11.41/11.19 [236]~E(x2361,x2362)+E(f718(x2363,x2361,x2364,x2365,x2366,x2367),f718(x2363,x2362,x2364,x2365,x2366,x2367))
% 11.41/11.19 [237]~E(x2371,x2372)+E(f718(x2373,x2374,x2371,x2375,x2376,x2377),f718(x2373,x2374,x2372,x2375,x2376,x2377))
% 11.41/11.19 [238]~E(x2381,x2382)+E(f718(x2383,x2384,x2385,x2381,x2386,x2387),f718(x2383,x2384,x2385,x2382,x2386,x2387))
% 11.41/11.19 [239]~E(x2391,x2392)+E(f718(x2393,x2394,x2395,x2396,x2391,x2397),f718(x2393,x2394,x2395,x2396,x2392,x2397))
% 11.41/11.19 [240]~E(x2401,x2402)+E(f718(x2403,x2404,x2405,x2406,x2407,x2401),f718(x2403,x2404,x2405,x2406,x2407,x2402))
% 11.41/11.19 [241]~E(x2411,x2412)+E(f337(x2411,x2413),f337(x2412,x2413))
% 11.41/11.19 [242]~E(x2421,x2422)+E(f337(x2423,x2421),f337(x2423,x2422))
% 11.41/11.19 [243]~E(x2431,x2432)+E(f734(x2431,x2433),f734(x2432,x2433))
% 11.41/11.19 [244]~E(x2441,x2442)+E(f734(x2443,x2441),f734(x2443,x2442))
% 11.41/11.19 [245]~E(x2451,x2452)+E(f501(x2451,x2453,x2454,x2455,x2456),f501(x2452,x2453,x2454,x2455,x2456))
% 11.41/11.19 [246]~E(x2461,x2462)+E(f501(x2463,x2461,x2464,x2465,x2466),f501(x2463,x2462,x2464,x2465,x2466))
% 11.41/11.19 [247]~E(x2471,x2472)+E(f501(x2473,x2474,x2471,x2475,x2476),f501(x2473,x2474,x2472,x2475,x2476))
% 11.41/11.19 [248]~E(x2481,x2482)+E(f501(x2483,x2484,x2485,x2481,x2486),f501(x2483,x2484,x2485,x2482,x2486))
% 11.41/11.19 [249]~E(x2491,x2492)+E(f501(x2493,x2494,x2495,x2496,x2491),f501(x2493,x2494,x2495,x2496,x2492))
% 11.41/11.19 [250]~E(x2501,x2502)+E(f529(x2501,x2503,x2504,x2505),f529(x2502,x2503,x2504,x2505))
% 11.41/11.19 [251]~E(x2511,x2512)+E(f529(x2513,x2511,x2514,x2515),f529(x2513,x2512,x2514,x2515))
% 11.41/11.19 [252]~E(x2521,x2522)+E(f529(x2523,x2524,x2521,x2525),f529(x2523,x2524,x2522,x2525))
% 11.41/11.19 [253]~E(x2531,x2532)+E(f529(x2533,x2534,x2535,x2531),f529(x2533,x2534,x2535,x2532))
% 11.41/11.19 [254]~E(x2541,x2542)+E(f252(x2541),f252(x2542))
% 11.41/11.19 [255]~E(x2551,x2552)+E(f136(x2551,x2553,x2554,x2555),f136(x2552,x2553,x2554,x2555))
% 11.41/11.19 [256]~E(x2561,x2562)+E(f136(x2563,x2561,x2564,x2565),f136(x2563,x2562,x2564,x2565))
% 11.41/11.19 [257]~E(x2571,x2572)+E(f136(x2573,x2574,x2571,x2575),f136(x2573,x2574,x2572,x2575))
% 11.41/11.19 [258]~E(x2581,x2582)+E(f136(x2583,x2584,x2585,x2581),f136(x2583,x2584,x2585,x2582))
% 11.41/11.19 [259]~E(x2591,x2592)+E(f335(x2591,x2593),f335(x2592,x2593))
% 11.41/11.19 [260]~E(x2601,x2602)+E(f335(x2603,x2601),f335(x2603,x2602))
% 11.41/11.19 [261]~E(x2611,x2612)+E(f11(x2611,x2613),f11(x2612,x2613))
% 11.41/11.19 [262]~E(x2621,x2622)+E(f11(x2623,x2621),f11(x2623,x2622))
% 11.41/11.19 [263]~E(x2631,x2632)+E(f675(x2631,x2633,x2634,x2635),f675(x2632,x2633,x2634,x2635))
% 11.41/11.19 [264]~E(x2641,x2642)+E(f675(x2643,x2641,x2644,x2645),f675(x2643,x2642,x2644,x2645))
% 11.41/11.19 [265]~E(x2651,x2652)+E(f675(x2653,x2654,x2651,x2655),f675(x2653,x2654,x2652,x2655))
% 11.41/11.19 [266]~E(x2661,x2662)+E(f675(x2663,x2664,x2665,x2661),f675(x2663,x2664,x2665,x2662))
% 11.41/11.19 [267]~E(x2671,x2672)+E(f30(x2671,x2673),f30(x2672,x2673))
% 11.41/11.19 [268]~E(x2681,x2682)+E(f30(x2683,x2681),f30(x2683,x2682))
% 11.41/11.19 [269]~E(x2691,x2692)+E(f37(x2691,x2693),f37(x2692,x2693))
% 11.41/11.19 [270]~E(x2701,x2702)+E(f37(x2703,x2701),f37(x2703,x2702))
% 11.41/11.19 [271]~E(x2711,x2712)+E(f100(x2711),f100(x2712))
% 11.41/11.19 [272]~E(x2721,x2722)+E(f361(x2721,x2723,x2724,x2725),f361(x2722,x2723,x2724,x2725))
% 11.41/11.19 [273]~E(x2731,x2732)+E(f361(x2733,x2731,x2734,x2735),f361(x2733,x2732,x2734,x2735))
% 11.41/11.19 [274]~E(x2741,x2742)+E(f361(x2743,x2744,x2741,x2745),f361(x2743,x2744,x2742,x2745))
% 11.41/11.19 [275]~E(x2751,x2752)+E(f361(x2753,x2754,x2755,x2751),f361(x2753,x2754,x2755,x2752))
% 11.41/11.19 [276]~E(x2761,x2762)+E(f179(x2761,x2763,x2764,x2765),f179(x2762,x2763,x2764,x2765))
% 11.41/11.19 [277]~E(x2771,x2772)+E(f179(x2773,x2771,x2774,x2775),f179(x2773,x2772,x2774,x2775))
% 11.41/11.19 [278]~E(x2781,x2782)+E(f179(x2783,x2784,x2781,x2785),f179(x2783,x2784,x2782,x2785))
% 11.41/11.19 [279]~E(x2791,x2792)+E(f179(x2793,x2794,x2795,x2791),f179(x2793,x2794,x2795,x2792))
% 11.41/11.19 [280]~E(x2801,x2802)+E(f858(x2801),f858(x2802))
% 11.41/11.19 [281]~E(x2811,x2812)+E(f315(x2811,x2813,x2814),f315(x2812,x2813,x2814))
% 11.41/11.19 [282]~E(x2821,x2822)+E(f315(x2823,x2821,x2824),f315(x2823,x2822,x2824))
% 11.41/11.19 [283]~E(x2831,x2832)+E(f315(x2833,x2834,x2831),f315(x2833,x2834,x2832))
% 11.41/11.19 [284]~E(x2841,x2842)+E(f195(x2841,x2843),f195(x2842,x2843))
% 11.41/11.19 [285]~E(x2851,x2852)+E(f195(x2853,x2851),f195(x2853,x2852))
% 11.41/11.19 [286]~E(x2861,x2862)+E(f268(x2861),f268(x2862))
% 11.41/11.19 [287]~E(x2871,x2872)+E(f261(x2871,x2873,x2874),f261(x2872,x2873,x2874))
% 11.41/11.19 [288]~E(x2881,x2882)+E(f261(x2883,x2881,x2884),f261(x2883,x2882,x2884))
% 11.41/11.19 [289]~E(x2891,x2892)+E(f261(x2893,x2894,x2891),f261(x2893,x2894,x2892))
% 11.41/11.19 [290]~E(x2901,x2902)+E(f585(x2901,x2903),f585(x2902,x2903))
% 11.41/11.19 [291]~E(x2911,x2912)+E(f585(x2913,x2911),f585(x2913,x2912))
% 11.41/11.19 [292]~E(x2921,x2922)+E(f13(x2921,x2923,x2924),f13(x2922,x2923,x2924))
% 11.41/11.19 [293]~E(x2931,x2932)+E(f13(x2933,x2931,x2934),f13(x2933,x2932,x2934))
% 11.41/11.19 [294]~E(x2941,x2942)+E(f13(x2943,x2944,x2941),f13(x2943,x2944,x2942))
% 11.41/11.19 [295]~E(x2951,x2952)+E(f840(x2951,x2953,x2954),f840(x2952,x2953,x2954))
% 11.41/11.19 [296]~E(x2961,x2962)+E(f840(x2963,x2961,x2964),f840(x2963,x2962,x2964))
% 11.41/11.19 [297]~E(x2971,x2972)+E(f840(x2973,x2974,x2971),f840(x2973,x2974,x2972))
% 11.41/11.19 [298]~E(x2981,x2982)+E(f121(x2981,x2983),f121(x2982,x2983))
% 11.41/11.19 [299]~E(x2991,x2992)+E(f121(x2993,x2991),f121(x2993,x2992))
% 11.41/11.19 [300]~E(x3001,x3002)+E(f73(x3001,x3003),f73(x3002,x3003))
% 11.41/11.19 [301]~E(x3011,x3012)+E(f73(x3013,x3011),f73(x3013,x3012))
% 11.41/11.19 [302]~E(x3021,x3022)+E(f191(x3021),f191(x3022))
% 11.41/11.19 [303]~E(x3031,x3032)+E(f688(x3031,x3033,x3034),f688(x3032,x3033,x3034))
% 11.41/11.19 [304]~E(x3041,x3042)+E(f688(x3043,x3041,x3044),f688(x3043,x3042,x3044))
% 11.41/11.19 [305]~E(x3051,x3052)+E(f688(x3053,x3054,x3051),f688(x3053,x3054,x3052))
% 11.41/11.19 [306]~E(x3061,x3062)+E(f122(x3061),f122(x3062))
% 11.41/11.19 [307]~E(x3071,x3072)+E(f717(x3071,x3073,x3074,x3075,x3076,x3077),f717(x3072,x3073,x3074,x3075,x3076,x3077))
% 11.41/11.19 [308]~E(x3081,x3082)+E(f717(x3083,x3081,x3084,x3085,x3086,x3087),f717(x3083,x3082,x3084,x3085,x3086,x3087))
% 11.41/11.19 [309]~E(x3091,x3092)+E(f717(x3093,x3094,x3091,x3095,x3096,x3097),f717(x3093,x3094,x3092,x3095,x3096,x3097))
% 11.41/11.19 [310]~E(x3101,x3102)+E(f717(x3103,x3104,x3105,x3101,x3106,x3107),f717(x3103,x3104,x3105,x3102,x3106,x3107))
% 11.41/11.19 [311]~E(x3111,x3112)+E(f717(x3113,x3114,x3115,x3116,x3111,x3117),f717(x3113,x3114,x3115,x3116,x3112,x3117))
% 11.41/11.19 [312]~E(x3121,x3122)+E(f717(x3123,x3124,x3125,x3126,x3127,x3121),f717(x3123,x3124,x3125,x3126,x3127,x3122))
% 11.41/11.19 [313]~E(x3131,x3132)+E(f375(x3131,x3133,x3134,x3135),f375(x3132,x3133,x3134,x3135))
% 11.41/11.19 [314]~E(x3141,x3142)+E(f375(x3143,x3141,x3144,x3145),f375(x3143,x3142,x3144,x3145))
% 11.41/11.19 [315]~E(x3151,x3152)+E(f375(x3153,x3154,x3151,x3155),f375(x3153,x3154,x3152,x3155))
% 11.41/11.19 [316]~E(x3161,x3162)+E(f375(x3163,x3164,x3165,x3161),f375(x3163,x3164,x3165,x3162))
% 11.41/11.19 [317]~E(x3171,x3172)+E(f33(x3171,x3173,x3174),f33(x3172,x3173,x3174))
% 11.41/11.19 [318]~E(x3181,x3182)+E(f33(x3183,x3181,x3184),f33(x3183,x3182,x3184))
% 11.41/11.19 [319]~E(x3191,x3192)+E(f33(x3193,x3194,x3191),f33(x3193,x3194,x3192))
% 11.41/11.19 [320]~E(x3201,x3202)+E(f723(x3201,x3203,x3204,x3205),f723(x3202,x3203,x3204,x3205))
% 11.41/11.19 [321]~E(x3211,x3212)+E(f723(x3213,x3211,x3214,x3215),f723(x3213,x3212,x3214,x3215))
% 11.41/11.19 [322]~E(x3221,x3222)+E(f723(x3223,x3224,x3221,x3225),f723(x3223,x3224,x3222,x3225))
% 11.41/11.19 [323]~E(x3231,x3232)+E(f723(x3233,x3234,x3235,x3231),f723(x3233,x3234,x3235,x3232))
% 11.41/11.19 [324]~E(x3241,x3242)+E(f81(x3241,x3243),f81(x3242,x3243))
% 11.41/11.19 [325]~E(x3251,x3252)+E(f81(x3253,x3251),f81(x3253,x3252))
% 11.41/11.19 [326]~E(x3261,x3262)+E(f135(x3261),f135(x3262))
% 11.41/11.19 [327]~E(x3271,x3272)+E(f76(x3271,x3273,x3274,x3275,x3276),f76(x3272,x3273,x3274,x3275,x3276))
% 11.41/11.19 [328]~E(x3281,x3282)+E(f76(x3283,x3281,x3284,x3285,x3286),f76(x3283,x3282,x3284,x3285,x3286))
% 11.41/11.19 [329]~E(x3291,x3292)+E(f76(x3293,x3294,x3291,x3295,x3296),f76(x3293,x3294,x3292,x3295,x3296))
% 11.41/11.19 [330]~E(x3301,x3302)+E(f76(x3303,x3304,x3305,x3301,x3306),f76(x3303,x3304,x3305,x3302,x3306))
% 11.41/11.19 [331]~E(x3311,x3312)+E(f76(x3313,x3314,x3315,x3316,x3311),f76(x3313,x3314,x3315,x3316,x3312))
% 11.41/11.19 [332]~E(x3321,x3322)+E(f258(x3321,x3323),f258(x3322,x3323))
% 11.41/11.19 [333]~E(x3331,x3332)+E(f258(x3333,x3331),f258(x3333,x3332))
% 11.41/11.19 [334]~E(x3341,x3342)+E(f157(x3341),f157(x3342))
% 11.41/11.19 [335]~E(x3351,x3352)+E(f163(x3351),f163(x3352))
% 11.41/11.19 [336]~E(x3361,x3362)+E(f611(x3361,x3363),f611(x3362,x3363))
% 11.41/11.19 [337]~E(x3371,x3372)+E(f611(x3373,x3371),f611(x3373,x3372))
% 11.41/11.19 [338]~E(x3381,x3382)+E(f237(x3381),f237(x3382))
% 11.41/11.19 [339]~E(x3391,x3392)+E(f262(x3391,x3393,x3394,x3395,x3396,x3397),f262(x3392,x3393,x3394,x3395,x3396,x3397))
% 11.41/11.19 [340]~E(x3401,x3402)+E(f262(x3403,x3401,x3404,x3405,x3406,x3407),f262(x3403,x3402,x3404,x3405,x3406,x3407))
% 11.41/11.19 [341]~E(x3411,x3412)+E(f262(x3413,x3414,x3411,x3415,x3416,x3417),f262(x3413,x3414,x3412,x3415,x3416,x3417))
% 11.41/11.19 [342]~E(x3421,x3422)+E(f262(x3423,x3424,x3425,x3421,x3426,x3427),f262(x3423,x3424,x3425,x3422,x3426,x3427))
% 11.41/11.19 [343]~E(x3431,x3432)+E(f262(x3433,x3434,x3435,x3436,x3431,x3437),f262(x3433,x3434,x3435,x3436,x3432,x3437))
% 11.41/11.19 [344]~E(x3441,x3442)+E(f262(x3443,x3444,x3445,x3446,x3447,x3441),f262(x3443,x3444,x3445,x3446,x3447,x3442))
% 11.41/11.19 [345]~E(x3451,x3452)+E(f161(x3451),f161(x3452))
% 11.41/11.19 [346]~E(x3461,x3462)+E(f567(x3461,x3463,x3464,x3465,x3466),f567(x3462,x3463,x3464,x3465,x3466))
% 11.41/11.19 [347]~E(x3471,x3472)+E(f567(x3473,x3471,x3474,x3475,x3476),f567(x3473,x3472,x3474,x3475,x3476))
% 11.41/11.19 [348]~E(x3481,x3482)+E(f567(x3483,x3484,x3481,x3485,x3486),f567(x3483,x3484,x3482,x3485,x3486))
% 11.41/11.19 [349]~E(x3491,x3492)+E(f567(x3493,x3494,x3495,x3491,x3496),f567(x3493,x3494,x3495,x3492,x3496))
% 11.41/11.19 [350]~E(x3501,x3502)+E(f567(x3503,x3504,x3505,x3506,x3501),f567(x3503,x3504,x3505,x3506,x3502))
% 11.41/11.19 [351]~E(x3511,x3512)+E(f154(x3511,x3513,x3514),f154(x3512,x3513,x3514))
% 11.41/11.19 [352]~E(x3521,x3522)+E(f154(x3523,x3521,x3524),f154(x3523,x3522,x3524))
% 11.41/11.19 [353]~E(x3531,x3532)+E(f154(x3533,x3534,x3531),f154(x3533,x3534,x3532))
% 11.41/11.19 [354]~E(x3541,x3542)+E(f271(x3541,x3543),f271(x3542,x3543))
% 11.41/11.19 [355]~E(x3551,x3552)+E(f271(x3553,x3551),f271(x3553,x3552))
% 11.41/11.19 [356]~E(x3561,x3562)+E(f440(x3561,x3563,x3564,x3565,x3566,x3567,x3568),f440(x3562,x3563,x3564,x3565,x3566,x3567,x3568))
% 11.41/11.19 [357]~E(x3571,x3572)+E(f440(x3573,x3571,x3574,x3575,x3576,x3577,x3578),f440(x3573,x3572,x3574,x3575,x3576,x3577,x3578))
% 11.41/11.19 [358]~E(x3581,x3582)+E(f440(x3583,x3584,x3581,x3585,x3586,x3587,x3588),f440(x3583,x3584,x3582,x3585,x3586,x3587,x3588))
% 11.41/11.19 [359]~E(x3591,x3592)+E(f440(x3593,x3594,x3595,x3591,x3596,x3597,x3598),f440(x3593,x3594,x3595,x3592,x3596,x3597,x3598))
% 11.41/11.19 [360]~E(x3601,x3602)+E(f440(x3603,x3604,x3605,x3606,x3601,x3607,x3608),f440(x3603,x3604,x3605,x3606,x3602,x3607,x3608))
% 11.41/11.19 [361]~E(x3611,x3612)+E(f440(x3613,x3614,x3615,x3616,x3617,x3611,x3618),f440(x3613,x3614,x3615,x3616,x3617,x3612,x3618))
% 11.41/11.19 [362]~E(x3621,x3622)+E(f440(x3623,x3624,x3625,x3626,x3627,x3628,x3621),f440(x3623,x3624,x3625,x3626,x3627,x3628,x3622))
% 11.41/11.19 [363]~E(x3631,x3632)+E(f624(x3631,x3633,x3634,x3635,x3636,x3637),f624(x3632,x3633,x3634,x3635,x3636,x3637))
% 11.41/11.19 [364]~E(x3641,x3642)+E(f624(x3643,x3641,x3644,x3645,x3646,x3647),f624(x3643,x3642,x3644,x3645,x3646,x3647))
% 11.41/11.19 [365]~E(x3651,x3652)+E(f624(x3653,x3654,x3651,x3655,x3656,x3657),f624(x3653,x3654,x3652,x3655,x3656,x3657))
% 11.41/11.19 [366]~E(x3661,x3662)+E(f624(x3663,x3664,x3665,x3661,x3666,x3667),f624(x3663,x3664,x3665,x3662,x3666,x3667))
% 11.41/11.19 [367]~E(x3671,x3672)+E(f624(x3673,x3674,x3675,x3676,x3671,x3677),f624(x3673,x3674,x3675,x3676,x3672,x3677))
% 11.41/11.19 [368]~E(x3681,x3682)+E(f624(x3683,x3684,x3685,x3686,x3687,x3681),f624(x3683,x3684,x3685,x3686,x3687,x3682))
% 11.41/11.19 [369]~E(x3691,x3692)+E(f35(x3691,x3693,x3694),f35(x3692,x3693,x3694))
% 11.41/11.19 [370]~E(x3701,x3702)+E(f35(x3703,x3701,x3704),f35(x3703,x3702,x3704))
% 11.41/11.19 [371]~E(x3711,x3712)+E(f35(x3713,x3714,x3711),f35(x3713,x3714,x3712))
% 11.41/11.19 [372]~E(x3721,x3722)+E(f387(x3721),f387(x3722))
% 11.41/11.19 [373]~E(x3731,x3732)+E(f654(x3731,x3733,x3734,x3735,x3736),f654(x3732,x3733,x3734,x3735,x3736))
% 11.41/11.19 [374]~E(x3741,x3742)+E(f654(x3743,x3741,x3744,x3745,x3746),f654(x3743,x3742,x3744,x3745,x3746))
% 11.41/11.19 [375]~E(x3751,x3752)+E(f654(x3753,x3754,x3751,x3755,x3756),f654(x3753,x3754,x3752,x3755,x3756))
% 11.41/11.19 [376]~E(x3761,x3762)+E(f654(x3763,x3764,x3765,x3761,x3766),f654(x3763,x3764,x3765,x3762,x3766))
% 11.41/11.19 [377]~E(x3771,x3772)+E(f654(x3773,x3774,x3775,x3776,x3771),f654(x3773,x3774,x3775,x3776,x3772))
% 11.41/11.19 [378]~E(x3781,x3782)+E(f821(x3781,x3783,x3784,x3785,x3786),f821(x3782,x3783,x3784,x3785,x3786))
% 11.41/11.19 [379]~E(x3791,x3792)+E(f821(x3793,x3791,x3794,x3795,x3796),f821(x3793,x3792,x3794,x3795,x3796))
% 11.41/11.19 [380]~E(x3801,x3802)+E(f821(x3803,x3804,x3801,x3805,x3806),f821(x3803,x3804,x3802,x3805,x3806))
% 11.41/11.19 [381]~E(x3811,x3812)+E(f821(x3813,x3814,x3815,x3811,x3816),f821(x3813,x3814,x3815,x3812,x3816))
% 11.41/11.19 [382]~E(x3821,x3822)+E(f821(x3823,x3824,x3825,x3826,x3821),f821(x3823,x3824,x3825,x3826,x3822))
% 11.41/11.19 [383]~E(x3831,x3832)+E(f850(x3831,x3833,x3834,x3835,x3836,x3837),f850(x3832,x3833,x3834,x3835,x3836,x3837))
% 11.41/11.19 [384]~E(x3841,x3842)+E(f850(x3843,x3841,x3844,x3845,x3846,x3847),f850(x3843,x3842,x3844,x3845,x3846,x3847))
% 11.41/11.19 [385]~E(x3851,x3852)+E(f850(x3853,x3854,x3851,x3855,x3856,x3857),f850(x3853,x3854,x3852,x3855,x3856,x3857))
% 11.41/11.19 [386]~E(x3861,x3862)+E(f850(x3863,x3864,x3865,x3861,x3866,x3867),f850(x3863,x3864,x3865,x3862,x3866,x3867))
% 11.41/11.19 [387]~E(x3871,x3872)+E(f850(x3873,x3874,x3875,x3876,x3871,x3877),f850(x3873,x3874,x3875,x3876,x3872,x3877))
% 11.41/11.19 [388]~E(x3881,x3882)+E(f850(x3883,x3884,x3885,x3886,x3887,x3881),f850(x3883,x3884,x3885,x3886,x3887,x3882))
% 11.41/11.19 [389]~E(x3891,x3892)+E(f593(x3891,x3893,x3894,x3895),f593(x3892,x3893,x3894,x3895))
% 11.41/11.19 [390]~E(x3901,x3902)+E(f593(x3903,x3901,x3904,x3905),f593(x3903,x3902,x3904,x3905))
% 11.41/11.19 [391]~E(x3911,x3912)+E(f593(x3913,x3914,x3911,x3915),f593(x3913,x3914,x3912,x3915))
% 11.41/11.19 [392]~E(x3921,x3922)+E(f593(x3923,x3924,x3925,x3921),f593(x3923,x3924,x3925,x3922))
% 11.41/11.19 [393]~E(x3931,x3932)+E(f469(x3931,x3933),f469(x3932,x3933))
% 11.41/11.19 [394]~E(x3941,x3942)+E(f469(x3943,x3941),f469(x3943,x3942))
% 11.41/11.19 [395]~E(x3951,x3952)+E(f801(x3951,x3953),f801(x3952,x3953))
% 11.41/11.19 [396]~E(x3961,x3962)+E(f801(x3963,x3961),f801(x3963,x3962))
% 11.41/11.19 [397]~E(x3971,x3972)+E(f861(x3971),f861(x3972))
% 11.41/11.19 [398]~E(x3981,x3982)+E(f292(x3981,x3983,x3984,x3985),f292(x3982,x3983,x3984,x3985))
% 11.41/11.19 [399]~E(x3991,x3992)+E(f292(x3993,x3991,x3994,x3995),f292(x3993,x3992,x3994,x3995))
% 11.41/11.19 [400]~E(x4001,x4002)+E(f292(x4003,x4004,x4001,x4005),f292(x4003,x4004,x4002,x4005))
% 11.41/11.19 [401]~E(x4011,x4012)+E(f292(x4013,x4014,x4015,x4011),f292(x4013,x4014,x4015,x4012))
% 11.41/11.19 [402]~E(x4021,x4022)+E(f18(x4021,x4023),f18(x4022,x4023))
% 11.41/11.19 [403]~E(x4031,x4032)+E(f18(x4033,x4031),f18(x4033,x4032))
% 11.41/11.19 [404]~E(x4041,x4042)+E(f303(x4041),f303(x4042))
% 11.41/11.19 [405]~E(x4051,x4052)+E(f194(x4051),f194(x4052))
% 11.41/11.19 [406]~E(x4061,x4062)+E(f91(x4061,x4063),f91(x4062,x4063))
% 11.41/11.19 [407]~E(x4071,x4072)+E(f91(x4073,x4071),f91(x4073,x4072))
% 11.41/11.19 [408]~E(x4081,x4082)+E(f165(x4081),f165(x4082))
% 11.41/11.19 [409]~E(x4091,x4092)+E(f565(x4091,x4093,x4094),f565(x4092,x4093,x4094))
% 11.41/11.19 [410]~E(x4101,x4102)+E(f565(x4103,x4101,x4104),f565(x4103,x4102,x4104))
% 11.41/11.19 [411]~E(x4111,x4112)+E(f565(x4113,x4114,x4111),f565(x4113,x4114,x4112))
% 11.41/11.19 [412]~E(x4121,x4122)+E(f338(x4121,x4123),f338(x4122,x4123))
% 11.41/11.19 [413]~E(x4131,x4132)+E(f338(x4133,x4131),f338(x4133,x4132))
% 11.41/11.19 [414]~E(x4141,x4142)+E(f794(x4141,x4143,x4144),f794(x4142,x4143,x4144))
% 11.41/11.19 [415]~E(x4151,x4152)+E(f794(x4153,x4151,x4154),f794(x4153,x4152,x4154))
% 11.41/11.19 [416]~E(x4161,x4162)+E(f794(x4163,x4164,x4161),f794(x4163,x4164,x4162))
% 11.41/11.19 [417]~E(x4171,x4172)+E(f848(x4171,x4173),f848(x4172,x4173))
% 11.41/11.20 [418]~E(x4181,x4182)+E(f848(x4183,x4181),f848(x4183,x4182))
% 11.41/11.20 [419]~E(x4191,x4192)+E(f156(x4191,x4193,x4194,x4195),f156(x4192,x4193,x4194,x4195))
% 11.41/11.20 [420]~E(x4201,x4202)+E(f156(x4203,x4201,x4204,x4205),f156(x4203,x4202,x4204,x4205))
% 11.41/11.20 [421]~E(x4211,x4212)+E(f156(x4213,x4214,x4211,x4215),f156(x4213,x4214,x4212,x4215))
% 11.41/11.20 [422]~E(x4221,x4222)+E(f156(x4223,x4224,x4225,x4221),f156(x4223,x4224,x4225,x4222))
% 11.41/11.20 [423]~E(x4231,x4232)+E(f358(x4231,x4233),f358(x4232,x4233))
% 11.41/11.20 [424]~E(x4241,x4242)+E(f358(x4243,x4241),f358(x4243,x4242))
% 11.41/11.20 [425]~E(x4251,x4252)+E(f444(x4251,x4253,x4254,x4255),f444(x4252,x4253,x4254,x4255))
% 11.41/11.20 [426]~E(x4261,x4262)+E(f444(x4263,x4261,x4264,x4265),f444(x4263,x4262,x4264,x4265))
% 11.41/11.20 [427]~E(x4271,x4272)+E(f444(x4273,x4274,x4271,x4275),f444(x4273,x4274,x4272,x4275))
% 11.41/11.20 [428]~E(x4281,x4282)+E(f444(x4283,x4284,x4285,x4281),f444(x4283,x4284,x4285,x4282))
% 11.41/11.20 [429]~E(x4291,x4292)+E(f53(x4291,x4293),f53(x4292,x4293))
% 11.41/11.20 [430]~E(x4301,x4302)+E(f53(x4303,x4301),f53(x4303,x4302))
% 11.41/11.20 [431]~E(x4311,x4312)+E(f495(x4311,x4313,x4314),f495(x4312,x4313,x4314))
% 11.41/11.20 [432]~E(x4321,x4322)+E(f495(x4323,x4321,x4324),f495(x4323,x4322,x4324))
% 11.41/11.20 [433]~E(x4331,x4332)+E(f495(x4333,x4334,x4331),f495(x4333,x4334,x4332))
% 11.41/11.20 [434]~E(x4341,x4342)+E(f330(x4341,x4343,x4344,x4345),f330(x4342,x4343,x4344,x4345))
% 11.41/11.20 [435]~E(x4351,x4352)+E(f330(x4353,x4351,x4354,x4355),f330(x4353,x4352,x4354,x4355))
% 11.41/11.20 [436]~E(x4361,x4362)+E(f330(x4363,x4364,x4361,x4365),f330(x4363,x4364,x4362,x4365))
% 11.41/11.20 [437]~E(x4371,x4372)+E(f330(x4373,x4374,x4375,x4371),f330(x4373,x4374,x4375,x4372))
% 11.41/11.20 [438]~E(x4381,x4382)+E(f824(x4381,x4383,x4384),f824(x4382,x4383,x4384))
% 11.41/11.20 [439]~E(x4391,x4392)+E(f824(x4393,x4391,x4394),f824(x4393,x4392,x4394))
% 11.41/11.20 [440]~E(x4401,x4402)+E(f824(x4403,x4404,x4401),f824(x4403,x4404,x4402))
% 11.41/11.20 [441]~E(x4411,x4412)+E(f622(x4411,x4413,x4414),f622(x4412,x4413,x4414))
% 11.41/11.20 [442]~E(x4421,x4422)+E(f622(x4423,x4421,x4424),f622(x4423,x4422,x4424))
% 11.41/11.20 [443]~E(x4431,x4432)+E(f622(x4433,x4434,x4431),f622(x4433,x4434,x4432))
% 11.41/11.20 [444]~E(x4441,x4442)+E(f138(x4441,x4443),f138(x4442,x4443))
% 11.41/11.20 [445]~E(x4451,x4452)+E(f138(x4453,x4451),f138(x4453,x4452))
% 11.41/11.20 [446]~E(x4461,x4462)+E(f621(x4461,x4463,x4464),f621(x4462,x4463,x4464))
% 11.41/11.20 [447]~E(x4471,x4472)+E(f621(x4473,x4471,x4474),f621(x4473,x4472,x4474))
% 11.41/11.20 [448]~E(x4481,x4482)+E(f621(x4483,x4484,x4481),f621(x4483,x4484,x4482))
% 11.41/11.20 [449]~E(x4491,x4492)+E(f217(x4491),f217(x4492))
% 11.41/11.20 [450]~E(x4501,x4502)+E(f24(x4501,x4503),f24(x4502,x4503))
% 11.41/11.20 [451]~E(x4511,x4512)+E(f24(x4513,x4511),f24(x4513,x4512))
% 11.41/11.20 [452]~E(x4521,x4522)+E(f402(x4521,x4523,x4524,x4525,x4526),f402(x4522,x4523,x4524,x4525,x4526))
% 11.41/11.20 [453]~E(x4531,x4532)+E(f402(x4533,x4531,x4534,x4535,x4536),f402(x4533,x4532,x4534,x4535,x4536))
% 11.41/11.20 [454]~E(x4541,x4542)+E(f402(x4543,x4544,x4541,x4545,x4546),f402(x4543,x4544,x4542,x4545,x4546))
% 11.41/11.20 [455]~E(x4551,x4552)+E(f402(x4553,x4554,x4555,x4551,x4556),f402(x4553,x4554,x4555,x4552,x4556))
% 11.41/11.20 [456]~E(x4561,x4562)+E(f402(x4563,x4564,x4565,x4566,x4561),f402(x4563,x4564,x4565,x4566,x4562))
% 11.41/11.20 [457]~E(x4571,x4572)+E(f710(x4571,x4573),f710(x4572,x4573))
% 11.41/11.20 [458]~E(x4581,x4582)+E(f710(x4583,x4581),f710(x4583,x4582))
% 11.41/11.20 [459]~E(x4591,x4592)+E(f94(x4591,x4593),f94(x4592,x4593))
% 11.41/11.20 [460]~E(x4601,x4602)+E(f94(x4603,x4601),f94(x4603,x4602))
% 11.41/11.20 [461]~E(x4611,x4612)+E(f799(x4611,x4613),f799(x4612,x4613))
% 11.41/11.20 [462]~E(x4621,x4622)+E(f799(x4623,x4621),f799(x4623,x4622))
% 11.41/11.20 [463]~E(x4631,x4632)+E(f62(x4631,x4633),f62(x4632,x4633))
% 11.41/11.20 [464]~E(x4641,x4642)+E(f62(x4643,x4641),f62(x4643,x4642))
% 11.41/11.20 [465]~E(x4651,x4652)+E(f169(x4651,x4653),f169(x4652,x4653))
% 11.41/11.20 [466]~E(x4661,x4662)+E(f169(x4663,x4661),f169(x4663,x4662))
% 11.41/11.20 [467]~E(x4671,x4672)+E(f376(x4671,x4673,x4674,x4675,x4676),f376(x4672,x4673,x4674,x4675,x4676))
% 11.41/11.20 [468]~E(x4681,x4682)+E(f376(x4683,x4681,x4684,x4685,x4686),f376(x4683,x4682,x4684,x4685,x4686))
% 11.41/11.20 [469]~E(x4691,x4692)+E(f376(x4693,x4694,x4691,x4695,x4696),f376(x4693,x4694,x4692,x4695,x4696))
% 11.41/11.20 [470]~E(x4701,x4702)+E(f376(x4703,x4704,x4705,x4701,x4706),f376(x4703,x4704,x4705,x4702,x4706))
% 11.41/11.20 [471]~E(x4711,x4712)+E(f376(x4713,x4714,x4715,x4716,x4711),f376(x4713,x4714,x4715,x4716,x4712))
% 11.41/11.20 [472]~E(x4721,x4722)+E(f241(x4721),f241(x4722))
% 11.41/11.20 [473]~E(x4731,x4732)+E(f65(x4731,x4733),f65(x4732,x4733))
% 11.41/11.20 [474]~E(x4741,x4742)+E(f65(x4743,x4741),f65(x4743,x4742))
% 11.41/11.20 [475]~E(x4751,x4752)+E(f554(x4751,x4753,x4754,x4755,x4756,x4757),f554(x4752,x4753,x4754,x4755,x4756,x4757))
% 11.41/11.20 [476]~E(x4761,x4762)+E(f554(x4763,x4761,x4764,x4765,x4766,x4767),f554(x4763,x4762,x4764,x4765,x4766,x4767))
% 11.41/11.20 [477]~E(x4771,x4772)+E(f554(x4773,x4774,x4771,x4775,x4776,x4777),f554(x4773,x4774,x4772,x4775,x4776,x4777))
% 11.41/11.20 [478]~E(x4781,x4782)+E(f554(x4783,x4784,x4785,x4781,x4786,x4787),f554(x4783,x4784,x4785,x4782,x4786,x4787))
% 11.41/11.20 [479]~E(x4791,x4792)+E(f554(x4793,x4794,x4795,x4796,x4791,x4797),f554(x4793,x4794,x4795,x4796,x4792,x4797))
% 11.41/11.20 [480]~E(x4801,x4802)+E(f554(x4803,x4804,x4805,x4806,x4807,x4801),f554(x4803,x4804,x4805,x4806,x4807,x4802))
% 11.41/11.20 [481]~E(x4811,x4812)+E(f332(x4811,x4813,x4814,x4815,x4816),f332(x4812,x4813,x4814,x4815,x4816))
% 11.41/11.20 [482]~E(x4821,x4822)+E(f332(x4823,x4821,x4824,x4825,x4826),f332(x4823,x4822,x4824,x4825,x4826))
% 11.41/11.20 [483]~E(x4831,x4832)+E(f332(x4833,x4834,x4831,x4835,x4836),f332(x4833,x4834,x4832,x4835,x4836))
% 11.41/11.20 [484]~E(x4841,x4842)+E(f332(x4843,x4844,x4845,x4841,x4846),f332(x4843,x4844,x4845,x4842,x4846))
% 11.41/11.20 [485]~E(x4851,x4852)+E(f332(x4853,x4854,x4855,x4856,x4851),f332(x4853,x4854,x4855,x4856,x4852))
% 11.41/11.20 [486]~E(x4861,x4862)+E(f267(x4861),f267(x4862))
% 11.41/11.20 [487]~E(x4871,x4872)+E(f86(x4871,x4873,x4874,x4875),f86(x4872,x4873,x4874,x4875))
% 11.41/11.20 [488]~E(x4881,x4882)+E(f86(x4883,x4881,x4884,x4885),f86(x4883,x4882,x4884,x4885))
% 11.41/11.20 [489]~E(x4891,x4892)+E(f86(x4893,x4894,x4891,x4895),f86(x4893,x4894,x4892,x4895))
% 11.41/11.20 [490]~E(x4901,x4902)+E(f86(x4903,x4904,x4905,x4901),f86(x4903,x4904,x4905,x4902))
% 11.41/11.20 [491]~E(x4911,x4912)+E(f870(x4911,x4913),f870(x4912,x4913))
% 11.41/11.20 [492]~E(x4921,x4922)+E(f870(x4923,x4921),f870(x4923,x4922))
% 11.41/11.20 [493]~E(x4931,x4932)+E(f436(x4931,x4933,x4934,x4935),f436(x4932,x4933,x4934,x4935))
% 11.41/11.20 [494]~E(x4941,x4942)+E(f436(x4943,x4941,x4944,x4945),f436(x4943,x4942,x4944,x4945))
% 11.41/11.20 [495]~E(x4951,x4952)+E(f436(x4953,x4954,x4951,x4955),f436(x4953,x4954,x4952,x4955))
% 11.41/11.20 [496]~E(x4961,x4962)+E(f436(x4963,x4964,x4965,x4961),f436(x4963,x4964,x4965,x4962))
% 11.41/11.20 [497]~E(x4971,x4972)+E(f105(x4971),f105(x4972))
% 11.41/11.20 [498]~E(x4981,x4982)+E(f17(x4981,x4983),f17(x4982,x4983))
% 11.41/11.20 [499]~E(x4991,x4992)+E(f17(x4993,x4991),f17(x4993,x4992))
% 11.41/11.20 [500]~E(x5001,x5002)+E(f172(x5001,x5003,x5004),f172(x5002,x5003,x5004))
% 11.41/11.20 [501]~E(x5011,x5012)+E(f172(x5013,x5011,x5014),f172(x5013,x5012,x5014))
% 11.41/11.20 [502]~E(x5021,x5022)+E(f172(x5023,x5024,x5021),f172(x5023,x5024,x5022))
% 11.41/11.20 [503]~E(x5031,x5032)+E(f158(x5031,x5033,x5034),f158(x5032,x5033,x5034))
% 11.41/11.20 [504]~E(x5041,x5042)+E(f158(x5043,x5041,x5044),f158(x5043,x5042,x5044))
% 11.41/11.20 [505]~E(x5051,x5052)+E(f158(x5053,x5054,x5051),f158(x5053,x5054,x5052))
% 11.41/11.20 [506]~E(x5061,x5062)+E(f63(x5061,x5063),f63(x5062,x5063))
% 11.41/11.20 [507]~E(x5071,x5072)+E(f63(x5073,x5071),f63(x5073,x5072))
% 11.41/11.20 [508]~E(x5081,x5082)+E(f750(x5081,x5083,x5084,x5085),f750(x5082,x5083,x5084,x5085))
% 11.41/11.20 [509]~E(x5091,x5092)+E(f750(x5093,x5091,x5094,x5095),f750(x5093,x5092,x5094,x5095))
% 11.41/11.20 [510]~E(x5101,x5102)+E(f750(x5103,x5104,x5101,x5105),f750(x5103,x5104,x5102,x5105))
% 11.41/11.20 [511]~E(x5111,x5112)+E(f750(x5113,x5114,x5115,x5111),f750(x5113,x5114,x5115,x5112))
% 11.41/11.20 [512]~E(x5121,x5122)+E(f684(x5121,x5123,x5124),f684(x5122,x5123,x5124))
% 11.41/11.20 [513]~E(x5131,x5132)+E(f684(x5133,x5131,x5134),f684(x5133,x5132,x5134))
% 11.41/11.20 [514]~E(x5141,x5142)+E(f684(x5143,x5144,x5141),f684(x5143,x5144,x5142))
% 11.41/11.20 [515]~E(x5151,x5152)+E(f775(x5151,x5153,x5154),f775(x5152,x5153,x5154))
% 11.41/11.20 [516]~E(x5161,x5162)+E(f775(x5163,x5161,x5164),f775(x5163,x5162,x5164))
% 11.41/11.20 [517]~E(x5171,x5172)+E(f775(x5173,x5174,x5171),f775(x5173,x5174,x5172))
% 11.41/11.20 [518]~E(x5181,x5182)+E(f506(x5181,x5183,x5184),f506(x5182,x5183,x5184))
% 11.41/11.20 [519]~E(x5191,x5192)+E(f506(x5193,x5191,x5194),f506(x5193,x5192,x5194))
% 11.41/11.20 [520]~E(x5201,x5202)+E(f506(x5203,x5204,x5201),f506(x5203,x5204,x5202))
% 11.41/11.20 [521]~E(x5211,x5212)+E(f143(x5211,x5213,x5214,x5215,x5216),f143(x5212,x5213,x5214,x5215,x5216))
% 11.41/11.20 [522]~E(x5221,x5222)+E(f143(x5223,x5221,x5224,x5225,x5226),f143(x5223,x5222,x5224,x5225,x5226))
% 11.41/11.20 [523]~E(x5231,x5232)+E(f143(x5233,x5234,x5231,x5235,x5236),f143(x5233,x5234,x5232,x5235,x5236))
% 11.41/11.20 [524]~E(x5241,x5242)+E(f143(x5243,x5244,x5245,x5241,x5246),f143(x5243,x5244,x5245,x5242,x5246))
% 11.41/11.20 [525]~E(x5251,x5252)+E(f143(x5253,x5254,x5255,x5256,x5251),f143(x5253,x5254,x5255,x5256,x5252))
% 11.41/11.20 [526]~E(x5261,x5262)+E(f813(x5261,x5263,x5264),f813(x5262,x5263,x5264))
% 11.41/11.20 [527]~E(x5271,x5272)+E(f813(x5273,x5271,x5274),f813(x5273,x5272,x5274))
% 11.41/11.20 [528]~E(x5281,x5282)+E(f813(x5283,x5284,x5281),f813(x5283,x5284,x5282))
% 11.41/11.20 [529]~E(x5291,x5292)+E(f150(x5291,x5293),f150(x5292,x5293))
% 11.41/11.20 [530]~E(x5301,x5302)+E(f150(x5303,x5301),f150(x5303,x5302))
% 11.41/11.20 [531]~E(x5311,x5312)+E(f170(x5311,x5313),f170(x5312,x5313))
% 11.41/11.20 [532]~E(x5321,x5322)+E(f170(x5323,x5321),f170(x5323,x5322))
% 11.41/11.20 [533]~E(x5331,x5332)+E(f322(x5331,x5333),f322(x5332,x5333))
% 11.41/11.20 [534]~E(x5341,x5342)+E(f322(x5343,x5341),f322(x5343,x5342))
% 11.41/11.20 [535]~E(x5351,x5352)+E(f407(x5351,x5353,x5354),f407(x5352,x5353,x5354))
% 11.41/11.20 [536]~E(x5361,x5362)+E(f407(x5363,x5361,x5364),f407(x5363,x5362,x5364))
% 11.41/11.20 [537]~E(x5371,x5372)+E(f407(x5373,x5374,x5371),f407(x5373,x5374,x5372))
% 11.41/11.20 [538]~E(x5381,x5382)+E(f260(x5381,x5383),f260(x5382,x5383))
% 11.41/11.20 [539]~E(x5391,x5392)+E(f260(x5393,x5391),f260(x5393,x5392))
% 11.41/11.20 [540]~E(x5401,x5402)+E(f139(x5401,x5403),f139(x5402,x5403))
% 11.41/11.20 [541]~E(x5411,x5412)+E(f139(x5413,x5411),f139(x5413,x5412))
% 11.41/11.20 [542]~E(x5421,x5422)+E(f15(x5421,x5423),f15(x5422,x5423))
% 11.41/11.20 [543]~E(x5431,x5432)+E(f15(x5433,x5431),f15(x5433,x5432))
% 11.41/11.20 [544]~E(x5441,x5442)+E(f477(x5441,x5443,x5444),f477(x5442,x5443,x5444))
% 11.41/11.20 [545]~E(x5451,x5452)+E(f477(x5453,x5451,x5454),f477(x5453,x5452,x5454))
% 11.41/11.20 [546]~E(x5461,x5462)+E(f477(x5463,x5464,x5461),f477(x5463,x5464,x5462))
% 11.41/11.20 [547]~E(x5471,x5472)+E(f149(x5471,x5473),f149(x5472,x5473))
% 11.41/11.20 [548]~E(x5481,x5482)+E(f149(x5483,x5481),f149(x5483,x5482))
% 11.41/11.20 [549]~E(x5491,x5492)+E(f309(x5491),f309(x5492))
% 11.41/11.20 [550]~E(x5501,x5502)+E(f811(x5501,x5503,x5504),f811(x5502,x5503,x5504))
% 11.41/11.20 [551]~E(x5511,x5512)+E(f811(x5513,x5511,x5514),f811(x5513,x5512,x5514))
% 11.41/11.20 [552]~E(x5521,x5522)+E(f811(x5523,x5524,x5521),f811(x5523,x5524,x5522))
% 11.41/11.20 [553]~E(x5531,x5532)+E(f538(x5531,x5533,x5534,x5535),f538(x5532,x5533,x5534,x5535))
% 11.41/11.20 [554]~E(x5541,x5542)+E(f538(x5543,x5541,x5544,x5545),f538(x5543,x5542,x5544,x5545))
% 11.41/11.20 [555]~E(x5551,x5552)+E(f538(x5553,x5554,x5551,x5555),f538(x5553,x5554,x5552,x5555))
% 11.41/11.20 [556]~E(x5561,x5562)+E(f538(x5563,x5564,x5565,x5561),f538(x5563,x5564,x5565,x5562))
% 11.41/11.20 [557]~E(x5571,x5572)+E(f299(x5571,x5573,x5574,x5575,x5576),f299(x5572,x5573,x5574,x5575,x5576))
% 11.41/11.20 [558]~E(x5581,x5582)+E(f299(x5583,x5581,x5584,x5585,x5586),f299(x5583,x5582,x5584,x5585,x5586))
% 11.41/11.20 [559]~E(x5591,x5592)+E(f299(x5593,x5594,x5591,x5595,x5596),f299(x5593,x5594,x5592,x5595,x5596))
% 11.41/11.20 [560]~E(x5601,x5602)+E(f299(x5603,x5604,x5605,x5601,x5606),f299(x5603,x5604,x5605,x5602,x5606))
% 11.41/11.20 [561]~E(x5611,x5612)+E(f299(x5613,x5614,x5615,x5616,x5611),f299(x5613,x5614,x5615,x5616,x5612))
% 11.41/11.20 [562]~E(x5621,x5622)+E(f152(x5621,x5623),f152(x5622,x5623))
% 11.41/11.20 [563]~E(x5631,x5632)+E(f152(x5633,x5631),f152(x5633,x5632))
% 11.41/11.20 [564]~E(x5641,x5642)+E(f746(x5641,x5643,x5644,x5645),f746(x5642,x5643,x5644,x5645))
% 11.41/11.20 [565]~E(x5651,x5652)+E(f746(x5653,x5651,x5654,x5655),f746(x5653,x5652,x5654,x5655))
% 11.41/11.20 [566]~E(x5661,x5662)+E(f746(x5663,x5664,x5661,x5665),f746(x5663,x5664,x5662,x5665))
% 11.41/11.20 [567]~E(x5671,x5672)+E(f746(x5673,x5674,x5675,x5671),f746(x5673,x5674,x5675,x5672))
% 11.41/11.20 [568]~E(x5681,x5682)+E(f127(x5681,x5683,x5684,x5685),f127(x5682,x5683,x5684,x5685))
% 11.41/11.20 [569]~E(x5691,x5692)+E(f127(x5693,x5691,x5694,x5695),f127(x5693,x5692,x5694,x5695))
% 11.41/11.20 [570]~E(x5701,x5702)+E(f127(x5703,x5704,x5701,x5705),f127(x5703,x5704,x5702,x5705))
% 11.41/11.20 [571]~E(x5711,x5712)+E(f127(x5713,x5714,x5715,x5711),f127(x5713,x5714,x5715,x5712))
% 11.41/11.20 [572]~E(x5721,x5722)+E(f657(x5721,x5723,x5724,x5725,x5726),f657(x5722,x5723,x5724,x5725,x5726))
% 11.41/11.20 [573]~E(x5731,x5732)+E(f657(x5733,x5731,x5734,x5735,x5736),f657(x5733,x5732,x5734,x5735,x5736))
% 11.41/11.20 [574]~E(x5741,x5742)+E(f657(x5743,x5744,x5741,x5745,x5746),f657(x5743,x5744,x5742,x5745,x5746))
% 11.41/11.20 [575]~E(x5751,x5752)+E(f657(x5753,x5754,x5755,x5751,x5756),f657(x5753,x5754,x5755,x5752,x5756))
% 11.41/11.20 [576]~E(x5761,x5762)+E(f657(x5763,x5764,x5765,x5766,x5761),f657(x5763,x5764,x5765,x5766,x5762))
% 11.41/11.20 [577]~E(x5771,x5772)+E(f147(x5771,x5773,x5774),f147(x5772,x5773,x5774))
% 11.41/11.20 [578]~E(x5781,x5782)+E(f147(x5783,x5781,x5784),f147(x5783,x5782,x5784))
% 11.41/11.20 [579]~E(x5791,x5792)+E(f147(x5793,x5794,x5791),f147(x5793,x5794,x5792))
% 11.41/11.20 [580]~E(x5801,x5802)+E(f409(x5801,x5803,x5804,x5805,x5806),f409(x5802,x5803,x5804,x5805,x5806))
% 11.41/11.20 [581]~E(x5811,x5812)+E(f409(x5813,x5811,x5814,x5815,x5816),f409(x5813,x5812,x5814,x5815,x5816))
% 11.41/11.20 [582]~E(x5821,x5822)+E(f409(x5823,x5824,x5821,x5825,x5826),f409(x5823,x5824,x5822,x5825,x5826))
% 11.41/11.20 [583]~E(x5831,x5832)+E(f409(x5833,x5834,x5835,x5831,x5836),f409(x5833,x5834,x5835,x5832,x5836))
% 11.41/11.20 [584]~E(x5841,x5842)+E(f409(x5843,x5844,x5845,x5846,x5841),f409(x5843,x5844,x5845,x5846,x5842))
% 11.41/11.20 [585]~E(x5851,x5852)+E(f457(x5851,x5853),f457(x5852,x5853))
% 11.41/11.20 [586]~E(x5861,x5862)+E(f457(x5863,x5861),f457(x5863,x5862))
% 11.41/11.20 [587]~E(x5871,x5872)+E(f458(x5871,x5873),f458(x5872,x5873))
% 11.41/11.20 [588]~E(x5881,x5882)+E(f458(x5883,x5881),f458(x5883,x5882))
% 11.41/11.20 [589]~E(x5891,x5892)+E(f34(x5891,x5893,x5894),f34(x5892,x5893,x5894))
% 11.41/11.20 [590]~E(x5901,x5902)+E(f34(x5903,x5901,x5904),f34(x5903,x5902,x5904))
% 11.41/11.20 [591]~E(x5911,x5912)+E(f34(x5913,x5914,x5911),f34(x5913,x5914,x5912))
% 11.41/11.20 [592]~E(x5921,x5922)+E(f808(x5921,x5923),f808(x5922,x5923))
% 11.41/11.20 [593]~E(x5931,x5932)+E(f808(x5933,x5931),f808(x5933,x5932))
% 11.41/11.20 [594]~E(x5941,x5942)+E(f327(x5941,x5943,x5944,x5945),f327(x5942,x5943,x5944,x5945))
% 11.41/11.20 [595]~E(x5951,x5952)+E(f327(x5953,x5951,x5954,x5955),f327(x5953,x5952,x5954,x5955))
% 11.41/11.20 [596]~E(x5961,x5962)+E(f327(x5963,x5964,x5961,x5965),f327(x5963,x5964,x5962,x5965))
% 11.41/11.20 [597]~E(x5971,x5972)+E(f327(x5973,x5974,x5975,x5971),f327(x5973,x5974,x5975,x5972))
% 11.41/11.20 [598]~E(x5981,x5982)+E(f211(x5981,x5983,x5984,x5985),f211(x5982,x5983,x5984,x5985))
% 11.41/11.20 [599]~E(x5991,x5992)+E(f211(x5993,x5991,x5994,x5995),f211(x5993,x5992,x5994,x5995))
% 11.41/11.20 [600]~E(x6001,x6002)+E(f211(x6003,x6004,x6001,x6005),f211(x6003,x6004,x6002,x6005))
% 11.41/11.20 [601]~E(x6011,x6012)+E(f211(x6013,x6014,x6015,x6011),f211(x6013,x6014,x6015,x6012))
% 11.41/11.20 [602]~E(x6021,x6022)+E(f104(x6021,x6023,x6024,x6025),f104(x6022,x6023,x6024,x6025))
% 11.41/11.20 [603]~E(x6031,x6032)+E(f104(x6033,x6031,x6034,x6035),f104(x6033,x6032,x6034,x6035))
% 11.41/11.20 [604]~E(x6041,x6042)+E(f104(x6043,x6044,x6041,x6045),f104(x6043,x6044,x6042,x6045))
% 11.41/11.20 [605]~E(x6051,x6052)+E(f104(x6053,x6054,x6055,x6051),f104(x6053,x6054,x6055,x6052))
% 11.41/11.20 [606]~E(x6061,x6062)+E(f614(x6061,x6063),f614(x6062,x6063))
% 11.41/11.20 [607]~E(x6071,x6072)+E(f614(x6073,x6071),f614(x6073,x6072))
% 11.41/11.20 [608]~E(x6081,x6082)+E(f301(x6081,x6083,x6084,x6085),f301(x6082,x6083,x6084,x6085))
% 11.41/11.20 [609]~E(x6091,x6092)+E(f301(x6093,x6091,x6094,x6095),f301(x6093,x6092,x6094,x6095))
% 11.41/11.20 [610]~E(x6101,x6102)+E(f301(x6103,x6104,x6101,x6105),f301(x6103,x6104,x6102,x6105))
% 11.41/11.20 [611]~E(x6111,x6112)+E(f301(x6113,x6114,x6115,x6111),f301(x6113,x6114,x6115,x6112))
% 11.41/11.20 [612]~E(x6121,x6122)+E(f618(x6121,x6123,x6124),f618(x6122,x6123,x6124))
% 11.41/11.20 [613]~E(x6131,x6132)+E(f618(x6133,x6131,x6134),f618(x6133,x6132,x6134))
% 11.41/11.20 [614]~E(x6141,x6142)+E(f618(x6143,x6144,x6141),f618(x6143,x6144,x6142))
% 11.41/11.20 [615]~E(x6151,x6152)+E(f508(x6151,x6153,x6154,x6155,x6156,x6157),f508(x6152,x6153,x6154,x6155,x6156,x6157))
% 11.41/11.20 [616]~E(x6161,x6162)+E(f508(x6163,x6161,x6164,x6165,x6166,x6167),f508(x6163,x6162,x6164,x6165,x6166,x6167))
% 11.41/11.20 [617]~E(x6171,x6172)+E(f508(x6173,x6174,x6171,x6175,x6176,x6177),f508(x6173,x6174,x6172,x6175,x6176,x6177))
% 11.41/11.20 [618]~E(x6181,x6182)+E(f508(x6183,x6184,x6185,x6181,x6186,x6187),f508(x6183,x6184,x6185,x6182,x6186,x6187))
% 11.41/11.20 [619]~E(x6191,x6192)+E(f508(x6193,x6194,x6195,x6196,x6191,x6197),f508(x6193,x6194,x6195,x6196,x6192,x6197))
% 11.41/11.20 [620]~E(x6201,x6202)+E(f508(x6203,x6204,x6205,x6206,x6207,x6201),f508(x6203,x6204,x6205,x6206,x6207,x6202))
% 11.41/11.20 [621]~E(x6211,x6212)+E(f311(x6211),f311(x6212))
% 11.41/11.20 [622]~E(x6221,x6222)+E(f465(x6221,x6223,x6224,x6225),f465(x6222,x6223,x6224,x6225))
% 11.41/11.20 [623]~E(x6231,x6232)+E(f465(x6233,x6231,x6234,x6235),f465(x6233,x6232,x6234,x6235))
% 11.41/11.20 [624]~E(x6241,x6242)+E(f465(x6243,x6244,x6241,x6245),f465(x6243,x6244,x6242,x6245))
% 11.41/11.20 [625]~E(x6251,x6252)+E(f465(x6253,x6254,x6255,x6251),f465(x6253,x6254,x6255,x6252))
% 11.41/11.20 [626]~E(x6261,x6262)+E(f206(x6261,x6263),f206(x6262,x6263))
% 11.41/11.20 [627]~E(x6271,x6272)+E(f206(x6273,x6271),f206(x6273,x6272))
% 11.41/11.20 [628]~E(x6281,x6282)+E(f151(x6281,x6283),f151(x6282,x6283))
% 11.41/11.20 [629]~E(x6291,x6292)+E(f151(x6293,x6291),f151(x6293,x6292))
% 11.41/11.20 [630]~E(x6301,x6302)+E(f671(x6301,x6303,x6304,x6305,x6306),f671(x6302,x6303,x6304,x6305,x6306))
% 11.41/11.20 [631]~E(x6311,x6312)+E(f671(x6313,x6311,x6314,x6315,x6316),f671(x6313,x6312,x6314,x6315,x6316))
% 11.41/11.20 [632]~E(x6321,x6322)+E(f671(x6323,x6324,x6321,x6325,x6326),f671(x6323,x6324,x6322,x6325,x6326))
% 11.41/11.20 [633]~E(x6331,x6332)+E(f671(x6333,x6334,x6335,x6331,x6336),f671(x6333,x6334,x6335,x6332,x6336))
% 11.41/11.20 [634]~E(x6341,x6342)+E(f671(x6343,x6344,x6345,x6346,x6341),f671(x6343,x6344,x6345,x6346,x6342))
% 11.41/11.20 [635]~E(x6351,x6352)+E(f331(x6351,x6353,x6354,x6355,x6356),f331(x6352,x6353,x6354,x6355,x6356))
% 11.41/11.20 [636]~E(x6361,x6362)+E(f331(x6363,x6361,x6364,x6365,x6366),f331(x6363,x6362,x6364,x6365,x6366))
% 11.41/11.20 [637]~E(x6371,x6372)+E(f331(x6373,x6374,x6371,x6375,x6376),f331(x6373,x6374,x6372,x6375,x6376))
% 11.41/11.20 [638]~E(x6381,x6382)+E(f331(x6383,x6384,x6385,x6381,x6386),f331(x6383,x6384,x6385,x6382,x6386))
% 11.41/11.20 [639]~E(x6391,x6392)+E(f331(x6393,x6394,x6395,x6396,x6391),f331(x6393,x6394,x6395,x6396,x6392))
% 11.41/11.20 [640]~E(x6401,x6402)+E(f470(x6401,x6403),f470(x6402,x6403))
% 11.41/11.20 [641]~E(x6411,x6412)+E(f470(x6413,x6411),f470(x6413,x6412))
% 11.41/11.20 [642]~E(x6421,x6422)+E(f284(x6421,x6423,x6424,x6425),f284(x6422,x6423,x6424,x6425))
% 11.41/11.20 [643]~E(x6431,x6432)+E(f284(x6433,x6431,x6434,x6435),f284(x6433,x6432,x6434,x6435))
% 11.41/11.20 [644]~E(x6441,x6442)+E(f284(x6443,x6444,x6441,x6445),f284(x6443,x6444,x6442,x6445))
% 11.41/11.20 [645]~E(x6451,x6452)+E(f284(x6453,x6454,x6455,x6451),f284(x6453,x6454,x6455,x6452))
% 11.41/11.20 [646]~E(x6461,x6462)+E(f412(x6461,x6463,x6464,x6465),f412(x6462,x6463,x6464,x6465))
% 11.41/11.20 [647]~E(x6471,x6472)+E(f412(x6473,x6471,x6474,x6475),f412(x6473,x6472,x6474,x6475))
% 11.41/11.20 [648]~E(x6481,x6482)+E(f412(x6483,x6484,x6481,x6485),f412(x6483,x6484,x6482,x6485))
% 11.41/11.20 [649]~E(x6491,x6492)+E(f412(x6493,x6494,x6495,x6491),f412(x6493,x6494,x6495,x6492))
% 11.41/11.20 [650]~E(x6501,x6502)+E(f40(x6501,x6503,x6504,x6505,x6506,x6507,x6508,x6509,x65010,x65011),f40(x6502,x6503,x6504,x6505,x6506,x6507,x6508,x6509,x65010,x65011))
% 11.41/11.20 [651]~E(x6511,x6512)+E(f40(x6513,x6511,x6514,x6515,x6516,x6517,x6518,x6519,x65110,x65111),f40(x6513,x6512,x6514,x6515,x6516,x6517,x6518,x6519,x65110,x65111))
% 11.41/11.20 [652]~E(x6521,x6522)+E(f40(x6523,x6524,x6521,x6525,x6526,x6527,x6528,x6529,x65210,x65211),f40(x6523,x6524,x6522,x6525,x6526,x6527,x6528,x6529,x65210,x65211))
% 11.41/11.20 [653]~E(x6531,x6532)+E(f40(x6533,x6534,x6535,x6531,x6536,x6537,x6538,x6539,x65310,x65311),f40(x6533,x6534,x6535,x6532,x6536,x6537,x6538,x6539,x65310,x65311))
% 11.41/11.20 [654]~E(x6541,x6542)+E(f40(x6543,x6544,x6545,x6546,x6541,x6547,x6548,x6549,x65410,x65411),f40(x6543,x6544,x6545,x6546,x6542,x6547,x6548,x6549,x65410,x65411))
% 11.41/11.20 [655]~E(x6551,x6552)+E(f40(x6553,x6554,x6555,x6556,x6557,x6551,x6558,x6559,x65510,x65511),f40(x6553,x6554,x6555,x6556,x6557,x6552,x6558,x6559,x65510,x65511))
% 11.41/11.20 [656]~E(x6561,x6562)+E(f40(x6563,x6564,x6565,x6566,x6567,x6568,x6561,x6569,x65610,x65611),f40(x6563,x6564,x6565,x6566,x6567,x6568,x6562,x6569,x65610,x65611))
% 11.41/11.20 [657]~E(x6571,x6572)+E(f40(x6573,x6574,x6575,x6576,x6577,x6578,x6579,x6571,x65710,x65711),f40(x6573,x6574,x6575,x6576,x6577,x6578,x6579,x6572,x65710,x65711))
% 11.41/11.20 [658]~E(x6581,x6582)+E(f40(x6583,x6584,x6585,x6586,x6587,x6588,x6589,x65810,x6581,x65811),f40(x6583,x6584,x6585,x6586,x6587,x6588,x6589,x65810,x6582,x65811))
% 11.41/11.20 [659]~E(x6591,x6592)+E(f40(x6593,x6594,x6595,x6596,x6597,x6598,x6599,x65910,x65911,x6591),f40(x6593,x6594,x6595,x6596,x6597,x6598,x6599,x65910,x65911,x6592))
% 11.41/11.20 [660]~E(x6601,x6602)+E(f236(x6601,x6603),f236(x6602,x6603))
% 11.41/11.20 [661]~E(x6611,x6612)+E(f236(x6613,x6611),f236(x6613,x6612))
% 11.41/11.20 [662]~E(x6621,x6622)+E(f308(x6621,x6623,x6624),f308(x6622,x6623,x6624))
% 11.41/11.20 [663]~E(x6631,x6632)+E(f308(x6633,x6631,x6634),f308(x6633,x6632,x6634))
% 11.41/11.20 [664]~E(x6641,x6642)+E(f308(x6643,x6644,x6641),f308(x6643,x6644,x6642))
% 11.41/11.20 [665]~E(x6651,x6652)+E(f366(x6651,x6653),f366(x6652,x6653))
% 11.41/11.20 [666]~E(x6661,x6662)+E(f366(x6663,x6661),f366(x6663,x6662))
% 11.41/11.20 [667]~E(x6671,x6672)+E(f95(x6671,x6673),f95(x6672,x6673))
% 11.41/11.20 [668]~E(x6681,x6682)+E(f95(x6683,x6681),f95(x6683,x6682))
% 11.41/11.20 [669]~E(x6691,x6692)+E(f835(x6691,x6693,x6694),f835(x6692,x6693,x6694))
% 11.41/11.20 [670]~E(x6701,x6702)+E(f835(x6703,x6701,x6704),f835(x6703,x6702,x6704))
% 11.41/11.20 [671]~E(x6711,x6712)+E(f835(x6713,x6714,x6711),f835(x6713,x6714,x6712))
% 11.41/11.20 [672]~E(x6721,x6722)+E(f46(x6721,x6723,x6724,x6725),f46(x6722,x6723,x6724,x6725))
% 11.41/11.20 [673]~E(x6731,x6732)+E(f46(x6733,x6731,x6734,x6735),f46(x6733,x6732,x6734,x6735))
% 11.41/11.20 [674]~E(x6741,x6742)+E(f46(x6743,x6744,x6741,x6745),f46(x6743,x6744,x6742,x6745))
% 11.41/11.20 [675]~E(x6751,x6752)+E(f46(x6753,x6754,x6755,x6751),f46(x6753,x6754,x6755,x6752))
% 11.41/11.20 [676]~E(x6761,x6762)+E(f434(x6761,x6763,x6764),f434(x6762,x6763,x6764))
% 11.41/11.20 [677]~E(x6771,x6772)+E(f434(x6773,x6771,x6774),f434(x6773,x6772,x6774))
% 11.41/11.20 [678]~E(x6781,x6782)+E(f434(x6783,x6784,x6781),f434(x6783,x6784,x6782))
% 11.41/11.20 [679]~E(x6791,x6792)+E(f141(x6791,x6793),f141(x6792,x6793))
% 11.41/11.20 [680]~E(x6801,x6802)+E(f141(x6803,x6801),f141(x6803,x6802))
% 11.41/11.20 [681]~E(x6811,x6812)+E(f259(x6811,x6813,x6814,x6815),f259(x6812,x6813,x6814,x6815))
% 11.41/11.20 [682]~E(x6821,x6822)+E(f259(x6823,x6821,x6824,x6825),f259(x6823,x6822,x6824,x6825))
% 11.41/11.20 [683]~E(x6831,x6832)+E(f259(x6833,x6834,x6831,x6835),f259(x6833,x6834,x6832,x6835))
% 11.41/11.20 [684]~E(x6841,x6842)+E(f259(x6843,x6844,x6845,x6841),f259(x6843,x6844,x6845,x6842))
% 11.41/11.20 [685]~E(x6851,x6852)+E(f779(x6851,x6853,x6854),f779(x6852,x6853,x6854))
% 11.41/11.20 [686]~E(x6861,x6862)+E(f779(x6863,x6861,x6864),f779(x6863,x6862,x6864))
% 11.41/11.20 [687]~E(x6871,x6872)+E(f779(x6873,x6874,x6871),f779(x6873,x6874,x6872))
% 11.41/11.20 [688]~E(x6881,x6882)+E(f431(x6881,x6883,x6884),f431(x6882,x6883,x6884))
% 11.41/11.20 [689]~E(x6891,x6892)+E(f431(x6893,x6891,x6894),f431(x6893,x6892,x6894))
% 11.41/11.20 [690]~E(x6901,x6902)+E(f431(x6903,x6904,x6901),f431(x6903,x6904,x6902))
% 11.41/11.20 [691]~E(x6911,x6912)+E(f645(x6911,x6913),f645(x6912,x6913))
% 11.41/11.20 [692]~E(x6921,x6922)+E(f645(x6923,x6921),f645(x6923,x6922))
% 11.41/11.20 [693]~E(x6931,x6932)+E(f683(x6931,x6933),f683(x6932,x6933))
% 11.41/11.20 [694]~E(x6941,x6942)+E(f683(x6943,x6941),f683(x6943,x6942))
% 11.41/11.20 [695]~E(x6951,x6952)+E(f178(x6951,x6953,x6954,x6955,x6956),f178(x6952,x6953,x6954,x6955,x6956))
% 11.41/11.20 [696]~E(x6961,x6962)+E(f178(x6963,x6961,x6964,x6965,x6966),f178(x6963,x6962,x6964,x6965,x6966))
% 11.41/11.20 [697]~E(x6971,x6972)+E(f178(x6973,x6974,x6971,x6975,x6976),f178(x6973,x6974,x6972,x6975,x6976))
% 11.41/11.20 [698]~E(x6981,x6982)+E(f178(x6983,x6984,x6985,x6981,x6986),f178(x6983,x6984,x6985,x6982,x6986))
% 11.41/11.20 [699]~E(x6991,x6992)+E(f178(x6993,x6994,x6995,x6996,x6991),f178(x6993,x6994,x6995,x6996,x6992))
% 11.41/11.20 [700]~E(x7001,x7002)+E(f408(x7001,x7003,x7004),f408(x7002,x7003,x7004))
% 11.41/11.20 [701]~E(x7011,x7012)+E(f408(x7013,x7011,x7014),f408(x7013,x7012,x7014))
% 11.41/11.20 [702]~E(x7021,x7022)+E(f408(x7023,x7024,x7021),f408(x7023,x7024,x7022))
% 11.41/11.20 [703]~E(x7031,x7032)+E(f223(x7031,x7033),f223(x7032,x7033))
% 11.41/11.20 [704]~E(x7041,x7042)+E(f223(x7043,x7041),f223(x7043,x7042))
% 11.41/11.20 [705]~E(x7051,x7052)+E(f423(x7051,x7053,x7054,x7055),f423(x7052,x7053,x7054,x7055))
% 11.41/11.20 [706]~E(x7061,x7062)+E(f423(x7063,x7061,x7064,x7065),f423(x7063,x7062,x7064,x7065))
% 11.41/11.20 [707]~E(x7071,x7072)+E(f423(x7073,x7074,x7071,x7075),f423(x7073,x7074,x7072,x7075))
% 11.41/11.20 [708]~E(x7081,x7082)+E(f423(x7083,x7084,x7085,x7081),f423(x7083,x7084,x7085,x7082))
% 11.41/11.20 [709]~E(x7091,x7092)+E(f682(x7091,x7093,x7094),f682(x7092,x7093,x7094))
% 11.41/11.20 [710]~E(x7101,x7102)+E(f682(x7103,x7101,x7104),f682(x7103,x7102,x7104))
% 11.41/11.20 [711]~E(x7111,x7112)+E(f682(x7113,x7114,x7111),f682(x7113,x7114,x7112))
% 11.41/11.20 [712]~E(x7121,x7122)+E(f288(x7121,x7123),f288(x7122,x7123))
% 11.41/11.20 [713]~E(x7131,x7132)+E(f288(x7133,x7131),f288(x7133,x7132))
% 11.41/11.20 [714]~E(x7141,x7142)+E(f269(x7141,x7143),f269(x7142,x7143))
% 11.41/11.20 [715]~E(x7151,x7152)+E(f269(x7153,x7151),f269(x7153,x7152))
% 11.41/11.20 [716]~E(x7161,x7162)+E(f757(x7161,x7163,x7164),f757(x7162,x7163,x7164))
% 11.41/11.20 [717]~E(x7171,x7172)+E(f757(x7173,x7171,x7174),f757(x7173,x7172,x7174))
% 11.41/11.20 [718]~E(x7181,x7182)+E(f757(x7183,x7184,x7181),f757(x7183,x7184,x7182))
% 11.41/11.20 [719]~E(x7191,x7192)+E(f333(x7191,x7193,x7194,x7195,x7196,x7197),f333(x7192,x7193,x7194,x7195,x7196,x7197))
% 11.41/11.20 [720]~E(x7201,x7202)+E(f333(x7203,x7201,x7204,x7205,x7206,x7207),f333(x7203,x7202,x7204,x7205,x7206,x7207))
% 11.41/11.20 [721]~E(x7211,x7212)+E(f333(x7213,x7214,x7211,x7215,x7216,x7217),f333(x7213,x7214,x7212,x7215,x7216,x7217))
% 11.41/11.20 [722]~E(x7221,x7222)+E(f333(x7223,x7224,x7225,x7221,x7226,x7227),f333(x7223,x7224,x7225,x7222,x7226,x7227))
% 11.41/11.20 [723]~E(x7231,x7232)+E(f333(x7233,x7234,x7235,x7236,x7231,x7237),f333(x7233,x7234,x7235,x7236,x7232,x7237))
% 11.41/11.20 [724]~E(x7241,x7242)+E(f333(x7243,x7244,x7245,x7246,x7247,x7241),f333(x7243,x7244,x7245,x7246,x7247,x7242))
% 11.41/11.20 [725]~E(x7251,x7252)+E(f253(x7251,x7253,x7254),f253(x7252,x7253,x7254))
% 11.41/11.20 [726]~E(x7261,x7262)+E(f253(x7263,x7261,x7264),f253(x7263,x7262,x7264))
% 11.41/11.20 [727]~E(x7271,x7272)+E(f253(x7273,x7274,x7271),f253(x7273,x7274,x7272))
% 11.41/11.20 [728]~E(x7281,x7282)+E(f837(x7281,x7283,x7284),f837(x7282,x7283,x7284))
% 11.41/11.20 [729]~E(x7291,x7292)+E(f837(x7293,x7291,x7294),f837(x7293,x7292,x7294))
% 11.41/11.20 [730]~E(x7301,x7302)+E(f837(x7303,x7304,x7301),f837(x7303,x7304,x7302))
% 11.41/11.20 [731]~E(x7311,x7312)+E(f307(x7311,x7313,x7314),f307(x7312,x7313,x7314))
% 11.41/11.20 [732]~E(x7321,x7322)+E(f307(x7323,x7321,x7324),f307(x7323,x7322,x7324))
% 11.41/11.20 [733]~E(x7331,x7332)+E(f307(x7333,x7334,x7331),f307(x7333,x7334,x7332))
% 11.41/11.20 [734]~E(x7341,x7342)+E(f606(x7341,x7343,x7344),f606(x7342,x7343,x7344))
% 11.41/11.20 [735]~E(x7351,x7352)+E(f606(x7353,x7351,x7354),f606(x7353,x7352,x7354))
% 11.41/11.20 [736]~E(x7361,x7362)+E(f606(x7363,x7364,x7361),f606(x7363,x7364,x7362))
% 11.41/11.20 [737]~E(x7371,x7372)+E(f365(x7371,x7373,x7374,x7375,x7376),f365(x7372,x7373,x7374,x7375,x7376))
% 11.41/11.20 [738]~E(x7381,x7382)+E(f365(x7383,x7381,x7384,x7385,x7386),f365(x7383,x7382,x7384,x7385,x7386))
% 11.41/11.20 [739]~E(x7391,x7392)+E(f365(x7393,x7394,x7391,x7395,x7396),f365(x7393,x7394,x7392,x7395,x7396))
% 11.41/11.20 [740]~E(x7401,x7402)+E(f365(x7403,x7404,x7405,x7401,x7406),f365(x7403,x7404,x7405,x7402,x7406))
% 11.41/11.20 [741]~E(x7411,x7412)+E(f365(x7413,x7414,x7415,x7416,x7411),f365(x7413,x7414,x7415,x7416,x7412))
% 11.41/11.20 [742]~E(x7421,x7422)+E(f691(x7421,x7423,x7424),f691(x7422,x7423,x7424))
% 11.41/11.20 [743]~E(x7431,x7432)+E(f691(x7433,x7431,x7434),f691(x7433,x7432,x7434))
% 11.41/11.20 [744]~E(x7441,x7442)+E(f691(x7443,x7444,x7441),f691(x7443,x7444,x7442))
% 11.41/11.20 [745]~E(x7451,x7452)+E(f597(x7451,x7453,x7454,x7455),f597(x7452,x7453,x7454,x7455))
% 11.41/11.20 [746]~E(x7461,x7462)+E(f597(x7463,x7461,x7464,x7465),f597(x7463,x7462,x7464,x7465))
% 11.41/11.20 [747]~E(x7471,x7472)+E(f597(x7473,x7474,x7471,x7475),f597(x7473,x7474,x7472,x7475))
% 11.41/11.20 [748]~E(x7481,x7482)+E(f597(x7483,x7484,x7485,x7481),f597(x7483,x7484,x7485,x7482))
% 11.41/11.20 [749]~E(x7491,x7492)+E(f392(x7491,x7493,x7494,x7495),f392(x7492,x7493,x7494,x7495))
% 11.41/11.20 [750]~E(x7501,x7502)+E(f392(x7503,x7501,x7504,x7505),f392(x7503,x7502,x7504,x7505))
% 11.41/11.20 [751]~E(x7511,x7512)+E(f392(x7513,x7514,x7511,x7515),f392(x7513,x7514,x7512,x7515))
% 11.41/11.20 [752]~E(x7521,x7522)+E(f392(x7523,x7524,x7525,x7521),f392(x7523,x7524,x7525,x7522))
% 11.41/11.20 [753]~E(x7531,x7532)+E(f220(x7531,x7533),f220(x7532,x7533))
% 11.41/11.20 [754]~E(x7541,x7542)+E(f220(x7543,x7541),f220(x7543,x7542))
% 11.41/11.20 [755]~E(x7551,x7552)+E(f686(x7551,x7553,x7554),f686(x7552,x7553,x7554))
% 11.41/11.20 [756]~E(x7561,x7562)+E(f686(x7563,x7561,x7564),f686(x7563,x7562,x7564))
% 11.41/11.20 [757]~E(x7571,x7572)+E(f686(x7573,x7574,x7571),f686(x7573,x7574,x7572))
% 11.41/11.20 [758]~E(x7581,x7582)+E(f355(x7581,x7583),f355(x7582,x7583))
% 11.41/11.20 [759]~E(x7591,x7592)+E(f355(x7593,x7591),f355(x7593,x7592))
% 11.41/11.20 [760]~E(x7601,x7602)+E(f219(x7601,x7603),f219(x7602,x7603))
% 11.41/11.20 [761]~E(x7611,x7612)+E(f219(x7613,x7611),f219(x7613,x7612))
% 11.41/11.20 [762]~E(x7621,x7622)+E(f846(x7621,x7623,x7624),f846(x7622,x7623,x7624))
% 11.41/11.20 [763]~E(x7631,x7632)+E(f846(x7633,x7631,x7634),f846(x7633,x7632,x7634))
% 11.41/11.20 [764]~E(x7641,x7642)+E(f846(x7643,x7644,x7641),f846(x7643,x7644,x7642))
% 11.41/11.20 [765]~E(x7651,x7652)+E(f547(x7651,x7653,x7654,x7655),f547(x7652,x7653,x7654,x7655))
% 11.41/11.20 [766]~E(x7661,x7662)+E(f547(x7663,x7661,x7664,x7665),f547(x7663,x7662,x7664,x7665))
% 11.41/11.20 [767]~E(x7671,x7672)+E(f547(x7673,x7674,x7671,x7675),f547(x7673,x7674,x7672,x7675))
% 11.41/11.20 [768]~E(x7681,x7682)+E(f547(x7683,x7684,x7685,x7681),f547(x7683,x7684,x7685,x7682))
% 11.41/11.20 [769]~E(x7691,x7692)+E(f404(x7691,x7693,x7694,x7695,x7696),f404(x7692,x7693,x7694,x7695,x7696))
% 11.41/11.20 [770]~E(x7701,x7702)+E(f404(x7703,x7701,x7704,x7705,x7706),f404(x7703,x7702,x7704,x7705,x7706))
% 11.41/11.20 [771]~E(x7711,x7712)+E(f404(x7713,x7714,x7711,x7715,x7716),f404(x7713,x7714,x7712,x7715,x7716))
% 11.41/11.20 [772]~E(x7721,x7722)+E(f404(x7723,x7724,x7725,x7721,x7726),f404(x7723,x7724,x7725,x7722,x7726))
% 11.41/11.20 [773]~E(x7731,x7732)+E(f404(x7733,x7734,x7735,x7736,x7731),f404(x7733,x7734,x7735,x7736,x7732))
% 11.41/11.20 [774]~E(x7741,x7742)+E(f696(x7741),f696(x7742))
% 11.41/11.20 [775]~E(x7751,x7752)+E(f601(x7751,x7753),f601(x7752,x7753))
% 11.41/11.20 [776]~E(x7761,x7762)+E(f601(x7763,x7761),f601(x7763,x7762))
% 11.41/11.20 [777]~E(x7771,x7772)+E(f719(x7771,x7773,x7774,x7775,x7776,x7777),f719(x7772,x7773,x7774,x7775,x7776,x7777))
% 11.41/11.20 [778]~E(x7781,x7782)+E(f719(x7783,x7781,x7784,x7785,x7786,x7787),f719(x7783,x7782,x7784,x7785,x7786,x7787))
% 11.41/11.20 [779]~E(x7791,x7792)+E(f719(x7793,x7794,x7791,x7795,x7796,x7797),f719(x7793,x7794,x7792,x7795,x7796,x7797))
% 11.41/11.20 [780]~E(x7801,x7802)+E(f719(x7803,x7804,x7805,x7801,x7806,x7807),f719(x7803,x7804,x7805,x7802,x7806,x7807))
% 11.41/11.20 [781]~E(x7811,x7812)+E(f719(x7813,x7814,x7815,x7816,x7811,x7817),f719(x7813,x7814,x7815,x7816,x7812,x7817))
% 11.41/11.20 [782]~E(x7821,x7822)+E(f719(x7823,x7824,x7825,x7826,x7827,x7821),f719(x7823,x7824,x7825,x7826,x7827,x7822))
% 11.41/11.20 [783]~E(x7831,x7832)+E(f61(x7831,x7833),f61(x7832,x7833))
% 11.41/11.20 [784]~E(x7841,x7842)+E(f61(x7843,x7841),f61(x7843,x7842))
% 11.41/11.20 [785]~E(x7851,x7852)+E(f509(x7851,x7853,x7854,x7855,x7856,x7857),f509(x7852,x7853,x7854,x7855,x7856,x7857))
% 11.41/11.20 [786]~E(x7861,x7862)+E(f509(x7863,x7861,x7864,x7865,x7866,x7867),f509(x7863,x7862,x7864,x7865,x7866,x7867))
% 11.41/11.20 [787]~E(x7871,x7872)+E(f509(x7873,x7874,x7871,x7875,x7876,x7877),f509(x7873,x7874,x7872,x7875,x7876,x7877))
% 11.41/11.20 [788]~E(x7881,x7882)+E(f509(x7883,x7884,x7885,x7881,x7886,x7887),f509(x7883,x7884,x7885,x7882,x7886,x7887))
% 11.41/11.20 [789]~E(x7891,x7892)+E(f509(x7893,x7894,x7895,x7896,x7891,x7897),f509(x7893,x7894,x7895,x7896,x7892,x7897))
% 11.41/11.20 [790]~E(x7901,x7902)+E(f509(x7903,x7904,x7905,x7906,x7907,x7901),f509(x7903,x7904,x7905,x7906,x7907,x7902))
% 11.41/11.20 [791]~E(x7911,x7912)+E(f800(x7911,x7913),f800(x7912,x7913))
% 11.41/11.20 [792]~E(x7921,x7922)+E(f800(x7923,x7921),f800(x7923,x7922))
% 11.41/11.20 [793]~E(x7931,x7932)+E(f552(x7931),f552(x7932))
% 11.41/11.20 [794]~E(x7941,x7942)+E(f148(x7941,x7943,x7944,x7945),f148(x7942,x7943,x7944,x7945))
% 11.41/11.20 [795]~E(x7951,x7952)+E(f148(x7953,x7951,x7954,x7955),f148(x7953,x7952,x7954,x7955))
% 11.41/11.20 [796]~E(x7961,x7962)+E(f148(x7963,x7964,x7961,x7965),f148(x7963,x7964,x7962,x7965))
% 11.41/11.20 [797]~E(x7971,x7972)+E(f148(x7973,x7974,x7975,x7971),f148(x7973,x7974,x7975,x7972))
% 11.41/11.20 [798]~E(x7981,x7982)+E(f297(x7981,x7983,x7984),f297(x7982,x7983,x7984))
% 11.41/11.20 [799]~E(x7991,x7992)+E(f297(x7993,x7991,x7994),f297(x7993,x7992,x7994))
% 11.41/11.20 [800]~E(x8001,x8002)+E(f297(x8003,x8004,x8001),f297(x8003,x8004,x8002))
% 11.41/11.20 [801]~E(x8011,x8012)+E(f270(x8011,x8013),f270(x8012,x8013))
% 11.41/11.20 [802]~E(x8021,x8022)+E(f270(x8023,x8021),f270(x8023,x8022))
% 11.41/11.20 [803]~E(x8031,x8032)+E(f531(x8031,x8033,x8034),f531(x8032,x8033,x8034))
% 11.41/11.20 [804]~E(x8041,x8042)+E(f531(x8043,x8041,x8044),f531(x8043,x8042,x8044))
% 11.41/11.20 [805]~E(x8051,x8052)+E(f531(x8053,x8054,x8051),f531(x8053,x8054,x8052))
% 11.41/11.20 [806]~E(x8061,x8062)+E(f705(x8061,x8063,x8064,x8065),f705(x8062,x8063,x8064,x8065))
% 11.41/11.20 [807]~E(x8071,x8072)+E(f705(x8073,x8071,x8074,x8075),f705(x8073,x8072,x8074,x8075))
% 11.41/11.20 [808]~E(x8081,x8082)+E(f705(x8083,x8084,x8081,x8085),f705(x8083,x8084,x8082,x8085))
% 11.41/11.20 [809]~E(x8091,x8092)+E(f705(x8093,x8094,x8095,x8091),f705(x8093,x8094,x8095,x8092))
% 11.41/11.20 [810]~E(x8101,x8102)+E(f764(x8101,x8103,x8104,x8105),f764(x8102,x8103,x8104,x8105))
% 11.41/11.20 [811]~E(x8111,x8112)+E(f764(x8113,x8111,x8114,x8115),f764(x8113,x8112,x8114,x8115))
% 11.41/11.20 [812]~E(x8121,x8122)+E(f764(x8123,x8124,x8121,x8125),f764(x8123,x8124,x8122,x8125))
% 11.41/11.20 [813]~E(x8131,x8132)+E(f764(x8133,x8134,x8135,x8131),f764(x8133,x8134,x8135,x8132))
% 11.41/11.20 [814]~E(x8141,x8142)+E(f430(x8141,x8143,x8144),f430(x8142,x8143,x8144))
% 11.41/11.20 [815]~E(x8151,x8152)+E(f430(x8153,x8151,x8154),f430(x8153,x8152,x8154))
% 11.41/11.20 [816]~E(x8161,x8162)+E(f430(x8163,x8164,x8161),f430(x8163,x8164,x8162))
% 11.41/11.20 [817]~E(x8171,x8172)+E(f741(x8171,x8173,x8174),f741(x8172,x8173,x8174))
% 11.41/11.20 [818]~E(x8181,x8182)+E(f741(x8183,x8181,x8184),f741(x8183,x8182,x8184))
% 11.41/11.20 [819]~E(x8191,x8192)+E(f741(x8193,x8194,x8191),f741(x8193,x8194,x8192))
% 11.41/11.20 [820]~E(x8201,x8202)+E(f849(x8201,x8203),f849(x8202,x8203))
% 11.41/11.20 [821]~E(x8211,x8212)+E(f849(x8213,x8211),f849(x8213,x8212))
% 11.41/11.20 [822]~E(x8221,x8222)+E(f521(x8221,x8223,x8224,x8225,x8226),f521(x8222,x8223,x8224,x8225,x8226))
% 11.41/11.20 [823]~E(x8231,x8232)+E(f521(x8233,x8231,x8234,x8235,x8236),f521(x8233,x8232,x8234,x8235,x8236))
% 11.41/11.20 [824]~E(x8241,x8242)+E(f521(x8243,x8244,x8241,x8245,x8246),f521(x8243,x8244,x8242,x8245,x8246))
% 11.41/11.20 [825]~E(x8251,x8252)+E(f521(x8253,x8254,x8255,x8251,x8256),f521(x8253,x8254,x8255,x8252,x8256))
% 11.41/11.20 [826]~E(x8261,x8262)+E(f521(x8263,x8264,x8265,x8266,x8261),f521(x8263,x8264,x8265,x8266,x8262))
% 11.41/11.20 [827]~E(x8271,x8272)+E(f83(x8271,x8273),f83(x8272,x8273))
% 11.41/11.20 [828]~E(x8281,x8282)+E(f83(x8283,x8281),f83(x8283,x8282))
% 11.41/11.20 [829]~E(x8291,x8292)+E(f486(x8291,x8293),f486(x8292,x8293))
% 11.41/11.20 [830]~E(x8301,x8302)+E(f486(x8303,x8301),f486(x8303,x8302))
% 11.41/11.20 [831]~E(x8311,x8312)+E(f326(x8311,x8313),f326(x8312,x8313))
% 11.41/11.20 [832]~E(x8321,x8322)+E(f326(x8323,x8321),f326(x8323,x8322))
% 11.41/11.20 [833]~E(x8331,x8332)+E(f535(x8331,x8333,x8334,x8335,x8336),f535(x8332,x8333,x8334,x8335,x8336))
% 11.41/11.20 [834]~E(x8341,x8342)+E(f535(x8343,x8341,x8344,x8345,x8346),f535(x8343,x8342,x8344,x8345,x8346))
% 11.41/11.20 [835]~E(x8351,x8352)+E(f535(x8353,x8354,x8351,x8355,x8356),f535(x8353,x8354,x8352,x8355,x8356))
% 11.41/11.20 [836]~E(x8361,x8362)+E(f535(x8363,x8364,x8365,x8361,x8366),f535(x8363,x8364,x8365,x8362,x8366))
% 11.41/11.20 [837]~E(x8371,x8372)+E(f535(x8373,x8374,x8375,x8376,x8371),f535(x8373,x8374,x8375,x8376,x8372))
% 11.41/11.20 [838]~E(x8381,x8382)+E(f517(x8381),f517(x8382))
% 11.41/11.20 [839]~E(x8391,x8392)+E(f479(x8391,x8393,x8394),f479(x8392,x8393,x8394))
% 11.41/11.20 [840]~E(x8401,x8402)+E(f479(x8403,x8401,x8404),f479(x8403,x8402,x8404))
% 11.41/11.20 [841]~E(x8411,x8412)+E(f479(x8413,x8414,x8411),f479(x8413,x8414,x8412))
% 11.41/11.20 [842]~E(x8421,x8422)+E(f694(x8421,x8423),f694(x8422,x8423))
% 11.41/11.20 [843]~E(x8431,x8432)+E(f694(x8433,x8431),f694(x8433,x8432))
% 11.41/11.20 [844]~E(x8441,x8442)+E(f773(x8441,x8443),f773(x8442,x8443))
% 11.41/11.20 [845]~E(x8451,x8452)+E(f773(x8453,x8451),f773(x8453,x8452))
% 11.41/11.20 [846]~E(x8461,x8462)+E(f306(x8461),f306(x8462))
% 11.41/11.20 [847]~E(x8471,x8472)+E(f96(x8471),f96(x8472))
% 11.41/11.20 [848]~E(x8481,x8482)+E(f372(x8481,x8483,x8484,x8485,x8486),f372(x8482,x8483,x8484,x8485,x8486))
% 11.41/11.20 [849]~E(x8491,x8492)+E(f372(x8493,x8491,x8494,x8495,x8496),f372(x8493,x8492,x8494,x8495,x8496))
% 11.41/11.20 [850]~E(x8501,x8502)+E(f372(x8503,x8504,x8501,x8505,x8506),f372(x8503,x8504,x8502,x8505,x8506))
% 11.41/11.20 [851]~E(x8511,x8512)+E(f372(x8513,x8514,x8515,x8511,x8516),f372(x8513,x8514,x8515,x8512,x8516))
% 11.41/11.20 [852]~E(x8521,x8522)+E(f372(x8523,x8524,x8525,x8526,x8521),f372(x8523,x8524,x8525,x8526,x8522))
% 11.41/11.20 [853]~E(x8531,x8532)+E(f382(x8531,x8533),f382(x8532,x8533))
% 11.41/11.20 [854]~E(x8541,x8542)+E(f382(x8543,x8541),f382(x8543,x8542))
% 11.41/11.20 [855]~E(x8551,x8552)+E(f72(x8551,x8553,x8554),f72(x8552,x8553,x8554))
% 11.41/11.20 [856]~E(x8561,x8562)+E(f72(x8563,x8561,x8564),f72(x8563,x8562,x8564))
% 11.41/11.20 [857]~E(x8571,x8572)+E(f72(x8573,x8574,x8571),f72(x8573,x8574,x8572))
% 11.41/11.20 [858]~E(x8581,x8582)+E(f137(x8581,x8583),f137(x8582,x8583))
% 11.41/11.20 [859]~E(x8591,x8592)+E(f137(x8593,x8591),f137(x8593,x8592))
% 11.41/11.20 [860]~E(x8601,x8602)+E(f534(x8601,x8603,x8604,x8605),f534(x8602,x8603,x8604,x8605))
% 11.41/11.20 [861]~E(x8611,x8612)+E(f534(x8613,x8611,x8614,x8615),f534(x8613,x8612,x8614,x8615))
% 11.41/11.20 [862]~E(x8621,x8622)+E(f534(x8623,x8624,x8621,x8625),f534(x8623,x8624,x8622,x8625))
% 11.41/11.20 [863]~E(x8631,x8632)+E(f534(x8633,x8634,x8635,x8631),f534(x8633,x8634,x8635,x8632))
% 11.41/11.20 [864]~E(x8641,x8642)+E(f329(x8641,x8643,x8644,x8645),f329(x8642,x8643,x8644,x8645))
% 11.41/11.20 [865]~E(x8651,x8652)+E(f329(x8653,x8651,x8654,x8655),f329(x8653,x8652,x8654,x8655))
% 11.41/11.20 [866]~E(x8661,x8662)+E(f329(x8663,x8664,x8661,x8665),f329(x8663,x8664,x8662,x8665))
% 11.41/11.20 [867]~E(x8671,x8672)+E(f329(x8673,x8674,x8675,x8671),f329(x8673,x8674,x8675,x8672))
% 11.41/11.20 [868]~E(x8681,x8682)+E(f687(x8681,x8683,x8684),f687(x8682,x8683,x8684))
% 11.41/11.20 [869]~E(x8691,x8692)+E(f687(x8693,x8691,x8694),f687(x8693,x8692,x8694))
% 11.41/11.20 [870]~E(x8701,x8702)+E(f687(x8703,x8704,x8701),f687(x8703,x8704,x8702))
% 11.41/11.20 [871]~E(x8711,x8712)+E(f176(x8711,x8713,x8714,x8715),f176(x8712,x8713,x8714,x8715))
% 11.41/11.20 [872]~E(x8721,x8722)+E(f176(x8723,x8721,x8724,x8725),f176(x8723,x8722,x8724,x8725))
% 11.41/11.20 [873]~E(x8731,x8732)+E(f176(x8733,x8734,x8731,x8735),f176(x8733,x8734,x8732,x8735))
% 11.41/11.20 [874]~E(x8741,x8742)+E(f176(x8743,x8744,x8745,x8741),f176(x8743,x8744,x8745,x8742))
% 11.41/11.20 [875]~E(x8751,x8752)+E(f316(x8751,x8753),f316(x8752,x8753))
% 11.41/11.20 [876]~E(x8761,x8762)+E(f316(x8763,x8761),f316(x8763,x8762))
% 11.41/11.20 [877]~E(x8771,x8772)+E(f560(x8771),f560(x8772))
% 11.41/11.20 [878]~E(x8781,x8782)+E(f256(x8781,x8783,x8784),f256(x8782,x8783,x8784))
% 11.41/11.20 [879]~E(x8791,x8792)+E(f256(x8793,x8791,x8794),f256(x8793,x8792,x8794))
% 11.41/11.20 [880]~E(x8801,x8802)+E(f256(x8803,x8804,x8801),f256(x8803,x8804,x8802))
% 11.41/11.20 [881]~E(x8811,x8812)+E(f255(x8811,x8813),f255(x8812,x8813))
% 11.41/11.20 [882]~E(x8821,x8822)+E(f255(x8823,x8821),f255(x8823,x8822))
% 11.41/11.20 [883]~E(x8831,x8832)+E(f566(x8831,x8833,x8834),f566(x8832,x8833,x8834))
% 11.41/11.20 [884]~E(x8841,x8842)+E(f566(x8843,x8841,x8844),f566(x8843,x8842,x8844))
% 11.41/11.20 [885]~E(x8851,x8852)+E(f566(x8853,x8854,x8851),f566(x8853,x8854,x8852))
% 11.41/11.20 [886]~E(x8861,x8862)+E(f497(x8861,x8863,x8864,x8865,x8866),f497(x8862,x8863,x8864,x8865,x8866))
% 11.41/11.20 [887]~E(x8871,x8872)+E(f497(x8873,x8871,x8874,x8875,x8876),f497(x8873,x8872,x8874,x8875,x8876))
% 11.41/11.20 [888]~E(x8881,x8882)+E(f497(x8883,x8884,x8881,x8885,x8886),f497(x8883,x8884,x8882,x8885,x8886))
% 11.41/11.20 [889]~E(x8891,x8892)+E(f497(x8893,x8894,x8895,x8891,x8896),f497(x8893,x8894,x8895,x8892,x8896))
% 11.41/11.20 [890]~E(x8901,x8902)+E(f497(x8903,x8904,x8905,x8906,x8901),f497(x8903,x8904,x8905,x8906,x8902))
% 11.41/11.20 [891]~E(x8911,x8912)+E(f64(x8911,x8913),f64(x8912,x8913))
% 11.41/11.20 [892]~E(x8921,x8922)+E(f64(x8923,x8921),f64(x8923,x8922))
% 11.41/11.20 [893]~E(x8931,x8932)+E(f119(x8931),f119(x8932))
% 11.41/11.20 [894]~E(x8941,x8942)+E(f481(x8941,x8943,x8944,x8945,x8946),f481(x8942,x8943,x8944,x8945,x8946))
% 11.41/11.20 [895]~E(x8951,x8952)+E(f481(x8953,x8951,x8954,x8955,x8956),f481(x8953,x8952,x8954,x8955,x8956))
% 11.41/11.20 [896]~E(x8961,x8962)+E(f481(x8963,x8964,x8961,x8965,x8966),f481(x8963,x8964,x8962,x8965,x8966))
% 11.41/11.20 [897]~E(x8971,x8972)+E(f481(x8973,x8974,x8975,x8971,x8976),f481(x8973,x8974,x8975,x8972,x8976))
% 11.41/11.20 [898]~E(x8981,x8982)+E(f481(x8983,x8984,x8985,x8986,x8981),f481(x8983,x8984,x8985,x8986,x8982))
% 11.41/11.20 [899]~E(x8991,x8992)+E(f451(x8991,x8993,x8994,x8995,x8996),f451(x8992,x8993,x8994,x8995,x8996))
% 11.41/11.20 [900]~E(x9001,x9002)+E(f451(x9003,x9001,x9004,x9005,x9006),f451(x9003,x9002,x9004,x9005,x9006))
% 11.41/11.20 [901]~E(x9011,x9012)+E(f451(x9013,x9014,x9011,x9015,x9016),f451(x9013,x9014,x9012,x9015,x9016))
% 11.41/11.20 [902]~E(x9021,x9022)+E(f451(x9023,x9024,x9025,x9021,x9026),f451(x9023,x9024,x9025,x9022,x9026))
% 11.41/11.20 [903]~E(x9031,x9032)+E(f451(x9033,x9034,x9035,x9036,x9031),f451(x9033,x9034,x9035,x9036,x9032))
% 11.41/11.20 [904]~E(x9041,x9042)+E(f592(x9041,x9043,x9044),f592(x9042,x9043,x9044))
% 11.41/11.20 [905]~E(x9051,x9052)+E(f592(x9053,x9051,x9054),f592(x9053,x9052,x9054))
% 11.41/11.20 [906]~E(x9061,x9062)+E(f592(x9063,x9064,x9061),f592(x9063,x9064,x9062))
% 11.41/11.20 [907]~E(x9071,x9072)+E(f282(x9071,x9073,x9074,x9075),f282(x9072,x9073,x9074,x9075))
% 11.41/11.20 [908]~E(x9081,x9082)+E(f282(x9083,x9081,x9084,x9085),f282(x9083,x9082,x9084,x9085))
% 11.41/11.20 [909]~E(x9091,x9092)+E(f282(x9093,x9094,x9091,x9095),f282(x9093,x9094,x9092,x9095))
% 11.41/11.20 [910]~E(x9101,x9102)+E(f282(x9103,x9104,x9105,x9101),f282(x9103,x9104,x9105,x9102))
% 11.41/11.20 [911]~E(x9111,x9112)+E(f58(x9111),f58(x9112))
% 11.41/11.20 [912]~E(x9121,x9122)+E(f558(x9121,x9123,x9124,x9125,x9126),f558(x9122,x9123,x9124,x9125,x9126))
% 11.41/11.20 [913]~E(x9131,x9132)+E(f558(x9133,x9131,x9134,x9135,x9136),f558(x9133,x9132,x9134,x9135,x9136))
% 11.41/11.20 [914]~E(x9141,x9142)+E(f558(x9143,x9144,x9141,x9145,x9146),f558(x9143,x9144,x9142,x9145,x9146))
% 11.41/11.20 [915]~E(x9151,x9152)+E(f558(x9153,x9154,x9155,x9151,x9156),f558(x9153,x9154,x9155,x9152,x9156))
% 11.41/11.20 [916]~E(x9161,x9162)+E(f558(x9163,x9164,x9165,x9166,x9161),f558(x9163,x9164,x9165,x9166,x9162))
% 11.41/11.20 [917]~E(x9171,x9172)+E(f476(x9171,x9173,x9174,x9175),f476(x9172,x9173,x9174,x9175))
% 11.41/11.20 [918]~E(x9181,x9182)+E(f476(x9183,x9181,x9184,x9185),f476(x9183,x9182,x9184,x9185))
% 11.41/11.20 [919]~E(x9191,x9192)+E(f476(x9193,x9194,x9191,x9195),f476(x9193,x9194,x9192,x9195))
% 11.41/11.20 [920]~E(x9201,x9202)+E(f476(x9203,x9204,x9205,x9201),f476(x9203,x9204,x9205,x9202))
% 11.41/11.20 [921]~E(x9211,x9212)+E(f227(x9211,x9213,x9214),f227(x9212,x9213,x9214))
% 11.41/11.20 [922]~E(x9221,x9222)+E(f227(x9223,x9221,x9224),f227(x9223,x9222,x9224))
% 11.41/11.20 [923]~E(x9231,x9232)+E(f227(x9233,x9234,x9231),f227(x9233,x9234,x9232))
% 11.41/11.20 [924]~E(x9241,x9242)+E(f225(x9241,x9243,x9244,x9245),f225(x9242,x9243,x9244,x9245))
% 11.41/11.20 [925]~E(x9251,x9252)+E(f225(x9253,x9251,x9254,x9255),f225(x9253,x9252,x9254,x9255))
% 11.41/11.20 [926]~E(x9261,x9262)+E(f225(x9263,x9264,x9261,x9265),f225(x9263,x9264,x9262,x9265))
% 11.41/11.20 [927]~E(x9271,x9272)+E(f225(x9273,x9274,x9275,x9271),f225(x9273,x9274,x9275,x9272))
% 11.41/11.20 [928]~E(x9281,x9282)+E(f672(x9281,x9283,x9284,x9285,x9286),f672(x9282,x9283,x9284,x9285,x9286))
% 11.41/11.20 [929]~E(x9291,x9292)+E(f672(x9293,x9291,x9294,x9295,x9296),f672(x9293,x9292,x9294,x9295,x9296))
% 11.41/11.20 [930]~E(x9301,x9302)+E(f672(x9303,x9304,x9301,x9305,x9306),f672(x9303,x9304,x9302,x9305,x9306))
% 11.41/11.20 [931]~E(x9311,x9312)+E(f672(x9313,x9314,x9315,x9311,x9316),f672(x9313,x9314,x9315,x9312,x9316))
% 11.41/11.20 [932]~E(x9321,x9322)+E(f672(x9323,x9324,x9325,x9326,x9321),f672(x9323,x9324,x9325,x9326,x9322))
% 11.41/11.20 [933]~E(x9331,x9332)+E(f780(x9331,x9333),f780(x9332,x9333))
% 11.41/11.20 [934]~E(x9341,x9342)+E(f780(x9343,x9341),f780(x9343,x9342))
% 11.41/11.20 [935]~E(x9351,x9352)+E(f420(x9351,x9353,x9354,x9355),f420(x9352,x9353,x9354,x9355))
% 11.41/11.20 [936]~E(x9361,x9362)+E(f420(x9363,x9361,x9364,x9365),f420(x9363,x9362,x9364,x9365))
% 11.41/11.20 [937]~E(x9371,x9372)+E(f420(x9373,x9374,x9371,x9375),f420(x9373,x9374,x9372,x9375))
% 11.41/11.20 [938]~E(x9381,x9382)+E(f420(x9383,x9384,x9385,x9381),f420(x9383,x9384,x9385,x9382))
% 11.41/11.20 [939]~E(x9391,x9392)+E(f280(x9391,x9393),f280(x9392,x9393))
% 11.41/11.20 [940]~E(x9401,x9402)+E(f280(x9403,x9401),f280(x9403,x9402))
% 11.41/11.20 [941]~E(x9411,x9412)+E(f626(x9411,x9413,x9414,x9415,x9416,x9417),f626(x9412,x9413,x9414,x9415,x9416,x9417))
% 11.41/11.20 [942]~E(x9421,x9422)+E(f626(x9423,x9421,x9424,x9425,x9426,x9427),f626(x9423,x9422,x9424,x9425,x9426,x9427))
% 11.41/11.20 [943]~E(x9431,x9432)+E(f626(x9433,x9434,x9431,x9435,x9436,x9437),f626(x9433,x9434,x9432,x9435,x9436,x9437))
% 11.41/11.20 [944]~E(x9441,x9442)+E(f626(x9443,x9444,x9445,x9441,x9446,x9447),f626(x9443,x9444,x9445,x9442,x9446,x9447))
% 11.41/11.20 [945]~E(x9451,x9452)+E(f626(x9453,x9454,x9455,x9456,x9451,x9457),f626(x9453,x9454,x9455,x9456,x9452,x9457))
% 11.41/11.20 [946]~E(x9461,x9462)+E(f626(x9463,x9464,x9465,x9466,x9467,x9461),f626(x9463,x9464,x9465,x9466,x9467,x9462))
% 11.41/11.20 [947]~E(x9471,x9472)+E(f204(x9471,x9473),f204(x9472,x9473))
% 11.41/11.20 [948]~E(x9481,x9482)+E(f204(x9483,x9481),f204(x9483,x9482))
% 11.41/11.20 [949]~E(x9491,x9492)+E(f742(x9491,x9493,x9494),f742(x9492,x9493,x9494))
% 11.41/11.20 [950]~E(x9501,x9502)+E(f742(x9503,x9501,x9504),f742(x9503,x9502,x9504))
% 11.41/11.20 [951]~E(x9511,x9512)+E(f742(x9513,x9514,x9511),f742(x9513,x9514,x9512))
% 11.41/11.20 [952]~E(x9521,x9522)+E(f125(x9521,x9523),f125(x9522,x9523))
% 11.41/11.20 [953]~E(x9531,x9532)+E(f125(x9533,x9531),f125(x9533,x9532))
% 11.41/11.20 [954]~E(x9541,x9542)+E(f192(x9541,x9543),f192(x9542,x9543))
% 11.41/11.20 [955]~E(x9551,x9552)+E(f192(x9553,x9551),f192(x9553,x9552))
% 11.41/11.20 [956]~E(x9561,x9562)+E(f234(x9561,x9563,x9564),f234(x9562,x9563,x9564))
% 11.41/11.20 [957]~E(x9571,x9572)+E(f234(x9573,x9571,x9574),f234(x9573,x9572,x9574))
% 11.41/11.20 [958]~E(x9581,x9582)+E(f234(x9583,x9584,x9581),f234(x9583,x9584,x9582))
% 11.41/11.20 [959]~E(x9591,x9592)+E(f126(x9591,x9593),f126(x9592,x9593))
% 11.41/11.20 [960]~E(x9601,x9602)+E(f126(x9603,x9601),f126(x9603,x9602))
% 11.41/11.20 [961]~E(x9611,x9612)+E(f446(x9611,x9613,x9614,x9615),f446(x9612,x9613,x9614,x9615))
% 11.41/11.20 [962]~E(x9621,x9622)+E(f446(x9623,x9621,x9624,x9625),f446(x9623,x9622,x9624,x9625))
% 11.41/11.20 [963]~E(x9631,x9632)+E(f446(x9633,x9634,x9631,x9635),f446(x9633,x9634,x9632,x9635))
% 11.41/11.20 [964]~E(x9641,x9642)+E(f446(x9643,x9644,x9645,x9641),f446(x9643,x9644,x9645,x9642))
% 11.41/11.20 [965]~E(x9651,x9652)+E(f432(x9651,x9653,x9654),f432(x9652,x9653,x9654))
% 11.41/11.20 [966]~E(x9661,x9662)+E(f432(x9663,x9661,x9664),f432(x9663,x9662,x9664))
% 11.41/11.20 [967]~E(x9671,x9672)+E(f432(x9673,x9674,x9671),f432(x9673,x9674,x9672))
% 11.41/11.20 [968]~E(x9681,x9682)+E(f825(x9681,x9683,x9684),f825(x9682,x9683,x9684))
% 11.41/11.20 [969]~E(x9691,x9692)+E(f825(x9693,x9691,x9694),f825(x9693,x9692,x9694))
% 11.41/11.20 [970]~E(x9701,x9702)+E(f825(x9703,x9704,x9701),f825(x9703,x9704,x9702))
% 11.41/11.20 [971]~E(x9711,x9712)+E(f786(x9711),f786(x9712))
% 11.41/11.20 [972]~E(x9721,x9722)+E(f492(x9721,x9723,x9724,x9725,x9726),f492(x9722,x9723,x9724,x9725,x9726))
% 11.41/11.20 [973]~E(x9731,x9732)+E(f492(x9733,x9731,x9734,x9735,x9736),f492(x9733,x9732,x9734,x9735,x9736))
% 11.41/11.20 [974]~E(x9741,x9742)+E(f492(x9743,x9744,x9741,x9745,x9746),f492(x9743,x9744,x9742,x9745,x9746))
% 11.41/11.20 [975]~E(x9751,x9752)+E(f492(x9753,x9754,x9755,x9751,x9756),f492(x9753,x9754,x9755,x9752,x9756))
% 11.41/11.20 [976]~E(x9761,x9762)+E(f492(x9763,x9764,x9765,x9766,x9761),f492(x9763,x9764,x9765,x9766,x9762))
% 11.41/11.20 [977]~E(x9771,x9772)+E(f273(x9771,x9773),f273(x9772,x9773))
% 11.41/11.20 [978]~E(x9781,x9782)+E(f273(x9783,x9781),f273(x9783,x9782))
% 11.41/11.20 [979]~E(x9791,x9792)+E(f390(x9791,x9793),f390(x9792,x9793))
% 11.41/11.20 [980]~E(x9801,x9802)+E(f390(x9803,x9801),f390(x9803,x9802))
% 11.41/11.20 [981]~E(x9811,x9812)+E(f827(x9811,x9813,x9814,x9815),f827(x9812,x9813,x9814,x9815))
% 11.41/11.20 [982]~E(x9821,x9822)+E(f827(x9823,x9821,x9824,x9825),f827(x9823,x9822,x9824,x9825))
% 11.41/11.20 [983]~E(x9831,x9832)+E(f827(x9833,x9834,x9831,x9835),f827(x9833,x9834,x9832,x9835))
% 11.41/11.20 [984]~E(x9841,x9842)+E(f827(x9843,x9844,x9845,x9841),f827(x9843,x9844,x9845,x9842))
% 11.41/11.20 [985]~E(x9851,x9852)+E(f359(x9851,x9853,x9854,x9855),f359(x9852,x9853,x9854,x9855))
% 11.41/11.20 [986]~E(x9861,x9862)+E(f359(x9863,x9861,x9864,x9865),f359(x9863,x9862,x9864,x9865))
% 11.41/11.20 [987]~E(x9871,x9872)+E(f359(x9873,x9874,x9871,x9875),f359(x9873,x9874,x9872,x9875))
% 11.41/11.20 [988]~E(x9881,x9882)+E(f359(x9883,x9884,x9885,x9881),f359(x9883,x9884,x9885,x9882))
% 11.41/11.20 [989]~E(x9891,x9892)+E(f403(x9891,x9893,x9894,x9895,x9896),f403(x9892,x9893,x9894,x9895,x9896))
% 11.41/11.20 [990]~E(x9901,x9902)+E(f403(x9903,x9901,x9904,x9905,x9906),f403(x9903,x9902,x9904,x9905,x9906))
% 11.41/11.20 [991]~E(x9911,x9912)+E(f403(x9913,x9914,x9911,x9915,x9916),f403(x9913,x9914,x9912,x9915,x9916))
% 11.41/11.20 [992]~E(x9921,x9922)+E(f403(x9923,x9924,x9925,x9921,x9926),f403(x9923,x9924,x9925,x9922,x9926))
% 11.41/11.20 [993]~E(x9931,x9932)+E(f403(x9933,x9934,x9935,x9936,x9931),f403(x9933,x9934,x9935,x9936,x9932))
% 11.41/11.20 [994]~E(x9941,x9942)+E(f819(x9941,x9943,x9944),f819(x9942,x9943,x9944))
% 11.41/11.20 [995]~E(x9951,x9952)+E(f819(x9953,x9951,x9954),f819(x9953,x9952,x9954))
% 11.41/11.20 [996]~E(x9961,x9962)+E(f819(x9963,x9964,x9961),f819(x9963,x9964,x9962))
% 11.41/11.20 [997]~E(x9971,x9972)+E(f843(x9971,x9973,x9974),f843(x9972,x9973,x9974))
% 11.41/11.20 [998]~E(x9981,x9982)+E(f843(x9983,x9981,x9984),f843(x9983,x9982,x9984))
% 11.41/11.20 [999]~E(x9991,x9992)+E(f843(x9993,x9994,x9991),f843(x9993,x9994,x9992))
% 11.41/11.20 [1000]~E(x10001,x10002)+E(f826(x10001,x10003,x10004,x10005),f826(x10002,x10003,x10004,x10005))
% 11.41/11.20 [1001]~E(x10011,x10012)+E(f826(x10013,x10011,x10014,x10015),f826(x10013,x10012,x10014,x10015))
% 11.41/11.20 [1002]~E(x10021,x10022)+E(f826(x10023,x10024,x10021,x10025),f826(x10023,x10024,x10022,x10025))
% 11.41/11.20 [1003]~E(x10031,x10032)+E(f826(x10033,x10034,x10035,x10031),f826(x10033,x10034,x10035,x10032))
% 11.41/11.20 [1004]~E(x10041,x10042)+E(f725(x10041,x10043,x10044,x10045,x10046),f725(x10042,x10043,x10044,x10045,x10046))
% 11.41/11.20 [1005]~E(x10051,x10052)+E(f725(x10053,x10051,x10054,x10055,x10056),f725(x10053,x10052,x10054,x10055,x10056))
% 11.41/11.20 [1006]~E(x10061,x10062)+E(f725(x10063,x10064,x10061,x10065,x10066),f725(x10063,x10064,x10062,x10065,x10066))
% 11.41/11.20 [1007]~E(x10071,x10072)+E(f725(x10073,x10074,x10075,x10071,x10076),f725(x10073,x10074,x10075,x10072,x10076))
% 11.41/11.20 [1008]~E(x10081,x10082)+E(f725(x10083,x10084,x10085,x10086,x10081),f725(x10083,x10084,x10085,x10086,x10082))
% 11.41/11.20 [1009]~E(x10091,x10092)+E(f752(x10091,x10093,x10094,x10095,x10096),f752(x10092,x10093,x10094,x10095,x10096))
% 11.41/11.20 [1010]~E(x10101,x10102)+E(f752(x10103,x10101,x10104,x10105,x10106),f752(x10103,x10102,x10104,x10105,x10106))
% 11.41/11.20 [1011]~E(x10111,x10112)+E(f752(x10113,x10114,x10111,x10115,x10116),f752(x10113,x10114,x10112,x10115,x10116))
% 11.41/11.20 [1012]~E(x10121,x10122)+E(f752(x10123,x10124,x10125,x10121,x10126),f752(x10123,x10124,x10125,x10122,x10126))
% 11.41/11.20 [1013]~E(x10131,x10132)+E(f752(x10133,x10134,x10135,x10136,x10131),f752(x10133,x10134,x10135,x10136,x10132))
% 11.41/11.20 [1014]~E(x10141,x10142)+E(f755(x10141,x10143,x10144,x10145),f755(x10142,x10143,x10144,x10145))
% 11.41/11.20 [1015]~E(x10151,x10152)+E(f755(x10153,x10151,x10154,x10155),f755(x10153,x10152,x10154,x10155))
% 11.41/11.20 [1016]~E(x10161,x10162)+E(f755(x10163,x10164,x10161,x10165),f755(x10163,x10164,x10162,x10165))
% 11.41/11.20 [1017]~E(x10171,x10172)+E(f755(x10173,x10174,x10175,x10171),f755(x10173,x10174,x10175,x10172))
% 11.41/11.20 [1018]~E(x10181,x10182)+E(f468(x10181,x10183),f468(x10182,x10183))
% 11.41/11.20 [1019]~E(x10191,x10192)+E(f468(x10193,x10191),f468(x10193,x10192))
% 11.41/11.20 [1020]~E(x10201,x10202)+E(f183(x10201),f183(x10202))
% 11.41/11.20 [1021]~E(x10211,x10212)+E(f212(x10211,x10213,x10214,x10215),f212(x10212,x10213,x10214,x10215))
% 11.41/11.20 [1022]~E(x10221,x10222)+E(f212(x10223,x10221,x10224,x10225),f212(x10223,x10222,x10224,x10225))
% 11.41/11.20 [1023]~E(x10231,x10232)+E(f212(x10233,x10234,x10231,x10235),f212(x10233,x10234,x10232,x10235))
% 11.41/11.20 [1024]~E(x10241,x10242)+E(f212(x10243,x10244,x10245,x10241),f212(x10243,x10244,x10245,x10242))
% 11.41/11.20 [1025]~E(x10251,x10252)+E(f692(x10251,x10253,x10254),f692(x10252,x10253,x10254))
% 11.41/11.20 [1026]~E(x10261,x10262)+E(f692(x10263,x10261,x10264),f692(x10263,x10262,x10264))
% 11.41/11.20 [1027]~E(x10271,x10272)+E(f692(x10273,x10274,x10271),f692(x10273,x10274,x10272))
% 11.41/11.20 [1028]~E(x10281,x10282)+E(f636(x10281,x10283,x10284,x10285,x10286),f636(x10282,x10283,x10284,x10285,x10286))
% 11.41/11.20 [1029]~E(x10291,x10292)+E(f636(x10293,x10291,x10294,x10295,x10296),f636(x10293,x10292,x10294,x10295,x10296))
% 11.41/11.20 [1030]~E(x10301,x10302)+E(f636(x10303,x10304,x10301,x10305,x10306),f636(x10303,x10304,x10302,x10305,x10306))
% 11.41/11.20 [1031]~E(x10311,x10312)+E(f636(x10313,x10314,x10315,x10311,x10316),f636(x10313,x10314,x10315,x10312,x10316))
% 11.41/11.20 [1032]~E(x10321,x10322)+E(f636(x10323,x10324,x10325,x10326,x10321),f636(x10323,x10324,x10325,x10326,x10322))
% 11.41/11.20 [1033]~E(x10331,x10332)+E(f490(x10331,x10333,x10334),f490(x10332,x10333,x10334))
% 11.41/11.20 [1034]~E(x10341,x10342)+E(f490(x10343,x10341,x10344),f490(x10343,x10342,x10344))
% 11.41/11.20 [1035]~E(x10351,x10352)+E(f490(x10353,x10354,x10351),f490(x10353,x10354,x10352))
% 11.41/11.20 [1036]~E(x10361,x10362)+E(f583(x10361,x10363,x10364,x10365,x10366,x10367,x10368),f583(x10362,x10363,x10364,x10365,x10366,x10367,x10368))
% 11.41/11.20 [1037]~E(x10371,x10372)+E(f583(x10373,x10371,x10374,x10375,x10376,x10377,x10378),f583(x10373,x10372,x10374,x10375,x10376,x10377,x10378))
% 11.41/11.20 [1038]~E(x10381,x10382)+E(f583(x10383,x10384,x10381,x10385,x10386,x10387,x10388),f583(x10383,x10384,x10382,x10385,x10386,x10387,x10388))
% 11.41/11.20 [1039]~E(x10391,x10392)+E(f583(x10393,x10394,x10395,x10391,x10396,x10397,x10398),f583(x10393,x10394,x10395,x10392,x10396,x10397,x10398))
% 11.41/11.20 [1040]~E(x10401,x10402)+E(f583(x10403,x10404,x10405,x10406,x10401,x10407,x10408),f583(x10403,x10404,x10405,x10406,x10402,x10407,x10408))
% 11.41/11.20 [1041]~E(x10411,x10412)+E(f583(x10413,x10414,x10415,x10416,x10417,x10411,x10418),f583(x10413,x10414,x10415,x10416,x10417,x10412,x10418))
% 11.41/11.20 [1042]~E(x10421,x10422)+E(f583(x10423,x10424,x10425,x10426,x10427,x10428,x10421),f583(x10423,x10424,x10425,x10426,x10427,x10428,x10422))
% 11.41/11.20 [1043]~E(x10431,x10432)+E(f528(x10431,x10433,x10434,x10435),f528(x10432,x10433,x10434,x10435))
% 11.41/11.20 [1044]~E(x10441,x10442)+E(f528(x10443,x10441,x10444,x10445),f528(x10443,x10442,x10444,x10445))
% 11.41/11.20 [1045]~E(x10451,x10452)+E(f528(x10453,x10454,x10451,x10455),f528(x10453,x10454,x10452,x10455))
% 11.41/11.20 [1046]~E(x10461,x10462)+E(f528(x10463,x10464,x10465,x10461),f528(x10463,x10464,x10465,x10462))
% 11.41/11.20 [1047]~E(x10471,x10472)+E(f544(x10471,x10473,x10474,x10475,x10476),f544(x10472,x10473,x10474,x10475,x10476))
% 11.41/11.20 [1048]~E(x10481,x10482)+E(f544(x10483,x10481,x10484,x10485,x10486),f544(x10483,x10482,x10484,x10485,x10486))
% 11.41/11.20 [1049]~E(x10491,x10492)+E(f544(x10493,x10494,x10491,x10495,x10496),f544(x10493,x10494,x10492,x10495,x10496))
% 11.41/11.20 [1050]~E(x10501,x10502)+E(f544(x10503,x10504,x10505,x10501,x10506),f544(x10503,x10504,x10505,x10502,x10506))
% 11.41/11.20 [1051]~E(x10511,x10512)+E(f544(x10513,x10514,x10515,x10516,x10511),f544(x10513,x10514,x10515,x10516,x10512))
% 11.41/11.20 [1052]~E(x10521,x10522)+E(f771(x10521),f771(x10522))
% 11.41/11.20 [1053]~E(x10531,x10532)+E(f320(x10531),f320(x10532))
% 11.41/11.20 [1054]~E(x10541,x10542)+E(f623(x10541,x10543,x10544),f623(x10542,x10543,x10544))
% 11.41/11.20 [1055]~E(x10551,x10552)+E(f623(x10553,x10551,x10554),f623(x10553,x10552,x10554))
% 11.41/11.20 [1056]~E(x10561,x10562)+E(f623(x10563,x10564,x10561),f623(x10563,x10564,x10562))
% 11.41/11.20 [1057]~E(x10571,x10572)+E(f406(x10571,x10573),f406(x10572,x10573))
% 11.41/11.20 [1058]~E(x10581,x10582)+E(f406(x10583,x10581),f406(x10583,x10582))
% 11.41/11.20 [1059]~E(x10591,x10592)+E(f543(x10591,x10593,x10594,x10595,x10596,x10597,x10598,x10599),f543(x10592,x10593,x10594,x10595,x10596,x10597,x10598,x10599))
% 11.41/11.20 [1060]~E(x10601,x10602)+E(f543(x10603,x10601,x10604,x10605,x10606,x10607,x10608,x10609),f543(x10603,x10602,x10604,x10605,x10606,x10607,x10608,x10609))
% 11.41/11.20 [1061]~E(x10611,x10612)+E(f543(x10613,x10614,x10611,x10615,x10616,x10617,x10618,x10619),f543(x10613,x10614,x10612,x10615,x10616,x10617,x10618,x10619))
% 11.41/11.20 [1062]~E(x10621,x10622)+E(f543(x10623,x10624,x10625,x10621,x10626,x10627,x10628,x10629),f543(x10623,x10624,x10625,x10622,x10626,x10627,x10628,x10629))
% 11.41/11.20 [1063]~E(x10631,x10632)+E(f543(x10633,x10634,x10635,x10636,x10631,x10637,x10638,x10639),f543(x10633,x10634,x10635,x10636,x10632,x10637,x10638,x10639))
% 11.41/11.20 [1064]~E(x10641,x10642)+E(f543(x10643,x10644,x10645,x10646,x10647,x10641,x10648,x10649),f543(x10643,x10644,x10645,x10646,x10647,x10642,x10648,x10649))
% 11.41/11.20 [1065]~E(x10651,x10652)+E(f543(x10653,x10654,x10655,x10656,x10657,x10658,x10651,x10659),f543(x10653,x10654,x10655,x10656,x10657,x10658,x10652,x10659))
% 11.41/11.20 [1066]~E(x10661,x10662)+E(f543(x10663,x10664,x10665,x10666,x10667,x10668,x10669,x10661),f543(x10663,x10664,x10665,x10666,x10667,x10668,x10669,x10662))
% 11.41/11.20 [1067]~E(x10671,x10672)+E(f816(x10671,x10673,x10674),f816(x10672,x10673,x10674))
% 11.41/11.20 [1068]~E(x10681,x10682)+E(f816(x10683,x10681,x10684),f816(x10683,x10682,x10684))
% 11.41/11.20 [1069]~E(x10691,x10692)+E(f816(x10693,x10694,x10691),f816(x10693,x10694,x10692))
% 11.41/11.20 [1070]~E(x10701,x10702)+E(f448(x10701,x10703,x10704,x10705),f448(x10702,x10703,x10704,x10705))
% 11.41/11.20 [1071]~E(x10711,x10712)+E(f448(x10713,x10711,x10714,x10715),f448(x10713,x10712,x10714,x10715))
% 11.41/11.20 [1072]~E(x10721,x10722)+E(f448(x10723,x10724,x10721,x10725),f448(x10723,x10724,x10722,x10725))
% 11.41/11.20 [1073]~E(x10731,x10732)+E(f448(x10733,x10734,x10735,x10731),f448(x10733,x10734,x10735,x10732))
% 11.41/11.20 [1074]~E(x10741,x10742)+E(f523(x10741,x10743,x10744,x10745,x10746),f523(x10742,x10743,x10744,x10745,x10746))
% 11.41/11.20 [1075]~E(x10751,x10752)+E(f523(x10753,x10751,x10754,x10755,x10756),f523(x10753,x10752,x10754,x10755,x10756))
% 11.41/11.20 [1076]~E(x10761,x10762)+E(f523(x10763,x10764,x10761,x10765,x10766),f523(x10763,x10764,x10762,x10765,x10766))
% 11.41/11.20 [1077]~E(x10771,x10772)+E(f523(x10773,x10774,x10775,x10771,x10776),f523(x10773,x10774,x10775,x10772,x10776))
% 11.41/11.20 [1078]~E(x10781,x10782)+E(f523(x10783,x10784,x10785,x10786,x10781),f523(x10783,x10784,x10785,x10786,x10782))
% 11.41/11.20 [1079]~E(x10791,x10792)+E(f810(x10791,x10793,x10794),f810(x10792,x10793,x10794))
% 11.41/11.20 [1080]~E(x10801,x10802)+E(f810(x10803,x10801,x10804),f810(x10803,x10802,x10804))
% 11.41/11.20 [1081]~E(x10811,x10812)+E(f810(x10813,x10814,x10811),f810(x10813,x10814,x10812))
% 11.41/11.20 [1082]~E(x10821,x10822)+E(f573(x10821),f573(x10822))
% 11.41/11.20 [1083]~E(x10831,x10832)+E(f101(x10831,x10833,x10834),f101(x10832,x10833,x10834))
% 11.41/11.20 [1084]~E(x10841,x10842)+E(f101(x10843,x10841,x10844),f101(x10843,x10842,x10844))
% 11.41/11.20 [1085]~E(x10851,x10852)+E(f101(x10853,x10854,x10851),f101(x10853,x10854,x10852))
% 11.41/11.20 [1086]~E(x10861,x10862)+E(f298(x10861,x10863,x10864),f298(x10862,x10863,x10864))
% 11.41/11.20 [1087]~E(x10871,x10872)+E(f298(x10873,x10871,x10874),f298(x10873,x10872,x10874))
% 11.41/11.20 [1088]~E(x10881,x10882)+E(f298(x10883,x10884,x10881),f298(x10883,x10884,x10882))
% 11.41/11.20 [1089]~E(x10891,x10892)+E(f751(x10891,x10893,x10894,x10895),f751(x10892,x10893,x10894,x10895))
% 11.41/11.20 [1090]~E(x10901,x10902)+E(f751(x10903,x10901,x10904,x10905),f751(x10903,x10902,x10904,x10905))
% 11.41/11.20 [1091]~E(x10911,x10912)+E(f751(x10913,x10914,x10911,x10915),f751(x10913,x10914,x10912,x10915))
% 11.41/11.20 [1092]~E(x10921,x10922)+E(f751(x10923,x10924,x10925,x10921),f751(x10923,x10924,x10925,x10922))
% 11.41/11.20 [1093]~E(x10931,x10932)+E(f275(x10931,x10933),f275(x10932,x10933))
% 11.41/11.20 [1094]~E(x10941,x10942)+E(f275(x10943,x10941),f275(x10943,x10942))
% 11.41/11.20 [1095]~E(x10951,x10952)+E(f240(x10951,x10953,x10954,x10955,x10956),f240(x10952,x10953,x10954,x10955,x10956))
% 11.41/11.20 [1096]~E(x10961,x10962)+E(f240(x10963,x10961,x10964,x10965,x10966),f240(x10963,x10962,x10964,x10965,x10966))
% 11.41/11.20 [1097]~E(x10971,x10972)+E(f240(x10973,x10974,x10971,x10975,x10976),f240(x10973,x10974,x10972,x10975,x10976))
% 11.41/11.20 [1098]~E(x10981,x10982)+E(f240(x10983,x10984,x10985,x10981,x10986),f240(x10983,x10984,x10985,x10982,x10986))
% 11.41/11.20 [1099]~E(x10991,x10992)+E(f240(x10993,x10994,x10995,x10996,x10991),f240(x10993,x10994,x10995,x10996,x10992))
% 11.41/11.20 [1100]~E(x11001,x11002)+E(f564(x11001,x11003,x11004),f564(x11002,x11003,x11004))
% 11.41/11.20 [1101]~E(x11011,x11012)+E(f564(x11013,x11011,x11014),f564(x11013,x11012,x11014))
% 11.41/11.20 [1102]~E(x11021,x11022)+E(f564(x11023,x11024,x11021),f564(x11023,x11024,x11022))
% 11.41/11.20 [1103]~E(x11031,x11032)+E(f711(x11031,x11033,x11034,x11035,x11036),f711(x11032,x11033,x11034,x11035,x11036))
% 11.41/11.20 [1104]~E(x11041,x11042)+E(f711(x11043,x11041,x11044,x11045,x11046),f711(x11043,x11042,x11044,x11045,x11046))
% 11.41/11.20 [1105]~E(x11051,x11052)+E(f711(x11053,x11054,x11051,x11055,x11056),f711(x11053,x11054,x11052,x11055,x11056))
% 11.41/11.20 [1106]~E(x11061,x11062)+E(f711(x11063,x11064,x11065,x11061,x11066),f711(x11063,x11064,x11065,x11062,x11066))
% 11.41/11.20 [1107]~E(x11071,x11072)+E(f711(x11073,x11074,x11075,x11076,x11071),f711(x11073,x11074,x11075,x11076,x11072))
% 11.41/11.20 [1108]~E(x11081,x11082)+E(f166(x11081,x11083,x11084),f166(x11082,x11083,x11084))
% 11.41/11.20 [1109]~E(x11091,x11092)+E(f166(x11093,x11091,x11094),f166(x11093,x11092,x11094))
% 11.41/11.20 [1110]~E(x11101,x11102)+E(f166(x11103,x11104,x11101),f166(x11103,x11104,x11102))
% 11.41/11.20 [1111]~E(x11111,x11112)+E(f527(x11111),f527(x11112))
% 11.41/11.20 [1112]~E(x11121,x11122)+E(f290(x11121,x11123),f290(x11122,x11123))
% 11.41/11.20 [1113]~E(x11131,x11132)+E(f290(x11133,x11131),f290(x11133,x11132))
% 11.41/11.20 [1114]~E(x11141,x11142)+E(f834(x11141,x11143,x11144),f834(x11142,x11143,x11144))
% 11.41/11.20 [1115]~E(x11151,x11152)+E(f834(x11153,x11151,x11154),f834(x11153,x11152,x11154))
% 11.41/11.20 [1116]~E(x11161,x11162)+E(f834(x11163,x11164,x11161),f834(x11163,x11164,x11162))
% 11.41/11.20 [1117]~E(x11171,x11172)+E(f728(x11171,x11173,x11174,x11175),f728(x11172,x11173,x11174,x11175))
% 11.41/11.20 [1118]~E(x11181,x11182)+E(f728(x11183,x11181,x11184,x11185),f728(x11183,x11182,x11184,x11185))
% 11.41/11.20 [1119]~E(x11191,x11192)+E(f728(x11193,x11194,x11191,x11195),f728(x11193,x11194,x11192,x11195))
% 11.41/11.20 [1120]~E(x11201,x11202)+E(f728(x11203,x11204,x11205,x11201),f728(x11203,x11204,x11205,x11202))
% 11.41/11.20 [1121]~E(x11211,x11212)+E(f168(x11211,x11213,x11214),f168(x11212,x11213,x11214))
% 11.41/11.20 [1122]~E(x11221,x11222)+E(f168(x11223,x11221,x11224),f168(x11223,x11222,x11224))
% 11.41/11.20 [1123]~E(x11231,x11232)+E(f168(x11233,x11234,x11231),f168(x11233,x11234,x11232))
% 11.41/11.20 [1124]~E(x11241,x11242)+E(f749(x11241,x11243),f749(x11242,x11243))
% 11.41/11.20 [1125]~E(x11251,x11252)+E(f749(x11253,x11251),f749(x11253,x11252))
% 11.41/11.20 [1126]~E(x11261,x11262)+E(f833(x11261,x11263,x11264),f833(x11262,x11263,x11264))
% 11.41/11.20 [1127]~E(x11271,x11272)+E(f833(x11273,x11271,x11274),f833(x11273,x11272,x11274))
% 11.41/11.20 [1128]~E(x11281,x11282)+E(f833(x11283,x11284,x11281),f833(x11283,x11284,x11282))
% 11.41/11.20 [1129]~E(x11291,x11292)+E(f700(x11291,x11293,x11294,x11295),f700(x11292,x11293,x11294,x11295))
% 11.41/11.20 [1130]~E(x11301,x11302)+E(f700(x11303,x11301,x11304,x11305),f700(x11303,x11302,x11304,x11305))
% 11.41/11.20 [1131]~E(x11311,x11312)+E(f700(x11313,x11314,x11311,x11315),f700(x11313,x11314,x11312,x11315))
% 11.41/11.20 [1132]~E(x11321,x11322)+E(f700(x11323,x11324,x11325,x11321),f700(x11323,x11324,x11325,x11322))
% 11.41/11.20 [1133]~E(x11331,x11332)+E(f797(x11331,x11333,x11334),f797(x11332,x11333,x11334))
% 11.41/11.20 [1134]~E(x11341,x11342)+E(f797(x11343,x11341,x11344),f797(x11343,x11342,x11344))
% 11.41/11.20 [1135]~E(x11351,x11352)+E(f797(x11353,x11354,x11351),f797(x11353,x11354,x11352))
% 11.41/11.20 [1136]~E(x11361,x11362)+E(f395(x11361,x11363,x11364,x11365),f395(x11362,x11363,x11364,x11365))
% 11.41/11.20 [1137]~E(x11371,x11372)+E(f395(x11373,x11371,x11374,x11375),f395(x11373,x11372,x11374,x11375))
% 11.41/11.20 [1138]~E(x11381,x11382)+E(f395(x11383,x11384,x11381,x11385),f395(x11383,x11384,x11382,x11385))
% 11.41/11.20 [1139]~E(x11391,x11392)+E(f395(x11393,x11394,x11395,x11391),f395(x11393,x11394,x11395,x11392))
% 11.41/11.20 [1140]~E(x11401,x11402)+E(f625(x11401,x11403,x11404,x11405,x11406,x11407),f625(x11402,x11403,x11404,x11405,x11406,x11407))
% 11.41/11.20 [1141]~E(x11411,x11412)+E(f625(x11413,x11411,x11414,x11415,x11416,x11417),f625(x11413,x11412,x11414,x11415,x11416,x11417))
% 11.41/11.20 [1142]~E(x11421,x11422)+E(f625(x11423,x11424,x11421,x11425,x11426,x11427),f625(x11423,x11424,x11422,x11425,x11426,x11427))
% 11.41/11.20 [1143]~E(x11431,x11432)+E(f625(x11433,x11434,x11435,x11431,x11436,x11437),f625(x11433,x11434,x11435,x11432,x11436,x11437))
% 11.41/11.20 [1144]~E(x11441,x11442)+E(f625(x11443,x11444,x11445,x11446,x11441,x11447),f625(x11443,x11444,x11445,x11446,x11442,x11447))
% 11.41/11.20 [1145]~E(x11451,x11452)+E(f625(x11453,x11454,x11455,x11456,x11457,x11451),f625(x11453,x11454,x11455,x11456,x11457,x11452))
% 11.41/11.20 [1146]~E(x11461,x11462)+E(f478(x11461,x11463,x11464),f478(x11462,x11463,x11464))
% 11.41/11.20 [1147]~E(x11471,x11472)+E(f478(x11473,x11471,x11474),f478(x11473,x11472,x11474))
% 11.41/11.20 [1148]~E(x11481,x11482)+E(f478(x11483,x11484,x11481),f478(x11483,x11484,x11482))
% 11.41/11.20 [1149]~E(x11491,x11492)+E(f761(x11491,x11493,x11494),f761(x11492,x11493,x11494))
% 11.41/11.20 [1150]~E(x11501,x11502)+E(f761(x11503,x11501,x11504),f761(x11503,x11502,x11504))
% 11.41/11.20 [1151]~E(x11511,x11512)+E(f761(x11513,x11514,x11511),f761(x11513,x11514,x11512))
% 11.41/11.20 [1152]~E(x11521,x11522)+E(f97(x11521),f97(x11522))
% 11.41/11.20 [1153]~E(x11531,x11532)+E(f661(x11531,x11533,x11534,x11535),f661(x11532,x11533,x11534,x11535))
% 11.41/11.20 [1154]~E(x11541,x11542)+E(f661(x11543,x11541,x11544,x11545),f661(x11543,x11542,x11544,x11545))
% 11.41/11.20 [1155]~E(x11551,x11552)+E(f661(x11553,x11554,x11551,x11555),f661(x11553,x11554,x11552,x11555))
% 11.41/11.20 [1156]~E(x11561,x11562)+E(f661(x11563,x11564,x11565,x11561),f661(x11563,x11564,x11565,x11562))
% 11.41/11.20 [1157]~E(x11571,x11572)+E(f720(x11571,x11573,x11574,x11575),f720(x11572,x11573,x11574,x11575))
% 11.41/11.20 [1158]~E(x11581,x11582)+E(f720(x11583,x11581,x11584,x11585),f720(x11583,x11582,x11584,x11585))
% 11.41/11.20 [1159]~E(x11591,x11592)+E(f720(x11593,x11594,x11591,x11595),f720(x11593,x11594,x11592,x11595))
% 11.41/11.20 [1160]~E(x11601,x11602)+E(f720(x11603,x11604,x11605,x11601),f720(x11603,x11604,x11605,x11602))
% 11.41/11.20 [1161]~E(x11611,x11612)+E(f698(x11611,x11613,x11614),f698(x11612,x11613,x11614))
% 11.41/11.20 [1162]~E(x11621,x11622)+E(f698(x11623,x11621,x11624),f698(x11623,x11622,x11624))
% 11.41/11.20 [1163]~E(x11631,x11632)+E(f698(x11633,x11634,x11631),f698(x11633,x11634,x11632))
% 11.41/11.20 [1164]~E(x11641,x11642)+E(f263(x11641,x11643,x11644,x11645),f263(x11642,x11643,x11644,x11645))
% 11.41/11.20 [1165]~E(x11651,x11652)+E(f263(x11653,x11651,x11654,x11655),f263(x11653,x11652,x11654,x11655))
% 11.41/11.20 [1166]~E(x11661,x11662)+E(f263(x11663,x11664,x11661,x11665),f263(x11663,x11664,x11662,x11665))
% 11.41/11.20 [1167]~E(x11671,x11672)+E(f263(x11673,x11674,x11675,x11671),f263(x11673,x11674,x11675,x11672))
% 11.41/11.20 [1168]~E(x11681,x11682)+E(f418(x11681,x11683,x11684),f418(x11682,x11683,x11684))
% 11.41/11.20 [1169]~E(x11691,x11692)+E(f418(x11693,x11691,x11694),f418(x11693,x11692,x11694))
% 11.41/11.20 [1170]~E(x11701,x11702)+E(f418(x11703,x11704,x11701),f418(x11703,x11704,x11702))
% 11.41/11.20 [1171]~E(x11711,x11712)+E(f639(x11711,x11713,x11714),f639(x11712,x11713,x11714))
% 11.41/11.20 [1172]~E(x11721,x11722)+E(f639(x11723,x11721,x11724),f639(x11723,x11722,x11724))
% 11.41/11.20 [1173]~E(x11731,x11732)+E(f639(x11733,x11734,x11731),f639(x11733,x11734,x11732))
% 11.41/11.20 [1174]~E(x11741,x11742)+E(f650(x11741,x11743),f650(x11742,x11743))
% 11.41/11.20 [1175]~E(x11751,x11752)+E(f650(x11753,x11751),f650(x11753,x11752))
% 11.41/11.20 [1176]~E(x11761,x11762)+E(f339(x11761,x11763,x11764,x11765),f339(x11762,x11763,x11764,x11765))
% 11.41/11.20 [1177]~E(x11771,x11772)+E(f339(x11773,x11771,x11774,x11775),f339(x11773,x11772,x11774,x11775))
% 11.41/11.20 [1178]~E(x11781,x11782)+E(f339(x11783,x11784,x11781,x11785),f339(x11783,x11784,x11782,x11785))
% 11.41/11.20 [1179]~E(x11791,x11792)+E(f339(x11793,x11794,x11795,x11791),f339(x11793,x11794,x11795,x11792))
% 11.41/11.20 [1180]~E(x11801,x11802)+E(f498(x11801,x11803,x11804,x11805),f498(x11802,x11803,x11804,x11805))
% 11.41/11.20 [1181]~E(x11811,x11812)+E(f498(x11813,x11811,x11814,x11815),f498(x11813,x11812,x11814,x11815))
% 11.41/11.20 [1182]~E(x11821,x11822)+E(f498(x11823,x11824,x11821,x11825),f498(x11823,x11824,x11822,x11825))
% 11.41/11.20 [1183]~E(x11831,x11832)+E(f498(x11833,x11834,x11835,x11831),f498(x11833,x11834,x11835,x11832))
% 11.41/11.20 [1184]~E(x11841,x11842)+E(f845(x11841,x11843,x11844,x11845,x11846,x11847,x11848),f845(x11842,x11843,x11844,x11845,x11846,x11847,x11848))
% 11.41/11.20 [1185]~E(x11851,x11852)+E(f845(x11853,x11851,x11854,x11855,x11856,x11857,x11858),f845(x11853,x11852,x11854,x11855,x11856,x11857,x11858))
% 11.41/11.20 [1186]~E(x11861,x11862)+E(f845(x11863,x11864,x11861,x11865,x11866,x11867,x11868),f845(x11863,x11864,x11862,x11865,x11866,x11867,x11868))
% 11.41/11.20 [1187]~E(x11871,x11872)+E(f845(x11873,x11874,x11875,x11871,x11876,x11877,x11878),f845(x11873,x11874,x11875,x11872,x11876,x11877,x11878))
% 11.41/11.20 [1188]~E(x11881,x11882)+E(f845(x11883,x11884,x11885,x11886,x11881,x11887,x11888),f845(x11883,x11884,x11885,x11886,x11882,x11887,x11888))
% 11.41/11.20 [1189]~E(x11891,x11892)+E(f845(x11893,x11894,x11895,x11896,x11897,x11891,x11898),f845(x11893,x11894,x11895,x11896,x11897,x11892,x11898))
% 11.41/11.20 [1190]~E(x11901,x11902)+E(f845(x11903,x11904,x11905,x11906,x11907,x11908,x11901),f845(x11903,x11904,x11905,x11906,x11907,x11908,x11902))
% 11.41/11.20 [1191]~E(x11911,x11912)+E(f823(x11911,x11913,x11914),f823(x11912,x11913,x11914))
% 11.41/11.20 [1192]~E(x11921,x11922)+E(f823(x11923,x11921,x11924),f823(x11923,x11922,x11924))
% 11.41/11.20 [1193]~E(x11931,x11932)+E(f823(x11933,x11934,x11931),f823(x11933,x11934,x11932))
% 11.41/11.20 [1194]~E(x11941,x11942)+E(f739(x11941),f739(x11942))
% 11.41/11.20 [1195]~E(x11951,x11952)+E(f818(x11951,x11953,x11954),f818(x11952,x11953,x11954))
% 11.41/11.20 [1196]~E(x11961,x11962)+E(f818(x11963,x11961,x11964),f818(x11963,x11962,x11964))
% 11.41/11.20 [1197]~E(x11971,x11972)+E(f818(x11973,x11974,x11971),f818(x11973,x11974,x11972))
% 11.41/11.20 [1198]~E(x11981,x11982)+E(f568(x11981,x11983,x11984,x11985,x11986,x11987,x11988,x11989),f568(x11982,x11983,x11984,x11985,x11986,x11987,x11988,x11989))
% 11.41/11.20 [1199]~E(x11991,x11992)+E(f568(x11993,x11991,x11994,x11995,x11996,x11997,x11998,x11999),f568(x11993,x11992,x11994,x11995,x11996,x11997,x11998,x11999))
% 11.41/11.20 [1200]~E(x12001,x12002)+E(f568(x12003,x12004,x12001,x12005,x12006,x12007,x12008,x12009),f568(x12003,x12004,x12002,x12005,x12006,x12007,x12008,x12009))
% 11.41/11.20 [1201]~E(x12011,x12012)+E(f568(x12013,x12014,x12015,x12011,x12016,x12017,x12018,x12019),f568(x12013,x12014,x12015,x12012,x12016,x12017,x12018,x12019))
% 11.41/11.20 [1202]~E(x12021,x12022)+E(f568(x12023,x12024,x12025,x12026,x12021,x12027,x12028,x12029),f568(x12023,x12024,x12025,x12026,x12022,x12027,x12028,x12029))
% 11.41/11.20 [1203]~E(x12031,x12032)+E(f568(x12033,x12034,x12035,x12036,x12037,x12031,x12038,x12039),f568(x12033,x12034,x12035,x12036,x12037,x12032,x12038,x12039))
% 11.41/11.20 [1204]~E(x12041,x12042)+E(f568(x12043,x12044,x12045,x12046,x12047,x12048,x12041,x12049),f568(x12043,x12044,x12045,x12046,x12047,x12048,x12042,x12049))
% 11.41/11.20 [1205]~E(x12051,x12052)+E(f568(x12053,x12054,x12055,x12056,x12057,x12058,x12059,x12051),f568(x12053,x12054,x12055,x12056,x12057,x12058,x12059,x12052))
% 11.41/11.20 [1206]~E(x12061,x12062)+E(f393(x12061,x12063,x12064,x12065),f393(x12062,x12063,x12064,x12065))
% 11.41/11.20 [1207]~E(x12071,x12072)+E(f393(x12073,x12071,x12074,x12075),f393(x12073,x12072,x12074,x12075))
% 11.41/11.20 [1208]~E(x12081,x12082)+E(f393(x12083,x12084,x12081,x12085),f393(x12083,x12084,x12082,x12085))
% 11.41/11.20 [1209]~E(x12091,x12092)+E(f393(x12093,x12094,x12095,x12091),f393(x12093,x12094,x12095,x12092))
% 11.41/11.20 [1210]~E(x12101,x12102)+E(f381(x12101,x12103,x12104,x12105,x12106),f381(x12102,x12103,x12104,x12105,x12106))
% 11.41/11.20 [1211]~E(x12111,x12112)+E(f381(x12113,x12111,x12114,x12115,x12116),f381(x12113,x12112,x12114,x12115,x12116))
% 11.41/11.20 [1212]~E(x12121,x12122)+E(f381(x12123,x12124,x12121,x12125,x12126),f381(x12123,x12124,x12122,x12125,x12126))
% 11.41/11.20 [1213]~E(x12131,x12132)+E(f381(x12133,x12134,x12135,x12131,x12136),f381(x12133,x12134,x12135,x12132,x12136))
% 11.41/11.20 [1214]~E(x12141,x12142)+E(f381(x12143,x12144,x12145,x12146,x12141),f381(x12143,x12144,x12145,x12146,x12142))
% 11.41/11.20 [1215]~E(x12151,x12152)+E(f438(x12151,x12153,x12154,x12155),f438(x12152,x12153,x12154,x12155))
% 11.41/11.20 [1216]~E(x12161,x12162)+E(f438(x12163,x12161,x12164,x12165),f438(x12163,x12162,x12164,x12165))
% 11.41/11.20 [1217]~E(x12171,x12172)+E(f438(x12173,x12174,x12171,x12175),f438(x12173,x12174,x12172,x12175))
% 11.41/11.20 [1218]~E(x12181,x12182)+E(f438(x12183,x12184,x12185,x12181),f438(x12183,x12184,x12185,x12182))
% 11.41/11.20 [1219]~E(x12191,x12192)+E(f753(x12191,x12193,x12194,x12195),f753(x12192,x12193,x12194,x12195))
% 11.41/11.20 [1220]~E(x12201,x12202)+E(f753(x12203,x12201,x12204,x12205),f753(x12203,x12202,x12204,x12205))
% 11.41/11.20 [1221]~E(x12211,x12212)+E(f753(x12213,x12214,x12211,x12215),f753(x12213,x12214,x12212,x12215))
% 11.41/11.20 [1222]~E(x12221,x12222)+E(f753(x12223,x12224,x12225,x12221),f753(x12223,x12224,x12225,x12222))
% 11.41/11.20 [1223]~E(x12231,x12232)+E(f530(x12231,x12233,x12234,x12235),f530(x12232,x12233,x12234,x12235))
% 11.41/11.20 [1224]~E(x12241,x12242)+E(f530(x12243,x12241,x12244,x12245),f530(x12243,x12242,x12244,x12245))
% 11.41/11.20 [1225]~E(x12251,x12252)+E(f530(x12253,x12254,x12251,x12255),f530(x12253,x12254,x12252,x12255))
% 11.41/11.20 [1226]~E(x12261,x12262)+E(f530(x12263,x12264,x12265,x12261),f530(x12263,x12264,x12265,x12262))
% 11.41/11.20 [1227]~E(x12271,x12272)+E(f294(x12271,x12273),f294(x12272,x12273))
% 11.41/11.20 [1228]~E(x12281,x12282)+E(f294(x12283,x12281),f294(x12283,x12282))
% 11.41/11.20 [1229]~E(x12291,x12292)+E(f836(x12291,x12293,x12294),f836(x12292,x12293,x12294))
% 11.41/11.20 [1230]~E(x12301,x12302)+E(f836(x12303,x12301,x12304),f836(x12303,x12302,x12304))
% 11.41/11.20 [1231]~E(x12311,x12312)+E(f836(x12313,x12314,x12311),f836(x12313,x12314,x12312))
% 11.41/11.20 [1232]~E(x12321,x12322)+E(f399(x12321,x12323,x12324,x12325,x12326),f399(x12322,x12323,x12324,x12325,x12326))
% 11.41/11.20 [1233]~E(x12331,x12332)+E(f399(x12333,x12331,x12334,x12335,x12336),f399(x12333,x12332,x12334,x12335,x12336))
% 11.41/11.20 [1234]~E(x12341,x12342)+E(f399(x12343,x12344,x12341,x12345,x12346),f399(x12343,x12344,x12342,x12345,x12346))
% 11.41/11.20 [1235]~E(x12351,x12352)+E(f399(x12353,x12354,x12355,x12351,x12356),f399(x12353,x12354,x12355,x12352,x12356))
% 11.41/11.20 [1236]~E(x12361,x12362)+E(f399(x12363,x12364,x12365,x12366,x12361),f399(x12363,x12364,x12365,x12366,x12362))
% 11.41/11.20 [1237]~E(x12371,x12372)+E(f413(x12371,x12373),f413(x12372,x12373))
% 11.41/11.20 [1238]~E(x12381,x12382)+E(f413(x12383,x12381),f413(x12383,x12382))
% 11.41/11.20 [1239]~E(x12391,x12392)+E(f685(x12391,x12393,x12394),f685(x12392,x12393,x12394))
% 11.41/11.20 [1240]~E(x12401,x12402)+E(f685(x12403,x12401,x12404),f685(x12403,x12402,x12404))
% 11.41/11.20 [1241]~E(x12411,x12412)+E(f685(x12413,x12414,x12411),f685(x12413,x12414,x12412))
% 11.41/11.20 [1242]~E(x12421,x12422)+E(f460(x12421,x12423,x12424,x12425,x12426,x12427,x12428),f460(x12422,x12423,x12424,x12425,x12426,x12427,x12428))
% 11.41/11.20 [1243]~E(x12431,x12432)+E(f460(x12433,x12431,x12434,x12435,x12436,x12437,x12438),f460(x12433,x12432,x12434,x12435,x12436,x12437,x12438))
% 11.41/11.20 [1244]~E(x12441,x12442)+E(f460(x12443,x12444,x12441,x12445,x12446,x12447,x12448),f460(x12443,x12444,x12442,x12445,x12446,x12447,x12448))
% 11.41/11.20 [1245]~E(x12451,x12452)+E(f460(x12453,x12454,x12455,x12451,x12456,x12457,x12458),f460(x12453,x12454,x12455,x12452,x12456,x12457,x12458))
% 11.41/11.20 [1246]~E(x12461,x12462)+E(f460(x12463,x12464,x12465,x12466,x12461,x12467,x12468),f460(x12463,x12464,x12465,x12466,x12462,x12467,x12468))
% 11.41/11.20 [1247]~E(x12471,x12472)+E(f460(x12473,x12474,x12475,x12476,x12477,x12471,x12478),f460(x12473,x12474,x12475,x12476,x12477,x12472,x12478))
% 11.41/11.20 [1248]~E(x12481,x12482)+E(f460(x12483,x12484,x12485,x12486,x12487,x12488,x12481),f460(x12483,x12484,x12485,x12486,x12487,x12488,x12482))
% 11.41/11.20 [1249]~E(x12491,x12492)+E(f743(x12491,x12493,x12494,x12495,x12496),f743(x12492,x12493,x12494,x12495,x12496))
% 11.41/11.20 [1250]~E(x12501,x12502)+E(f743(x12503,x12501,x12504,x12505,x12506),f743(x12503,x12502,x12504,x12505,x12506))
% 11.41/11.20 [1251]~E(x12511,x12512)+E(f743(x12513,x12514,x12511,x12515,x12516),f743(x12513,x12514,x12512,x12515,x12516))
% 11.41/11.20 [1252]~E(x12521,x12522)+E(f743(x12523,x12524,x12525,x12521,x12526),f743(x12523,x12524,x12525,x12522,x12526))
% 11.41/11.20 [1253]~E(x12531,x12532)+E(f743(x12533,x12534,x12535,x12536,x12531),f743(x12533,x12534,x12535,x12536,x12532))
% 11.41/11.20 [1254]~E(x12541,x12542)+E(f620(x12541,x12543,x12544,x12545),f620(x12542,x12543,x12544,x12545))
% 11.41/11.20 [1255]~E(x12551,x12552)+E(f620(x12553,x12551,x12554,x12555),f620(x12553,x12552,x12554,x12555))
% 11.41/11.20 [1256]~E(x12561,x12562)+E(f620(x12563,x12564,x12561,x12565),f620(x12563,x12564,x12562,x12565))
% 11.41/11.20 [1257]~E(x12571,x12572)+E(f620(x12573,x12574,x12575,x12571),f620(x12573,x12574,x12575,x12572))
% 11.41/11.20 [1258]~E(x12581,x12582)+E(f371(x12581,x12583,x12584,x12585,x12586),f371(x12582,x12583,x12584,x12585,x12586))
% 11.41/11.20 [1259]~E(x12591,x12592)+E(f371(x12593,x12591,x12594,x12595,x12596),f371(x12593,x12592,x12594,x12595,x12596))
% 11.41/11.20 [1260]~E(x12601,x12602)+E(f371(x12603,x12604,x12601,x12605,x12606),f371(x12603,x12604,x12602,x12605,x12606))
% 11.41/11.20 [1261]~E(x12611,x12612)+E(f371(x12613,x12614,x12615,x12611,x12616),f371(x12613,x12614,x12615,x12612,x12616))
% 11.41/11.20 [1262]~E(x12621,x12622)+E(f371(x12623,x12624,x12625,x12626,x12621),f371(x12623,x12624,x12625,x12626,x12622))
% 11.41/11.20 [1263]~E(x12631,x12632)+E(f279(x12631,x12633,x12634),f279(x12632,x12633,x12634))
% 11.41/11.20 [1264]~E(x12641,x12642)+E(f279(x12643,x12641,x12644),f279(x12643,x12642,x12644))
% 11.41/11.20 [1265]~E(x12651,x12652)+E(f279(x12653,x12654,x12651),f279(x12653,x12654,x12652))
% 11.41/11.20 [1266]~E(x12661,x12662)+E(f563(x12661,x12663,x12664),f563(x12662,x12663,x12664))
% 11.41/11.20 [1267]~E(x12671,x12672)+E(f563(x12673,x12671,x12674),f563(x12673,x12672,x12674))
% 11.41/11.20 [1268]~E(x12681,x12682)+E(f563(x12683,x12684,x12681),f563(x12683,x12684,x12682))
% 11.41/11.20 [1269]~E(x12691,x12692)+E(f681(x12691,x12693,x12694,x12695,x12696,x12697,x12698),f681(x12692,x12693,x12694,x12695,x12696,x12697,x12698))
% 11.41/11.20 [1270]~E(x12701,x12702)+E(f681(x12703,x12701,x12704,x12705,x12706,x12707,x12708),f681(x12703,x12702,x12704,x12705,x12706,x12707,x12708))
% 11.41/11.20 [1271]~E(x12711,x12712)+E(f681(x12713,x12714,x12711,x12715,x12716,x12717,x12718),f681(x12713,x12714,x12712,x12715,x12716,x12717,x12718))
% 11.41/11.20 [1272]~E(x12721,x12722)+E(f681(x12723,x12724,x12725,x12721,x12726,x12727,x12728),f681(x12723,x12724,x12725,x12722,x12726,x12727,x12728))
% 11.41/11.20 [1273]~E(x12731,x12732)+E(f681(x12733,x12734,x12735,x12736,x12731,x12737,x12738),f681(x12733,x12734,x12735,x12736,x12732,x12737,x12738))
% 11.41/11.20 [1274]~E(x12741,x12742)+E(f681(x12743,x12744,x12745,x12746,x12747,x12741,x12748),f681(x12743,x12744,x12745,x12746,x12747,x12742,x12748))
% 11.41/11.20 [1275]~E(x12751,x12752)+E(f681(x12753,x12754,x12755,x12756,x12757,x12758,x12751),f681(x12753,x12754,x12755,x12756,x12757,x12758,x12752))
% 11.41/11.20 [1276]~E(x12761,x12762)+E(f655(x12761,x12763,x12764,x12765,x12766),f655(x12762,x12763,x12764,x12765,x12766))
% 11.41/11.20 [1277]~E(x12771,x12772)+E(f655(x12773,x12771,x12774,x12775,x12776),f655(x12773,x12772,x12774,x12775,x12776))
% 11.41/11.20 [1278]~E(x12781,x12782)+E(f655(x12783,x12784,x12781,x12785,x12786),f655(x12783,x12784,x12782,x12785,x12786))
% 11.41/11.20 [1279]~E(x12791,x12792)+E(f655(x12793,x12794,x12795,x12791,x12796),f655(x12793,x12794,x12795,x12792,x12796))
% 11.41/11.20 [1280]~E(x12801,x12802)+E(f655(x12803,x12804,x12805,x12806,x12801),f655(x12803,x12804,x12805,x12806,x12802))
% 11.41/11.20 [1281]~E(x12811,x12812)+E(f634(x12811,x12813,x12814,x12815),f634(x12812,x12813,x12814,x12815))
% 11.41/11.20 [1282]~E(x12821,x12822)+E(f634(x12823,x12821,x12824,x12825),f634(x12823,x12822,x12824,x12825))
% 11.41/11.20 [1283]~E(x12831,x12832)+E(f634(x12833,x12834,x12831,x12835),f634(x12833,x12834,x12832,x12835))
% 11.41/11.20 [1284]~E(x12841,x12842)+E(f634(x12843,x12844,x12845,x12841),f634(x12843,x12844,x12845,x12842))
% 11.41/11.20 [1285]~E(x12851,x12852)+E(f809(x12851,x12853,x12854),f809(x12852,x12853,x12854))
% 11.41/11.20 [1286]~E(x12861,x12862)+E(f809(x12863,x12861,x12864),f809(x12863,x12862,x12864))
% 11.41/11.20 [1287]~E(x12871,x12872)+E(f809(x12873,x12874,x12871),f809(x12873,x12874,x12872))
% 11.41/11.20 [1288]~E(x12881,x12882)+E(f317(x12881,x12883,x12884),f317(x12882,x12883,x12884))
% 11.41/11.20 [1289]~E(x12891,x12892)+E(f317(x12893,x12891,x12894),f317(x12893,x12892,x12894))
% 11.41/11.20 [1290]~E(x12901,x12902)+E(f317(x12903,x12904,x12901),f317(x12903,x12904,x12902))
% 11.41/11.20 [1291]~E(x12911,x12912)+E(f733(x12911,x12913),f733(x12912,x12913))
% 11.41/11.20 [1292]~E(x12921,x12922)+E(f733(x12923,x12921),f733(x12923,x12922))
% 11.41/11.20 [1293]~E(x12931,x12932)+E(f690(x12931,x12933,x12934,x12935,x12936,x12937,x12938,x12939),f690(x12932,x12933,x12934,x12935,x12936,x12937,x12938,x12939))
% 11.41/11.20 [1294]~E(x12941,x12942)+E(f690(x12943,x12941,x12944,x12945,x12946,x12947,x12948,x12949),f690(x12943,x12942,x12944,x12945,x12946,x12947,x12948,x12949))
% 11.41/11.20 [1295]~E(x12951,x12952)+E(f690(x12953,x12954,x12951,x12955,x12956,x12957,x12958,x12959),f690(x12953,x12954,x12952,x12955,x12956,x12957,x12958,x12959))
% 11.41/11.20 [1296]~E(x12961,x12962)+E(f690(x12963,x12964,x12965,x12961,x12966,x12967,x12968,x12969),f690(x12963,x12964,x12965,x12962,x12966,x12967,x12968,x12969))
% 11.41/11.20 [1297]~E(x12971,x12972)+E(f690(x12973,x12974,x12975,x12976,x12971,x12977,x12978,x12979),f690(x12973,x12974,x12975,x12976,x12972,x12977,x12978,x12979))
% 11.41/11.20 [1298]~E(x12981,x12982)+E(f690(x12983,x12984,x12985,x12986,x12987,x12981,x12988,x12989),f690(x12983,x12984,x12985,x12986,x12987,x12982,x12988,x12989))
% 11.41/11.20 [1299]~E(x12991,x12992)+E(f690(x12993,x12994,x12995,x12996,x12997,x12998,x12991,x12999),f690(x12993,x12994,x12995,x12996,x12997,x12998,x12992,x12999))
% 11.41/11.20 [1300]~E(x13001,x13002)+E(f690(x13003,x13004,x13005,x13006,x13007,x13008,x13009,x13001),f690(x13003,x13004,x13005,x13006,x13007,x13008,x13009,x13002))
% 11.41/11.20 [1301]~E(x13011,x13012)+E(f747(x13011,x13013,x13014,x13015,x13016),f747(x13012,x13013,x13014,x13015,x13016))
% 11.41/11.20 [1302]~E(x13021,x13022)+E(f747(x13023,x13021,x13024,x13025,x13026),f747(x13023,x13022,x13024,x13025,x13026))
% 11.41/11.20 [1303]~E(x13031,x13032)+E(f747(x13033,x13034,x13031,x13035,x13036),f747(x13033,x13034,x13032,x13035,x13036))
% 11.41/11.20 [1304]~E(x13041,x13042)+E(f747(x13043,x13044,x13045,x13041,x13046),f747(x13043,x13044,x13045,x13042,x13046))
% 11.41/11.20 [1305]~E(x13051,x13052)+E(f747(x13053,x13054,x13055,x13056,x13051),f747(x13053,x13054,x13055,x13056,x13052))
% 11.41/11.20 [1306]~E(x13061,x13062)+E(f640(x13061,x13063,x13064),f640(x13062,x13063,x13064))
% 11.41/11.20 [1307]~E(x13071,x13072)+E(f640(x13073,x13071,x13074),f640(x13073,x13072,x13074))
% 11.41/11.20 [1308]~E(x13081,x13082)+E(f640(x13083,x13084,x13081),f640(x13083,x13084,x13082))
% 11.41/11.20 [1309]~E(x13091,x13092)+E(f274(x13091),f274(x13092))
% 11.41/11.20 [1310]~E(x13101,x13102)+E(f216(x13101,x13103,x13104,x13105,x13106,x13107,x13108),f216(x13102,x13103,x13104,x13105,x13106,x13107,x13108))
% 11.41/11.20 [1311]~E(x13111,x13112)+E(f216(x13113,x13111,x13114,x13115,x13116,x13117,x13118),f216(x13113,x13112,x13114,x13115,x13116,x13117,x13118))
% 11.41/11.20 [1312]~E(x13121,x13122)+E(f216(x13123,x13124,x13121,x13125,x13126,x13127,x13128),f216(x13123,x13124,x13122,x13125,x13126,x13127,x13128))
% 11.41/11.20 [1313]~E(x13131,x13132)+E(f216(x13133,x13134,x13135,x13131,x13136,x13137,x13138),f216(x13133,x13134,x13135,x13132,x13136,x13137,x13138))
% 11.41/11.20 [1314]~E(x13141,x13142)+E(f216(x13143,x13144,x13145,x13146,x13141,x13147,x13148),f216(x13143,x13144,x13145,x13146,x13142,x13147,x13148))
% 11.41/11.20 [1315]~E(x13151,x13152)+E(f216(x13153,x13154,x13155,x13156,x13157,x13151,x13158),f216(x13153,x13154,x13155,x13156,x13157,x13152,x13158))
% 11.41/11.20 [1316]~E(x13161,x13162)+E(f216(x13163,x13164,x13165,x13166,x13167,x13168,x13161),f216(x13163,x13164,x13165,x13166,x13167,x13168,x13162))
% 11.41/11.20 [1317]~E(x13171,x13172)+E(f203(x13171,x13173,x13174,x13175),f203(x13172,x13173,x13174,x13175))
% 11.41/11.20 [1318]~E(x13181,x13182)+E(f203(x13183,x13181,x13184,x13185),f203(x13183,x13182,x13184,x13185))
% 11.41/11.20 [1319]~E(x13191,x13192)+E(f203(x13193,x13194,x13191,x13195),f203(x13193,x13194,x13192,x13195))
% 11.41/11.20 [1320]~E(x13201,x13202)+E(f203(x13203,x13204,x13205,x13201),f203(x13203,x13204,x13205,x13202))
% 11.41/11.20 [1321]~E(x13211,x13212)+E(f181(x13211,x13213,x13214),f181(x13212,x13213,x13214))
% 11.41/11.20 [1322]~E(x13221,x13222)+E(f181(x13223,x13221,x13224),f181(x13223,x13222,x13224))
% 11.41/11.20 [1323]~E(x13231,x13232)+E(f181(x13233,x13234,x13231),f181(x13233,x13234,x13232))
% 11.41/11.20 [1324]~E(x13241,x13242)+E(f416(x13241,x13243,x13244),f416(x13242,x13243,x13244))
% 11.41/11.20 [1325]~E(x13251,x13252)+E(f416(x13253,x13251,x13254),f416(x13253,x13252,x13254))
% 11.41/11.20 [1326]~E(x13261,x13262)+E(f416(x13263,x13264,x13261),f416(x13263,x13264,x13262))
% 11.41/11.20 [1327]~E(x13271,x13272)+E(f235(x13271,x13273,x13274,x13275),f235(x13272,x13273,x13274,x13275))
% 11.41/11.20 [1328]~E(x13281,x13282)+E(f235(x13283,x13281,x13284,x13285),f235(x13283,x13282,x13284,x13285))
% 11.41/11.20 [1329]~E(x13291,x13292)+E(f235(x13293,x13294,x13291,x13295),f235(x13293,x13294,x13292,x13295))
% 11.41/11.20 [1330]~E(x13301,x13302)+E(f235(x13303,x13304,x13305,x13301),f235(x13303,x13304,x13305,x13302))
% 11.41/11.20 [1331]~E(x13311,x13312)+E(f177(x13311,x13313,x13314),f177(x13312,x13313,x13314))
% 11.41/11.20 [1332]~E(x13321,x13322)+E(f177(x13323,x13321,x13324),f177(x13323,x13322,x13324))
% 11.41/11.20 [1333]~E(x13331,x13332)+E(f177(x13333,x13334,x13331),f177(x13333,x13334,x13332))
% 11.41/11.20 [1334]~E(x13341,x13342)+E(f340(x13341,x13343,x13344),f340(x13342,x13343,x13344))
% 11.41/11.20 [1335]~E(x13351,x13352)+E(f340(x13353,x13351,x13354),f340(x13353,x13352,x13354))
% 11.41/11.20 [1336]~E(x13361,x13362)+E(f340(x13363,x13364,x13361),f340(x13363,x13364,x13362))
% 11.41/11.20 [1337]~E(x13371,x13372)+E(f68(x13371,x13373),f68(x13372,x13373))
% 11.41/11.20 [1338]~E(x13381,x13382)+E(f68(x13383,x13381),f68(x13383,x13382))
% 11.41/11.20 [1339]~E(x13391,x13392)+E(f319(x13391,x13393,x13394),f319(x13392,x13393,x13394))
% 11.41/11.20 [1340]~E(x13401,x13402)+E(f319(x13403,x13401,x13404),f319(x13403,x13402,x13404))
% 11.41/11.20 [1341]~E(x13411,x13412)+E(f319(x13413,x13414,x13411),f319(x13413,x13414,x13412))
% 11.41/11.20 [1342]~E(x13421,x13422)+E(f394(x13421,x13423,x13424,x13425,x13426),f394(x13422,x13423,x13424,x13425,x13426))
% 11.41/11.20 [1343]~E(x13431,x13432)+E(f394(x13433,x13431,x13434,x13435,x13436),f394(x13433,x13432,x13434,x13435,x13436))
% 11.41/11.20 [1344]~E(x13441,x13442)+E(f394(x13443,x13444,x13441,x13445,x13446),f394(x13443,x13444,x13442,x13445,x13446))
% 11.41/11.20 [1345]~E(x13451,x13452)+E(f394(x13453,x13454,x13455,x13451,x13456),f394(x13453,x13454,x13455,x13452,x13456))
% 11.41/11.20 [1346]~E(x13461,x13462)+E(f394(x13463,x13464,x13465,x13466,x13461),f394(x13463,x13464,x13465,x13466,x13462))
% 11.41/11.20 [1347]~E(x13471,x13472)+E(f812(x13471,x13473,x13474),f812(x13472,x13473,x13474))
% 11.41/11.20 [1348]~E(x13481,x13482)+E(f812(x13483,x13481,x13484),f812(x13483,x13482,x13484))
% 11.41/11.20 [1349]~E(x13491,x13492)+E(f812(x13493,x13494,x13491),f812(x13493,x13494,x13492))
% 11.41/11.20 [1350]~E(x13501,x13502)+E(f401(x13501,x13503,x13504,x13505,x13506),f401(x13502,x13503,x13504,x13505,x13506))
% 11.41/11.20 [1351]~E(x13511,x13512)+E(f401(x13513,x13511,x13514,x13515,x13516),f401(x13513,x13512,x13514,x13515,x13516))
% 11.41/11.20 [1352]~E(x13521,x13522)+E(f401(x13523,x13524,x13521,x13525,x13526),f401(x13523,x13524,x13522,x13525,x13526))
% 11.41/11.20 [1353]~E(x13531,x13532)+E(f401(x13533,x13534,x13535,x13531,x13536),f401(x13533,x13534,x13535,x13532,x13536))
% 11.41/11.20 [1354]~E(x13541,x13542)+E(f401(x13543,x13544,x13545,x13546,x13541),f401(x13543,x13544,x13545,x13546,x13542))
% 11.41/11.20 [1355]~E(x13551,x13552)+E(f364(x13551,x13553),f364(x13552,x13553))
% 11.41/11.20 [1356]~E(x13561,x13562)+E(f364(x13563,x13561),f364(x13563,x13562))
% 11.41/11.20 [1357]~E(x13571,x13572)+E(f410(x13571,x13573,x13574,x13575),f410(x13572,x13573,x13574,x13575))
% 11.41/11.20 [1358]~E(x13581,x13582)+E(f410(x13583,x13581,x13584,x13585),f410(x13583,x13582,x13584,x13585))
% 11.41/11.20 [1359]~E(x13591,x13592)+E(f410(x13593,x13594,x13591,x13595),f410(x13593,x13594,x13592,x13595))
% 11.41/11.20 [1360]~E(x13601,x13602)+E(f410(x13603,x13604,x13605,x13601),f410(x13603,x13604,x13605,x13602))
% 11.41/11.20 [1361]~E(x13611,x13612)+E(f351(x13611),f351(x13612))
% 11.41/11.20 [1362]~E(x13621,x13622)+E(f744(x13621,x13623,x13624,x13625,x13626),f744(x13622,x13623,x13624,x13625,x13626))
% 11.41/11.20 [1363]~E(x13631,x13632)+E(f744(x13633,x13631,x13634,x13635,x13636),f744(x13633,x13632,x13634,x13635,x13636))
% 11.41/11.20 [1364]~E(x13641,x13642)+E(f744(x13643,x13644,x13641,x13645,x13646),f744(x13643,x13644,x13642,x13645,x13646))
% 11.41/11.20 [1365]~E(x13651,x13652)+E(f744(x13653,x13654,x13655,x13651,x13656),f744(x13653,x13654,x13655,x13652,x13656))
% 11.41/11.20 [1366]~E(x13661,x13662)+E(f744(x13663,x13664,x13665,x13666,x13661),f744(x13663,x13664,x13665,x13666,x13662))
% 11.41/11.20 [1367]~E(x13671,x13672)+E(f577(x13671,x13673),f577(x13672,x13673))
% 11.41/11.20 [1368]~E(x13681,x13682)+E(f577(x13683,x13681),f577(x13683,x13682))
% 11.41/11.20 [1369]~E(x13691,x13692)+E(f778(x13691,x13693),f778(x13692,x13693))
% 11.41/11.20 [1370]~E(x13701,x13702)+E(f778(x13703,x13701),f778(x13703,x13702))
% 11.41/11.20 [1371]~E(x13711,x13712)+E(f129(x13711),f129(x13712))
% 11.41/11.20 [1372]~E(x13721,x13722)+E(f447(x13721,x13723,x13724,x13725,x13726,x13727),f447(x13722,x13723,x13724,x13725,x13726,x13727))
% 11.41/11.20 [1373]~E(x13731,x13732)+E(f447(x13733,x13731,x13734,x13735,x13736,x13737),f447(x13733,x13732,x13734,x13735,x13736,x13737))
% 11.41/11.20 [1374]~E(x13741,x13742)+E(f447(x13743,x13744,x13741,x13745,x13746,x13747),f447(x13743,x13744,x13742,x13745,x13746,x13747))
% 11.41/11.20 [1375]~E(x13751,x13752)+E(f447(x13753,x13754,x13755,x13751,x13756,x13757),f447(x13753,x13754,x13755,x13752,x13756,x13757))
% 11.41/11.20 [1376]~E(x13761,x13762)+E(f447(x13763,x13764,x13765,x13766,x13761,x13767),f447(x13763,x13764,x13765,x13766,x13762,x13767))
% 11.41/11.20 [1377]~E(x13771,x13772)+E(f447(x13773,x13774,x13775,x13776,x13777,x13771),f447(x13773,x13774,x13775,x13776,x13777,x13772))
% 11.41/11.20 [1378]~E(x13781,x13782)+E(f820(x13781,x13783,x13784),f820(x13782,x13783,x13784))
% 11.41/11.20 [1379]~E(x13791,x13792)+E(f820(x13793,x13791,x13794),f820(x13793,x13792,x13794))
% 11.41/11.20 [1380]~E(x13801,x13802)+E(f820(x13803,x13804,x13801),f820(x13803,x13804,x13802))
% 11.41/11.20 [1381]~E(x13811,x13812)+E(f579(x13811,x13813,x13814),f579(x13812,x13813,x13814))
% 11.41/11.20 [1382]~E(x13821,x13822)+E(f579(x13823,x13821,x13824),f579(x13823,x13822,x13824))
% 11.41/11.20 [1383]~E(x13831,x13832)+E(f579(x13833,x13834,x13831),f579(x13833,x13834,x13832))
% 11.41/11.20 [1384]~E(x13841,x13842)+E(f362(x13841,x13843,x13844,x13845),f362(x13842,x13843,x13844,x13845))
% 11.41/11.20 [1385]~E(x13851,x13852)+E(f362(x13853,x13851,x13854,x13855),f362(x13853,x13852,x13854,x13855))
% 11.41/11.20 [1386]~E(x13861,x13862)+E(f362(x13863,x13864,x13861,x13865),f362(x13863,x13864,x13862,x13865))
% 11.41/11.20 [1387]~E(x13871,x13872)+E(f362(x13873,x13874,x13875,x13871),f362(x13873,x13874,x13875,x13872))
% 11.41/11.20 [1388]~E(x13881,x13882)+E(f633(x13881,x13883,x13884),f633(x13882,x13883,x13884))
% 11.41/11.20 [1389]~E(x13891,x13892)+E(f633(x13893,x13891,x13894),f633(x13893,x13892,x13894))
% 11.41/11.20 [1390]~E(x13901,x13902)+E(f633(x13903,x13904,x13901),f633(x13903,x13904,x13902))
% 11.41/11.20 [1391]~E(x13911,x13912)+E(f673(x13911,x13913,x13914,x13915,x13916),f673(x13912,x13913,x13914,x13915,x13916))
% 11.41/11.20 [1392]~E(x13921,x13922)+E(f673(x13923,x13921,x13924,x13925,x13926),f673(x13923,x13922,x13924,x13925,x13926))
% 11.41/11.20 [1393]~E(x13931,x13932)+E(f673(x13933,x13934,x13931,x13935,x13936),f673(x13933,x13934,x13932,x13935,x13936))
% 11.41/11.20 [1394]~E(x13941,x13942)+E(f673(x13943,x13944,x13945,x13941,x13946),f673(x13943,x13944,x13945,x13942,x13946))
% 11.41/11.20 [1395]~E(x13951,x13952)+E(f673(x13953,x13954,x13955,x13956,x13951),f673(x13953,x13954,x13955,x13956,x13952))
% 11.41/11.20 [1396]~E(x13961,x13962)+E(f323(x13961,x13963,x13964),f323(x13962,x13963,x13964))
% 11.41/11.20 [1397]~E(x13971,x13972)+E(f323(x13973,x13971,x13974),f323(x13973,x13972,x13974))
% 11.41/11.20 [1398]~E(x13981,x13982)+E(f323(x13983,x13984,x13981),f323(x13983,x13984,x13982))
% 11.41/11.20 [1399]~E(x13991,x13992)+E(f765(x13991,x13993,x13994,x13995,x13996),f765(x13992,x13993,x13994,x13995,x13996))
% 11.41/11.20 [1400]~E(x14001,x14002)+E(f765(x14003,x14001,x14004,x14005,x14006),f765(x14003,x14002,x14004,x14005,x14006))
% 11.41/11.20 [1401]~E(x14011,x14012)+E(f765(x14013,x14014,x14011,x14015,x14016),f765(x14013,x14014,x14012,x14015,x14016))
% 11.41/11.20 [1402]~E(x14021,x14022)+E(f765(x14023,x14024,x14025,x14021,x14026),f765(x14023,x14024,x14025,x14022,x14026))
% 11.41/11.20 [1403]~E(x14031,x14032)+E(f765(x14033,x14034,x14035,x14036,x14031),f765(x14033,x14034,x14035,x14036,x14032))
% 11.41/11.20 [1404]~E(x14041,x14042)+E(f257(x14041,x14043,x14044),f257(x14042,x14043,x14044))
% 11.41/11.20 [1405]~E(x14051,x14052)+E(f257(x14053,x14051,x14054),f257(x14053,x14052,x14054))
% 11.41/11.20 [1406]~E(x14061,x14062)+E(f257(x14063,x14064,x14061),f257(x14063,x14064,x14062))
% 11.41/11.20 [1407]~E(x14071,x14072)+E(f712(x14071,x14073,x14074,x14075),f712(x14072,x14073,x14074,x14075))
% 11.41/11.20 [1408]~E(x14081,x14082)+E(f712(x14083,x14081,x14084,x14085),f712(x14083,x14082,x14084,x14085))
% 11.41/11.20 [1409]~E(x14091,x14092)+E(f712(x14093,x14094,x14091,x14095),f712(x14093,x14094,x14092,x14095))
% 11.41/11.20 [1410]~E(x14101,x14102)+E(f712(x14103,x14104,x14105,x14101),f712(x14103,x14104,x14105,x14102))
% 11.41/11.20 [1411]~E(x14111,x14112)+E(f652(x14111,x14113,x14114),f652(x14112,x14113,x14114))
% 11.41/11.20 [1412]~E(x14121,x14122)+E(f652(x14123,x14121,x14124),f652(x14123,x14122,x14124))
% 11.41/11.20 [1413]~E(x14131,x14132)+E(f652(x14133,x14134,x14131),f652(x14133,x14134,x14132))
% 11.41/11.20 [1414]~E(x14141,x14142)+E(f200(x14141,x14143,x14144,x14145),f200(x14142,x14143,x14144,x14145))
% 11.41/11.20 [1415]~E(x14151,x14152)+E(f200(x14153,x14151,x14154,x14155),f200(x14153,x14152,x14154,x14155))
% 11.41/11.20 [1416]~E(x14161,x14162)+E(f200(x14163,x14164,x14161,x14165),f200(x14163,x14164,x14162,x14165))
% 11.41/11.20 [1417]~E(x14171,x14172)+E(f200(x14173,x14174,x14175,x14171),f200(x14173,x14174,x14175,x14172))
% 11.41/11.20 [1418]~E(x14181,x14182)+E(f762(x14181,x14183,x14184),f762(x14182,x14183,x14184))
% 11.41/11.20 [1419]~E(x14191,x14192)+E(f762(x14193,x14191,x14194),f762(x14193,x14192,x14194))
% 11.41/11.20 [1420]~E(x14201,x14202)+E(f762(x14203,x14204,x14201),f762(x14203,x14204,x14202))
% 11.41/11.20 [1421]~E(x14211,x14212)+E(f658(x14211,x14213,x14214),f658(x14212,x14213,x14214))
% 11.41/11.20 [1422]~E(x14221,x14222)+E(f658(x14223,x14221,x14224),f658(x14223,x14222,x14224))
% 11.41/11.20 [1423]~E(x14231,x14232)+E(f658(x14233,x14234,x14231),f658(x14233,x14234,x14232))
% 11.41/11.20 [1424]~E(x14241,x14242)+E(f363(x14241,x14243),f363(x14242,x14243))
% 11.41/11.20 [1425]~E(x14251,x14252)+E(f363(x14253,x14251),f363(x14253,x14252))
% 11.41/11.20 [1426]~E(x14261,x14262)+E(f475(x14261,x14263,x14264,x14265,x14266,x14267),f475(x14262,x14263,x14264,x14265,x14266,x14267))
% 11.41/11.20 [1427]~E(x14271,x14272)+E(f475(x14273,x14271,x14274,x14275,x14276,x14277),f475(x14273,x14272,x14274,x14275,x14276,x14277))
% 11.41/11.20 [1428]~E(x14281,x14282)+E(f475(x14283,x14284,x14281,x14285,x14286,x14287),f475(x14283,x14284,x14282,x14285,x14286,x14287))
% 11.41/11.20 [1429]~E(x14291,x14292)+E(f475(x14293,x14294,x14295,x14291,x14296,x14297),f475(x14293,x14294,x14295,x14292,x14296,x14297))
% 11.41/11.20 [1430]~E(x14301,x14302)+E(f475(x14303,x14304,x14305,x14306,x14301,x14307),f475(x14303,x14304,x14305,x14306,x14302,x14307))
% 11.41/11.20 [1431]~E(x14311,x14312)+E(f475(x14313,x14314,x14315,x14316,x14317,x14311),f475(x14313,x14314,x14315,x14316,x14317,x14312))
% 11.41/11.20 [1432]~E(x14321,x14322)+E(f792(x14321,x14323,x14324),f792(x14322,x14323,x14324))
% 11.41/11.20 [1433]~E(x14331,x14332)+E(f792(x14333,x14331,x14334),f792(x14333,x14332,x14334))
% 11.41/11.20 [1434]~E(x14341,x14342)+E(f792(x14343,x14344,x14341),f792(x14343,x14344,x14342))
% 11.41/11.20 [1435]~E(x14351,x14352)+E(f350(x14351),f350(x14352))
% 11.41/11.20 [1436]~E(x14361,x14362)+E(f782(x14361,x14363,x14364),f782(x14362,x14363,x14364))
% 11.41/11.20 [1437]~E(x14371,x14372)+E(f782(x14373,x14371,x14374),f782(x14373,x14372,x14374))
% 11.41/11.20 [1438]~E(x14381,x14382)+E(f782(x14383,x14384,x14381),f782(x14383,x14384,x14382))
% 11.41/11.20 [1439]~E(x14391,x14392)+E(f254(x14391,x14393,x14394),f254(x14392,x14393,x14394))
% 11.41/11.20 [1440]~E(x14401,x14402)+E(f254(x14403,x14401,x14404),f254(x14403,x14402,x14404))
% 11.41/11.20 [1441]~E(x14411,x14412)+E(f254(x14413,x14414,x14411),f254(x14413,x14414,x14412))
% 11.41/11.20 [1442]~E(x14421,x14422)+E(f666(x14421,x14423),f666(x14422,x14423))
% 11.41/11.20 [1443]~E(x14431,x14432)+E(f666(x14433,x14431),f666(x14433,x14432))
% 11.41/11.20 [1444]~E(x14441,x14442)+E(f357(x14441,x14443,x14444,x14445),f357(x14442,x14443,x14444,x14445))
% 11.41/11.20 [1445]~E(x14451,x14452)+E(f357(x14453,x14451,x14454,x14455),f357(x14453,x14452,x14454,x14455))
% 11.41/11.20 [1446]~E(x14461,x14462)+E(f357(x14463,x14464,x14461,x14465),f357(x14463,x14464,x14462,x14465))
% 11.41/11.20 [1447]~E(x14471,x14472)+E(f357(x14473,x14474,x14475,x14471),f357(x14473,x14474,x14475,x14472))
% 11.41/11.20 [1448]~E(x14481,x14482)+E(f238(x14481,x14483,x14484),f238(x14482,x14483,x14484))
% 11.41/11.20 [1449]~E(x14491,x14492)+E(f238(x14493,x14491,x14494),f238(x14493,x14492,x14494))
% 11.41/11.20 [1450]~E(x14501,x14502)+E(f238(x14503,x14504,x14501),f238(x14503,x14504,x14502))
% 11.41/11.20 [1451]~E(x14511,x14512)+E(f85(x14511,x14513,x14514,x14515,x14516),f85(x14512,x14513,x14514,x14515,x14516))
% 11.41/11.20 [1452]~E(x14521,x14522)+E(f85(x14523,x14521,x14524,x14525,x14526),f85(x14523,x14522,x14524,x14525,x14526))
% 11.41/11.20 [1453]~E(x14531,x14532)+E(f85(x14533,x14534,x14531,x14535,x14536),f85(x14533,x14534,x14532,x14535,x14536))
% 11.41/11.20 [1454]~E(x14541,x14542)+E(f85(x14543,x14544,x14545,x14541,x14546),f85(x14543,x14544,x14545,x14542,x14546))
% 11.41/11.20 [1455]~E(x14551,x14552)+E(f85(x14553,x14554,x14555,x14556,x14551),f85(x14553,x14554,x14555,x14556,x14552))
% 11.41/11.20 [1456]~E(x14561,x14562)+E(f822(x14561,x14563,x14564),f822(x14562,x14563,x14564))
% 11.41/11.20 [1457]~E(x14571,x14572)+E(f822(x14573,x14571,x14574),f822(x14573,x14572,x14574))
% 11.41/11.20 [1458]~E(x14581,x14582)+E(f822(x14583,x14584,x14581),f822(x14583,x14584,x14582))
% 11.41/11.20 [1459]~E(x14591,x14592)+E(f484(x14591,x14593,x14594),f484(x14592,x14593,x14594))
% 11.41/11.20 [1460]~E(x14601,x14602)+E(f484(x14603,x14601,x14604),f484(x14603,x14602,x14604))
% 11.41/11.20 [1461]~E(x14611,x14612)+E(f484(x14613,x14614,x14611),f484(x14613,x14614,x14612))
% 11.41/11.20 [1462]~E(x14621,x14622)+E(f766(x14621,x14623,x14624,x14625),f766(x14622,x14623,x14624,x14625))
% 11.41/11.20 [1463]~E(x14631,x14632)+E(f766(x14633,x14631,x14634,x14635),f766(x14633,x14632,x14634,x14635))
% 11.41/11.20 [1464]~E(x14641,x14642)+E(f766(x14643,x14644,x14641,x14645),f766(x14643,x14644,x14642,x14645))
% 11.41/11.20 [1465]~E(x14651,x14652)+E(f766(x14653,x14654,x14655,x14651),f766(x14653,x14654,x14655,x14652))
% 11.41/11.20 [1466]~E(x14661,x14662)+E(f602(x14661,x14663,x14664,x14665),f602(x14662,x14663,x14664,x14665))
% 11.41/11.20 [1467]~E(x14671,x14672)+E(f602(x14673,x14671,x14674,x14675),f602(x14673,x14672,x14674,x14675))
% 11.41/11.20 [1468]~E(x14681,x14682)+E(f602(x14683,x14684,x14681,x14685),f602(x14683,x14684,x14682,x14685))
% 11.41/11.20 [1469]~E(x14691,x14692)+E(f602(x14693,x14694,x14695,x14691),f602(x14693,x14694,x14695,x14692))
% 11.41/11.20 [1470]~E(x14701,x14702)+E(f603(x14701,x14703,x14704,x14705),f603(x14702,x14703,x14704,x14705))
% 11.41/11.20 [1471]~E(x14711,x14712)+E(f603(x14713,x14711,x14714,x14715),f603(x14713,x14712,x14714,x14715))
% 11.41/11.20 [1472]~E(x14721,x14722)+E(f603(x14723,x14724,x14721,x14725),f603(x14723,x14724,x14722,x14725))
% 11.41/11.20 [1473]~E(x14731,x14732)+E(f603(x14733,x14734,x14735,x14731),f603(x14733,x14734,x14735,x14732))
% 11.41/11.20 [1474]~E(x14741,x14742)+E(f736(x14741,x14743,x14744),f736(x14742,x14743,x14744))
% 11.41/11.20 [1475]~E(x14751,x14752)+E(f736(x14753,x14751,x14754),f736(x14753,x14752,x14754))
% 11.41/11.20 [1476]~E(x14761,x14762)+E(f736(x14763,x14764,x14761),f736(x14763,x14764,x14762))
% 11.41/11.20 [1477]~E(x14771,x14772)+E(f537(x14771,x14773,x14774),f537(x14772,x14773,x14774))
% 11.41/11.20 [1478]~E(x14781,x14782)+E(f537(x14783,x14781,x14784),f537(x14783,x14782,x14784))
% 11.41/11.20 [1479]~E(x14791,x14792)+E(f537(x14793,x14794,x14791),f537(x14793,x14794,x14792))
% 11.41/11.20 [1480]~E(x14801,x14802)+E(f45(x14801,x14803,x14804,x14805),f45(x14802,x14803,x14804,x14805))
% 11.41/11.20 [1481]~E(x14811,x14812)+E(f45(x14813,x14811,x14814,x14815),f45(x14813,x14812,x14814,x14815))
% 11.41/11.20 [1482]~E(x14821,x14822)+E(f45(x14823,x14824,x14821,x14825),f45(x14823,x14824,x14822,x14825))
% 11.41/11.20 [1483]~E(x14831,x14832)+E(f45(x14833,x14834,x14835,x14831),f45(x14833,x14834,x14835,x14832))
% 11.41/11.20 [1484]~E(x14841,x14842)+E(f353(x14841,x14843,x14844),f353(x14842,x14843,x14844))
% 11.41/11.20 [1485]~E(x14851,x14852)+E(f353(x14853,x14851,x14854),f353(x14853,x14852,x14854))
% 11.41/11.20 [1486]~E(x14861,x14862)+E(f353(x14863,x14864,x14861),f353(x14863,x14864,x14862))
% 11.41/11.20 [1487]~E(x14871,x14872)+E(f277(x14871,x14873),f277(x14872,x14873))
% 11.41/11.20 [1488]~E(x14881,x14882)+E(f277(x14883,x14881),f277(x14883,x14882))
% 11.41/11.20 [1489]~E(x14891,x14892)+E(f244(x14891,x14893),f244(x14892,x14893))
% 11.41/11.20 [1490]~E(x14901,x14902)+E(f244(x14903,x14901),f244(x14903,x14902))
% 11.41/11.20 [1491]~E(x14911,x14912)+E(f695(x14911,x14913),f695(x14912,x14913))
% 11.41/11.20 [1492]~E(x14921,x14922)+E(f695(x14923,x14921),f695(x14923,x14922))
% 11.41/11.20 [1493]~E(x14931,x14932)+E(f802(x14931,x14933,x14934),f802(x14932,x14933,x14934))
% 11.41/11.20 [1494]~E(x14941,x14942)+E(f802(x14943,x14941,x14944),f802(x14943,x14942,x14944))
% 11.41/11.20 [1495]~E(x14951,x14952)+E(f802(x14953,x14954,x14951),f802(x14953,x14954,x14952))
% 11.41/11.20 [1496]~E(x14961,x14962)+E(f182(x14961,x14963,x14964,x14965),f182(x14962,x14963,x14964,x14965))
% 11.41/11.20 [1497]~E(x14971,x14972)+E(f182(x14973,x14971,x14974,x14975),f182(x14973,x14972,x14974,x14975))
% 11.41/11.20 [1498]~E(x14981,x14982)+E(f182(x14983,x14984,x14981,x14985),f182(x14983,x14984,x14982,x14985))
% 11.41/11.20 [1499]~E(x14991,x14992)+E(f182(x14993,x14994,x14995,x14991),f182(x14993,x14994,x14995,x14992))
% 11.41/11.20 [1500]~E(x15001,x15002)+E(f452(x15001,x15003,x15004,x15005,x15006),f452(x15002,x15003,x15004,x15005,x15006))
% 11.41/11.20 [1501]~E(x15011,x15012)+E(f452(x15013,x15011,x15014,x15015,x15016),f452(x15013,x15012,x15014,x15015,x15016))
% 11.41/11.20 [1502]~E(x15021,x15022)+E(f452(x15023,x15024,x15021,x15025,x15026),f452(x15023,x15024,x15022,x15025,x15026))
% 11.41/11.20 [1503]~E(x15031,x15032)+E(f452(x15033,x15034,x15035,x15031,x15036),f452(x15033,x15034,x15035,x15032,x15036))
% 11.41/11.20 [1504]~E(x15041,x15042)+E(f452(x15043,x15044,x15045,x15046,x15041),f452(x15043,x15044,x15045,x15046,x15042))
% 11.41/11.20 [1505]~E(x15051,x15052)+E(f578(x15051,x15053),f578(x15052,x15053))
% 11.41/11.20 [1506]~E(x15061,x15062)+E(f578(x15063,x15061),f578(x15063,x15062))
% 11.41/11.20 [1507]~E(x15071,x15072)+E(f599(x15071,x15073,x15074,x15075),f599(x15072,x15073,x15074,x15075))
% 11.41/11.20 [1508]~E(x15081,x15082)+E(f599(x15083,x15081,x15084,x15085),f599(x15083,x15082,x15084,x15085))
% 11.41/11.20 [1509]~E(x15091,x15092)+E(f599(x15093,x15094,x15091,x15095),f599(x15093,x15094,x15092,x15095))
% 11.41/11.20 [1510]~E(x15101,x15102)+E(f599(x15103,x15104,x15105,x15101),f599(x15103,x15104,x15105,x15102))
% 11.41/11.20 [1511]~E(x15111,x15112)+E(f276(x15111,x15113),f276(x15112,x15113))
% 11.41/11.20 [1512]~E(x15121,x15122)+E(f276(x15123,x15121),f276(x15123,x15122))
% 11.41/11.20 [1513]~E(x15131,x15132)+E(f513(x15131,x15133,x15134,x15135,x15136,x15137,x15138),f513(x15132,x15133,x15134,x15135,x15136,x15137,x15138))
% 11.41/11.20 [1514]~E(x15141,x15142)+E(f513(x15143,x15141,x15144,x15145,x15146,x15147,x15148),f513(x15143,x15142,x15144,x15145,x15146,x15147,x15148))
% 11.41/11.20 [1515]~E(x15151,x15152)+E(f513(x15153,x15154,x15151,x15155,x15156,x15157,x15158),f513(x15153,x15154,x15152,x15155,x15156,x15157,x15158))
% 11.41/11.20 [1516]~E(x15161,x15162)+E(f513(x15163,x15164,x15165,x15161,x15166,x15167,x15168),f513(x15163,x15164,x15165,x15162,x15166,x15167,x15168))
% 11.41/11.20 [1517]~E(x15171,x15172)+E(f513(x15173,x15174,x15175,x15176,x15171,x15177,x15178),f513(x15173,x15174,x15175,x15176,x15172,x15177,x15178))
% 11.41/11.20 [1518]~E(x15181,x15182)+E(f513(x15183,x15184,x15185,x15186,x15187,x15181,x15188),f513(x15183,x15184,x15185,x15186,x15187,x15182,x15188))
% 11.41/11.20 [1519]~E(x15191,x15192)+E(f513(x15193,x15194,x15195,x15196,x15197,x15198,x15191),f513(x15193,x15194,x15195,x15196,x15197,x15198,x15192))
% 11.41/11.20 [1520]~E(x15201,x15202)+E(f756(x15201,x15203,x15204,x15205),f756(x15202,x15203,x15204,x15205))
% 11.41/11.20 [1521]~E(x15211,x15212)+E(f756(x15213,x15211,x15214,x15215),f756(x15213,x15212,x15214,x15215))
% 11.41/11.20 [1522]~E(x15221,x15222)+E(f756(x15223,x15224,x15221,x15225),f756(x15223,x15224,x15222,x15225))
% 11.41/11.20 [1523]~E(x15231,x15232)+E(f756(x15233,x15234,x15235,x15231),f756(x15233,x15234,x15235,x15232))
% 11.41/11.20 [1524]~E(x15241,x15242)+E(f803(x15241,x15243,x15244),f803(x15242,x15243,x15244))
% 11.41/11.20 [1525]~E(x15251,x15252)+E(f803(x15253,x15251,x15254),f803(x15253,x15252,x15254))
% 11.41/11.20 [1526]~E(x15261,x15262)+E(f803(x15263,x15264,x15261),f803(x15263,x15264,x15262))
% 11.41/11.20 [1527]~E(x15271,x15272)+E(f356(x15271,x15273),f356(x15272,x15273))
% 11.41/11.20 [1528]~E(x15281,x15282)+E(f356(x15283,x15281),f356(x15283,x15282))
% 11.41/11.20 [1529]~E(x15291,x15292)+E(f796(x15291,x15293,x15294,x15295,x15296),f796(x15292,x15293,x15294,x15295,x15296))
% 11.41/11.20 [1530]~E(x15301,x15302)+E(f796(x15303,x15301,x15304,x15305,x15306),f796(x15303,x15302,x15304,x15305,x15306))
% 11.41/11.20 [1531]~E(x15311,x15312)+E(f796(x15313,x15314,x15311,x15315,x15316),f796(x15313,x15314,x15312,x15315,x15316))
% 11.41/11.20 [1532]~E(x15321,x15322)+E(f796(x15323,x15324,x15325,x15321,x15326),f796(x15323,x15324,x15325,x15322,x15326))
% 11.41/11.20 [1533]~E(x15331,x15332)+E(f796(x15333,x15334,x15335,x15336,x15331),f796(x15333,x15334,x15335,x15336,x15332))
% 11.41/11.20 [1534]~E(x15341,x15342)+E(f239(x15341,x15343,x15344,x15345),f239(x15342,x15343,x15344,x15345))
% 11.41/11.20 [1535]~E(x15351,x15352)+E(f239(x15353,x15351,x15354,x15355),f239(x15353,x15352,x15354,x15355))
% 11.41/11.20 [1536]~E(x15361,x15362)+E(f239(x15363,x15364,x15361,x15365),f239(x15363,x15364,x15362,x15365))
% 11.41/11.20 [1537]~E(x15371,x15372)+E(f239(x15373,x15374,x15375,x15371),f239(x15373,x15374,x15375,x15372))
% 11.41/11.20 [1538]~E(x15381,x15382)+E(f689(x15381,x15383,x15384),f689(x15382,x15383,x15384))
% 11.41/11.20 [1539]~E(x15391,x15392)+E(f689(x15393,x15391,x15394),f689(x15393,x15392,x15394))
% 11.41/11.20 [1540]~E(x15401,x15402)+E(f689(x15403,x15404,x15401),f689(x15403,x15404,x15402))
% 11.41/11.20 [1541]~E(x15411,x15412)+E(f759(x15411,x15413,x15414),f759(x15412,x15413,x15414))
% 11.41/11.20 [1542]~E(x15421,x15422)+E(f759(x15423,x15421,x15424),f759(x15423,x15422,x15424))
% 11.41/11.20 [1543]~E(x15431,x15432)+E(f759(x15433,x15434,x15431),f759(x15433,x15434,x15432))
% 11.41/11.20 [1544]~E(x15441,x15442)+E(f651(x15441,x15443,x15444),f651(x15442,x15443,x15444))
% 11.41/11.20 [1545]~E(x15451,x15452)+E(f651(x15453,x15451,x15454),f651(x15453,x15452,x15454))
% 11.41/11.20 [1546]~E(x15461,x15462)+E(f651(x15463,x15464,x15461),f651(x15463,x15464,x15462))
% 11.41/11.20 [1547]~E(x15471,x15472)+E(f608(x15471,x15473,x15474,x15475),f608(x15472,x15473,x15474,x15475))
% 11.41/11.20 [1548]~E(x15481,x15482)+E(f608(x15483,x15481,x15484,x15485),f608(x15483,x15482,x15484,x15485))
% 11.41/11.20 [1549]~E(x15491,x15492)+E(f608(x15493,x15494,x15491,x15495),f608(x15493,x15494,x15492,x15495))
% 11.41/11.20 [1550]~E(x15501,x15502)+E(f608(x15503,x15504,x15505,x15501),f608(x15503,x15504,x15505,x15502))
% 11.41/11.20 [1551]~E(x15511,x15512)+E(f425(x15511,x15513,x15514,x15515),f425(x15512,x15513,x15514,x15515))
% 11.41/11.20 [1552]~E(x15521,x15522)+E(f425(x15523,x15521,x15524,x15525),f425(x15523,x15522,x15524,x15525))
% 11.41/11.20 [1553]~E(x15531,x15532)+E(f425(x15533,x15534,x15531,x15535),f425(x15533,x15534,x15532,x15535))
% 11.41/11.20 [1554]~E(x15541,x15542)+E(f425(x15543,x15544,x15545,x15541),f425(x15543,x15544,x15545,x15542))
% 11.41/11.20 [1555]~E(x15551,x15552)+E(f302(x15551,x15553,x15554,x15555,x15556),f302(x15552,x15553,x15554,x15555,x15556))
% 11.41/11.20 [1556]~E(x15561,x15562)+E(f302(x15563,x15561,x15564,x15565,x15566),f302(x15563,x15562,x15564,x15565,x15566))
% 11.41/11.20 [1557]~E(x15571,x15572)+E(f302(x15573,x15574,x15571,x15575,x15576),f302(x15573,x15574,x15572,x15575,x15576))
% 11.41/11.20 [1558]~E(x15581,x15582)+E(f302(x15583,x15584,x15585,x15581,x15586),f302(x15583,x15584,x15585,x15582,x15586))
% 11.41/11.20 [1559]~E(x15591,x15592)+E(f302(x15593,x15594,x15595,x15596,x15591),f302(x15593,x15594,x15595,x15596,x15592))
% 11.41/11.20 [1560]~E(x15601,x15602)+E(f649(x15601,x15603,x15604),f649(x15602,x15603,x15604))
% 11.41/11.20 [1561]~E(x15611,x15612)+E(f649(x15613,x15611,x15614),f649(x15613,x15612,x15614))
% 11.41/11.20 [1562]~E(x15621,x15622)+E(f649(x15623,x15624,x15621),f649(x15623,x15624,x15622))
% 11.41/11.20 [1563]~E(x15631,x15632)+E(f417(x15631,x15633,x15634),f417(x15632,x15633,x15634))
% 11.41/11.20 [1564]~E(x15641,x15642)+E(f417(x15643,x15641,x15644),f417(x15643,x15642,x15644))
% 11.41/11.20 [1565]~E(x15651,x15652)+E(f417(x15653,x15654,x15651),f417(x15653,x15654,x15652))
% 11.41/11.20 [1566]~E(x15661,x15662)+E(f667(x15661,x15663,x15664,x15665),f667(x15662,x15663,x15664,x15665))
% 11.41/11.20 [1567]~E(x15671,x15672)+E(f667(x15673,x15671,x15674,x15675),f667(x15673,x15672,x15674,x15675))
% 11.41/11.20 [1568]~E(x15681,x15682)+E(f667(x15683,x15684,x15681,x15685),f667(x15683,x15684,x15682,x15685))
% 11.41/11.20 [1569]~E(x15691,x15692)+E(f667(x15693,x15694,x15695,x15691),f667(x15693,x15694,x15695,x15692))
% 11.41/11.20 [1570]~E(x15701,x15702)+E(f569(x15701,x15703,x15704,x15705,x15706,x15707,x15708,x15709),f569(x15702,x15703,x15704,x15705,x15706,x15707,x15708,x15709))
% 11.41/11.20 [1571]~E(x15711,x15712)+E(f569(x15713,x15711,x15714,x15715,x15716,x15717,x15718,x15719),f569(x15713,x15712,x15714,x15715,x15716,x15717,x15718,x15719))
% 11.41/11.20 [1572]~E(x15721,x15722)+E(f569(x15723,x15724,x15721,x15725,x15726,x15727,x15728,x15729),f569(x15723,x15724,x15722,x15725,x15726,x15727,x15728,x15729))
% 11.41/11.20 [1573]~E(x15731,x15732)+E(f569(x15733,x15734,x15735,x15731,x15736,x15737,x15738,x15739),f569(x15733,x15734,x15735,x15732,x15736,x15737,x15738,x15739))
% 11.41/11.20 [1574]~E(x15741,x15742)+E(f569(x15743,x15744,x15745,x15746,x15741,x15747,x15748,x15749),f569(x15743,x15744,x15745,x15746,x15742,x15747,x15748,x15749))
% 11.41/11.20 [1575]~E(x15751,x15752)+E(f569(x15753,x15754,x15755,x15756,x15757,x15751,x15758,x15759),f569(x15753,x15754,x15755,x15756,x15757,x15752,x15758,x15759))
% 11.41/11.20 [1576]~E(x15761,x15762)+E(f569(x15763,x15764,x15765,x15766,x15767,x15768,x15761,x15769),f569(x15763,x15764,x15765,x15766,x15767,x15768,x15762,x15769))
% 11.41/11.20 [1577]~E(x15771,x15772)+E(f569(x15773,x15774,x15775,x15776,x15777,x15778,x15779,x15771),f569(x15773,x15774,x15775,x15776,x15777,x15778,x15779,x15772))
% 11.41/11.20 [1578]~E(x15781,x15782)+E(f207(x15781),f207(x15782))
% 11.41/11.20 [1579]~E(x15791,x15792)+E(f632(x15791,x15793,x15794,x15795,x15796,x15797),f632(x15792,x15793,x15794,x15795,x15796,x15797))
% 11.41/11.20 [1580]~E(x15801,x15802)+E(f632(x15803,x15801,x15804,x15805,x15806,x15807),f632(x15803,x15802,x15804,x15805,x15806,x15807))
% 11.41/11.20 [1581]~E(x15811,x15812)+E(f632(x15813,x15814,x15811,x15815,x15816,x15817),f632(x15813,x15814,x15812,x15815,x15816,x15817))
% 11.41/11.20 [1582]~E(x15821,x15822)+E(f632(x15823,x15824,x15825,x15821,x15826,x15827),f632(x15823,x15824,x15825,x15822,x15826,x15827))
% 11.41/11.20 [1583]~E(x15831,x15832)+E(f632(x15833,x15834,x15835,x15836,x15831,x15837),f632(x15833,x15834,x15835,x15836,x15832,x15837))
% 11.41/11.20 [1584]~E(x15841,x15842)+E(f632(x15843,x15844,x15845,x15846,x15847,x15841),f632(x15843,x15844,x15845,x15846,x15847,x15842))
% 11.41/11.20 [1585]~E(x15851,x15852)+E(f551(x15851,x15853,x15854,x15855,x15856),f551(x15852,x15853,x15854,x15855,x15856))
% 11.41/11.20 [1586]~E(x15861,x15862)+E(f551(x15863,x15861,x15864,x15865,x15866),f551(x15863,x15862,x15864,x15865,x15866))
% 11.41/11.20 [1587]~E(x15871,x15872)+E(f551(x15873,x15874,x15871,x15875,x15876),f551(x15873,x15874,x15872,x15875,x15876))
% 11.41/11.20 [1588]~E(x15881,x15882)+E(f551(x15883,x15884,x15885,x15881,x15886),f551(x15883,x15884,x15885,x15882,x15886))
% 11.41/11.20 [1589]~E(x15891,x15892)+E(f551(x15893,x15894,x15895,x15896,x15891),f551(x15893,x15894,x15895,x15896,x15892))
% 11.41/11.20 [1590]~E(x15901,x15902)+E(f77(x15901,x15903,x15904),f77(x15902,x15903,x15904))
% 11.41/11.20 [1591]~E(x15911,x15912)+E(f77(x15913,x15911,x15914),f77(x15913,x15912,x15914))
% 11.41/11.20 [1592]~E(x15921,x15922)+E(f77(x15923,x15924,x15921),f77(x15923,x15924,x15922))
% 11.41/11.20 [1593]~E(x15931,x15932)+E(f153(x15931,x15933),f153(x15932,x15933))
% 11.41/11.20 [1594]~E(x15941,x15942)+E(f153(x15943,x15941),f153(x15943,x15942))
% 11.41/11.20 [1595]~E(x15951,x15952)+E(f265(x15951,x15953,x15954,x15955,x15956),f265(x15952,x15953,x15954,x15955,x15956))
% 11.41/11.20 [1596]~E(x15961,x15962)+E(f265(x15963,x15961,x15964,x15965,x15966),f265(x15963,x15962,x15964,x15965,x15966))
% 11.41/11.20 [1597]~E(x15971,x15972)+E(f265(x15973,x15974,x15971,x15975,x15976),f265(x15973,x15974,x15972,x15975,x15976))
% 11.41/11.20 [1598]~E(x15981,x15982)+E(f265(x15983,x15984,x15985,x15981,x15986),f265(x15983,x15984,x15985,x15982,x15986))
% 11.41/11.20 [1599]~E(x15991,x15992)+E(f265(x15993,x15994,x15995,x15996,x15991),f265(x15993,x15994,x15995,x15996,x15992))
% 11.41/11.20 [1600]~E(x16001,x16002)+E(f665(x16001,x16003,x16004,x16005),f665(x16002,x16003,x16004,x16005))
% 11.41/11.20 [1601]~E(x16011,x16012)+E(f665(x16013,x16011,x16014,x16015),f665(x16013,x16012,x16014,x16015))
% 11.41/11.20 [1602]~E(x16021,x16022)+E(f665(x16023,x16024,x16021,x16025),f665(x16023,x16024,x16022,x16025))
% 11.41/11.20 [1603]~E(x16031,x16032)+E(f665(x16033,x16034,x16035,x16031),f665(x16033,x16034,x16035,x16032))
% 11.41/11.20 [1604]~E(x16041,x16042)+E(f485(x16041,x16043,x16044),f485(x16042,x16043,x16044))
% 11.41/11.20 [1605]~E(x16051,x16052)+E(f485(x16053,x16051,x16054),f485(x16053,x16052,x16054))
% 11.41/11.20 [1606]~E(x16061,x16062)+E(f485(x16063,x16064,x16061),f485(x16063,x16064,x16062))
% 11.41/11.20 [1607]~E(x16071,x16072)+E(f511(x16071,x16073,x16074,x16075,x16076,x16077,x16078),f511(x16072,x16073,x16074,x16075,x16076,x16077,x16078))
% 11.41/11.20 [1608]~E(x16081,x16082)+E(f511(x16083,x16081,x16084,x16085,x16086,x16087,x16088),f511(x16083,x16082,x16084,x16085,x16086,x16087,x16088))
% 11.41/11.20 [1609]~E(x16091,x16092)+E(f511(x16093,x16094,x16091,x16095,x16096,x16097,x16098),f511(x16093,x16094,x16092,x16095,x16096,x16097,x16098))
% 11.41/11.20 [1610]~E(x16101,x16102)+E(f511(x16103,x16104,x16105,x16101,x16106,x16107,x16108),f511(x16103,x16104,x16105,x16102,x16106,x16107,x16108))
% 11.41/11.20 [1611]~E(x16111,x16112)+E(f511(x16113,x16114,x16115,x16116,x16111,x16117,x16118),f511(x16113,x16114,x16115,x16116,x16112,x16117,x16118))
% 11.41/11.20 [1612]~E(x16121,x16122)+E(f511(x16123,x16124,x16125,x16126,x16127,x16121,x16128),f511(x16123,x16124,x16125,x16126,x16127,x16122,x16128))
% 11.41/11.20 [1613]~E(x16131,x16132)+E(f511(x16133,x16134,x16135,x16136,x16137,x16138,x16131),f511(x16133,x16134,x16135,x16136,x16137,x16138,x16132))
% 11.41/11.20 [1614]~E(x16141,x16142)+E(f459(x16141,x16143,x16144,x16145,x16146),f459(x16142,x16143,x16144,x16145,x16146))
% 11.41/11.20 [1615]~E(x16151,x16152)+E(f459(x16153,x16151,x16154,x16155,x16156),f459(x16153,x16152,x16154,x16155,x16156))
% 11.41/11.20 [1616]~E(x16161,x16162)+E(f459(x16163,x16164,x16161,x16165,x16166),f459(x16163,x16164,x16162,x16165,x16166))
% 11.41/11.20 [1617]~E(x16171,x16172)+E(f459(x16173,x16174,x16175,x16171,x16176),f459(x16173,x16174,x16175,x16172,x16176))
% 11.41/11.20 [1618]~E(x16181,x16182)+E(f459(x16183,x16184,x16185,x16186,x16181),f459(x16183,x16184,x16185,x16186,x16182))
% 11.41/11.20 [1619]~E(x16191,x16192)+E(f229(x16191,x16193,x16194,x16195,x16196),f229(x16192,x16193,x16194,x16195,x16196))
% 11.41/11.20 [1620]~E(x16201,x16202)+E(f229(x16203,x16201,x16204,x16205,x16206),f229(x16203,x16202,x16204,x16205,x16206))
% 11.41/11.20 [1621]~E(x16211,x16212)+E(f229(x16213,x16214,x16211,x16215,x16216),f229(x16213,x16214,x16212,x16215,x16216))
% 11.41/11.20 [1622]~E(x16221,x16222)+E(f229(x16223,x16224,x16225,x16221,x16226),f229(x16223,x16224,x16225,x16222,x16226))
% 11.41/11.20 [1623]~E(x16231,x16232)+E(f229(x16233,x16234,x16235,x16236,x16231),f229(x16233,x16234,x16235,x16236,x16232))
% 11.41/11.20 [1624]~E(x16241,x16242)+E(f360(x16241,x16243,x16244,x16245),f360(x16242,x16243,x16244,x16245))
% 11.41/11.20 [1625]~E(x16251,x16252)+E(f360(x16253,x16251,x16254,x16255),f360(x16253,x16252,x16254,x16255))
% 11.41/11.20 [1626]~E(x16261,x16262)+E(f360(x16263,x16264,x16261,x16265),f360(x16263,x16264,x16262,x16265))
% 11.41/11.20 [1627]~E(x16271,x16272)+E(f360(x16273,x16274,x16275,x16271),f360(x16273,x16274,x16275,x16272))
% 11.41/11.20 [1628]~E(x16281,x16282)+E(f296(x16281,x16283,x16284),f296(x16282,x16283,x16284))
% 11.41/11.20 [1629]~E(x16291,x16292)+E(f296(x16293,x16291,x16294),f296(x16293,x16292,x16294))
% 11.41/11.20 [1630]~E(x16301,x16302)+E(f296(x16303,x16304,x16301),f296(x16303,x16304,x16302))
% 11.41/11.20 [1631]~E(x16311,x16312)+E(f502(x16311,x16313,x16314,x16315,x16316),f502(x16312,x16313,x16314,x16315,x16316))
% 11.41/11.20 [1632]~E(x16321,x16322)+E(f502(x16323,x16321,x16324,x16325,x16326),f502(x16323,x16322,x16324,x16325,x16326))
% 11.41/11.20 [1633]~E(x16331,x16332)+E(f502(x16333,x16334,x16331,x16335,x16336),f502(x16333,x16334,x16332,x16335,x16336))
% 11.41/11.20 [1634]~E(x16341,x16342)+E(f502(x16343,x16344,x16345,x16341,x16346),f502(x16343,x16344,x16345,x16342,x16346))
% 11.41/11.20 [1635]~E(x16351,x16352)+E(f502(x16353,x16354,x16355,x16356,x16351),f502(x16353,x16354,x16355,x16356,x16352))
% 11.41/11.20 [1636]~E(x16361,x16362)+E(f709(x16361,x16363,x16364),f709(x16362,x16363,x16364))
% 11.41/11.20 [1637]~E(x16371,x16372)+E(f709(x16373,x16371,x16374),f709(x16373,x16372,x16374))
% 11.41/11.20 [1638]~E(x16381,x16382)+E(f709(x16383,x16384,x16381),f709(x16383,x16384,x16382))
% 11.41/11.20 [1639]~E(x16391,x16392)+E(f740(x16391),f740(x16392))
% 11.41/11.20 [1640]~E(x16401,x16402)+E(f369(x16401,x16403,x16404,x16405),f369(x16402,x16403,x16404,x16405))
% 11.41/11.20 [1641]~E(x16411,x16412)+E(f369(x16413,x16411,x16414,x16415),f369(x16413,x16412,x16414,x16415))
% 11.41/11.20 [1642]~E(x16421,x16422)+E(f369(x16423,x16424,x16421,x16425),f369(x16423,x16424,x16422,x16425))
% 11.41/11.20 [1643]~E(x16431,x16432)+E(f369(x16433,x16434,x16435,x16431),f369(x16433,x16434,x16435,x16432))
% 11.41/11.20 [1644]~E(x16441,x16442)+E(f791(x16441,x16443,x16444),f791(x16442,x16443,x16444))
% 11.41/11.20 [1645]~E(x16451,x16452)+E(f791(x16453,x16451,x16454),f791(x16453,x16452,x16454))
% 11.41/11.20 [1646]~E(x16461,x16462)+E(f791(x16463,x16464,x16461),f791(x16463,x16464,x16462))
% 11.41/11.20 [1647]~E(x16471,x16472)+E(f647(x16471,x16473,x16474,x16475,x16476,x16477,x16478,x16479),f647(x16472,x16473,x16474,x16475,x16476,x16477,x16478,x16479))
% 11.41/11.20 [1648]~E(x16481,x16482)+E(f647(x16483,x16481,x16484,x16485,x16486,x16487,x16488,x16489),f647(x16483,x16482,x16484,x16485,x16486,x16487,x16488,x16489))
% 11.41/11.20 [1649]~E(x16491,x16492)+E(f647(x16493,x16494,x16491,x16495,x16496,x16497,x16498,x16499),f647(x16493,x16494,x16492,x16495,x16496,x16497,x16498,x16499))
% 11.41/11.20 [1650]~E(x16501,x16502)+E(f647(x16503,x16504,x16505,x16501,x16506,x16507,x16508,x16509),f647(x16503,x16504,x16505,x16502,x16506,x16507,x16508,x16509))
% 11.41/11.20 [1651]~E(x16511,x16512)+E(f647(x16513,x16514,x16515,x16516,x16511,x16517,x16518,x16519),f647(x16513,x16514,x16515,x16516,x16512,x16517,x16518,x16519))
% 11.41/11.20 [1652]~E(x16521,x16522)+E(f647(x16523,x16524,x16525,x16526,x16527,x16521,x16528,x16529),f647(x16523,x16524,x16525,x16526,x16527,x16522,x16528,x16529))
% 11.41/11.20 [1653]~E(x16531,x16532)+E(f647(x16533,x16534,x16535,x16536,x16537,x16538,x16531,x16539),f647(x16533,x16534,x16535,x16536,x16537,x16538,x16532,x16539))
% 11.41/11.20 [1654]~E(x16541,x16542)+E(f647(x16543,x16544,x16545,x16546,x16547,x16548,x16549,x16541),f647(x16543,x16544,x16545,x16546,x16547,x16548,x16549,x16542))
% 11.41/11.20 [1655]~E(x16551,x16552)+E(f21(x16551,x16553,x16554,x16555),f21(x16552,x16553,x16554,x16555))
% 11.41/11.20 [1656]~E(x16561,x16562)+E(f21(x16563,x16561,x16564,x16565),f21(x16563,x16562,x16564,x16565))
% 11.41/11.20 [1657]~E(x16571,x16572)+E(f21(x16573,x16574,x16571,x16575),f21(x16573,x16574,x16572,x16575))
% 11.41/11.20 [1658]~E(x16581,x16582)+E(f21(x16583,x16584,x16585,x16581),f21(x16583,x16584,x16585,x16582))
% 11.41/11.20 [1659]~E(x16591,x16592)+E(f769(x16591,x16593,x16594,x16595),f769(x16592,x16593,x16594,x16595))
% 11.41/11.20 [1660]~E(x16601,x16602)+E(f769(x16603,x16601,x16604,x16605),f769(x16603,x16602,x16604,x16605))
% 11.41/11.20 [1661]~E(x16611,x16612)+E(f769(x16613,x16614,x16611,x16615),f769(x16613,x16614,x16612,x16615))
% 11.41/11.20 [1662]~E(x16621,x16622)+E(f769(x16623,x16624,x16625,x16621),f769(x16623,x16624,x16625,x16622))
% 11.41/11.20 [1663]~E(x16631,x16632)+E(f429(x16631,x16633,x16634,x16635,x16636),f429(x16632,x16633,x16634,x16635,x16636))
% 11.41/11.20 [1664]~E(x16641,x16642)+E(f429(x16643,x16641,x16644,x16645,x16646),f429(x16643,x16642,x16644,x16645,x16646))
% 11.41/11.20 [1665]~E(x16651,x16652)+E(f429(x16653,x16654,x16651,x16655,x16656),f429(x16653,x16654,x16652,x16655,x16656))
% 11.41/11.20 [1666]~E(x16661,x16662)+E(f429(x16663,x16664,x16665,x16661,x16666),f429(x16663,x16664,x16665,x16662,x16666))
% 11.41/11.20 [1667]~E(x16671,x16672)+E(f429(x16673,x16674,x16675,x16676,x16671),f429(x16673,x16674,x16675,x16676,x16672))
% 11.41/11.20 [1668]~E(x16681,x16682)+E(f807(x16681,x16683,x16684,x16685),f807(x16682,x16683,x16684,x16685))
% 11.41/11.20 [1669]~E(x16691,x16692)+E(f807(x16693,x16691,x16694,x16695),f807(x16693,x16692,x16694,x16695))
% 11.41/11.20 [1670]~E(x16701,x16702)+E(f807(x16703,x16704,x16701,x16705),f807(x16703,x16704,x16702,x16705))
% 11.41/11.20 [1671]~E(x16711,x16712)+E(f807(x16713,x16714,x16715,x16711),f807(x16713,x16714,x16715,x16712))
% 11.41/11.20 [1672]~E(x16721,x16722)+E(f385(x16721,x16723),f385(x16722,x16723))
% 11.41/11.20 [1673]~E(x16731,x16732)+E(f385(x16733,x16731),f385(x16733,x16732))
% 11.41/11.20 [1674]~E(x16741,x16742)+E(f628(x16741,x16743),f628(x16742,x16743))
% 11.41/11.20 [1675]~E(x16751,x16752)+E(f628(x16753,x16751),f628(x16753,x16752))
% 11.41/11.20 [1676]~E(x16761,x16762)+E(f702(x16761,x16763,x16764,x16765),f702(x16762,x16763,x16764,x16765))
% 11.41/11.20 [1677]~E(x16771,x16772)+E(f702(x16773,x16771,x16774,x16775),f702(x16773,x16772,x16774,x16775))
% 11.41/11.20 [1678]~E(x16781,x16782)+E(f702(x16783,x16784,x16781,x16785),f702(x16783,x16784,x16782,x16785))
% 11.41/11.20 [1679]~E(x16791,x16792)+E(f702(x16793,x16794,x16795,x16791),f702(x16793,x16794,x16795,x16792))
% 11.41/11.20 [1680]~E(x16801,x16802)+E(f285(x16801,x16803,x16804,x16805),f285(x16802,x16803,x16804,x16805))
% 11.41/11.20 [1681]~E(x16811,x16812)+E(f285(x16813,x16811,x16814,x16815),f285(x16813,x16812,x16814,x16815))
% 11.41/11.20 [1682]~E(x16821,x16822)+E(f285(x16823,x16824,x16821,x16825),f285(x16823,x16824,x16822,x16825))
% 11.41/11.20 [1683]~E(x16831,x16832)+E(f285(x16833,x16834,x16835,x16831),f285(x16833,x16834,x16835,x16832))
% 11.41/11.20 [1684]~E(x16841,x16842)+E(f496(x16841,x16843,x16844),f496(x16842,x16843,x16844))
% 11.41/11.20 [1685]~E(x16851,x16852)+E(f496(x16853,x16851,x16854),f496(x16853,x16852,x16854))
% 11.41/11.20 [1686]~E(x16861,x16862)+E(f496(x16863,x16864,x16861),f496(x16863,x16864,x16862))
% 11.41/11.20 [1687]~E(x16871,x16872)+E(f102(x16871,x16873,x16874),f102(x16872,x16873,x16874))
% 11.41/11.20 [1688]~E(x16881,x16882)+E(f102(x16883,x16881,x16884),f102(x16883,x16882,x16884))
% 11.41/11.20 [1689]~E(x16891,x16892)+E(f102(x16893,x16894,x16891),f102(x16893,x16894,x16892))
% 11.41/11.20 [1690]~E(x16901,x16902)+E(f398(x16901,x16903,x16904,x16905),f398(x16902,x16903,x16904,x16905))
% 11.41/11.20 [1691]~E(x16911,x16912)+E(f398(x16913,x16911,x16914,x16915),f398(x16913,x16912,x16914,x16915))
% 11.41/11.20 [1692]~E(x16921,x16922)+E(f398(x16923,x16924,x16921,x16925),f398(x16923,x16924,x16922,x16925))
% 11.41/11.20 [1693]~E(x16931,x16932)+E(f398(x16933,x16934,x16935,x16931),f398(x16933,x16934,x16935,x16932))
% 11.41/11.20 [1694]~E(x16941,x16942)+E(f57(x16941),f57(x16942))
% 11.41/11.20 [1695]~E(x16951,x16952)+E(f646(x16951,x16953,x16954),f646(x16952,x16953,x16954))
% 11.41/11.20 [1696]~E(x16961,x16962)+E(f646(x16963,x16961,x16964),f646(x16963,x16962,x16964))
% 11.41/11.20 [1697]~E(x16971,x16972)+E(f646(x16973,x16974,x16971),f646(x16973,x16974,x16972))
% 11.41/11.20 [1698]~E(x16981,x16982)+E(f605(x16981,x16983,x16984),f605(x16982,x16983,x16984))
% 11.41/11.20 [1699]~E(x16991,x16992)+E(f605(x16993,x16991,x16994),f605(x16993,x16992,x16994))
% 11.41/11.20 [1700]~E(x17001,x17002)+E(f605(x17003,x17004,x17001),f605(x17003,x17004,x17002))
% 11.41/11.20 [1701]~E(x17011,x17012)+E(f422(x17011,x17013,x17014,x17015),f422(x17012,x17013,x17014,x17015))
% 11.41/11.20 [1702]~E(x17021,x17022)+E(f422(x17023,x17021,x17024,x17025),f422(x17023,x17022,x17024,x17025))
% 11.41/11.20 [1703]~E(x17031,x17032)+E(f422(x17033,x17034,x17031,x17035),f422(x17033,x17034,x17032,x17035))
% 11.41/11.20 [1704]~E(x17041,x17042)+E(f422(x17043,x17044,x17045,x17041),f422(x17043,x17044,x17045,x17042))
% 11.41/11.20 [1705]~E(x17051,x17052)+E(f844(x17051,x17053,x17054,x17055,x17056,x17057,x17058),f844(x17052,x17053,x17054,x17055,x17056,x17057,x17058))
% 11.41/11.20 [1706]~E(x17061,x17062)+E(f844(x17063,x17061,x17064,x17065,x17066,x17067,x17068),f844(x17063,x17062,x17064,x17065,x17066,x17067,x17068))
% 11.41/11.20 [1707]~E(x17071,x17072)+E(f844(x17073,x17074,x17071,x17075,x17076,x17077,x17078),f844(x17073,x17074,x17072,x17075,x17076,x17077,x17078))
% 11.41/11.20 [1708]~E(x17081,x17082)+E(f844(x17083,x17084,x17085,x17081,x17086,x17087,x17088),f844(x17083,x17084,x17085,x17082,x17086,x17087,x17088))
% 11.41/11.20 [1709]~E(x17091,x17092)+E(f844(x17093,x17094,x17095,x17096,x17091,x17097,x17098),f844(x17093,x17094,x17095,x17096,x17092,x17097,x17098))
% 11.41/11.20 [1710]~E(x17101,x17102)+E(f844(x17103,x17104,x17105,x17106,x17107,x17101,x17108),f844(x17103,x17104,x17105,x17106,x17107,x17102,x17108))
% 11.41/11.20 [1711]~E(x17111,x17112)+E(f844(x17113,x17114,x17115,x17116,x17117,x17118,x17111),f844(x17113,x17114,x17115,x17116,x17117,x17118,x17112))
% 11.41/11.20 [1712]~E(x17121,x17122)+E(f124(x17121,x17123,x17124,x17125),f124(x17122,x17123,x17124,x17125))
% 11.41/11.20 [1713]~E(x17131,x17132)+E(f124(x17133,x17131,x17134,x17135),f124(x17133,x17132,x17134,x17135))
% 11.41/11.20 [1714]~E(x17141,x17142)+E(f124(x17143,x17144,x17141,x17145),f124(x17143,x17144,x17142,x17145))
% 11.41/11.20 [1715]~E(x17151,x17152)+E(f124(x17153,x17154,x17155,x17151),f124(x17153,x17154,x17155,x17152))
% 11.41/11.20 [1716]~E(x17161,x17162)+E(f443(x17161,x17163,x17164,x17165),f443(x17162,x17163,x17164,x17165))
% 11.41/11.20 [1717]~E(x17171,x17172)+E(f443(x17173,x17171,x17174,x17175),f443(x17173,x17172,x17174,x17175))
% 11.41/11.20 [1718]~E(x17181,x17182)+E(f443(x17183,x17184,x17181,x17185),f443(x17183,x17184,x17182,x17185))
% 11.41/11.20 [1719]~E(x17191,x17192)+E(f443(x17193,x17194,x17195,x17191),f443(x17193,x17194,x17195,x17192))
% 11.41/11.20 [1720]~E(x17201,x17202)+E(f324(x17201,x17203,x17204),f324(x17202,x17203,x17204))
% 11.41/11.20 [1721]~E(x17211,x17212)+E(f324(x17213,x17211,x17214),f324(x17213,x17212,x17214))
% 11.41/11.20 [1722]~E(x17221,x17222)+E(f324(x17223,x17224,x17221),f324(x17223,x17224,x17222))
% 11.41/11.20 [1723]~E(x17231,x17232)+E(f604(x17231,x17233,x17234),f604(x17232,x17233,x17234))
% 11.41/11.20 [1724]~E(x17241,x17242)+E(f604(x17243,x17241,x17244),f604(x17243,x17242,x17244))
% 11.41/11.20 [1725]~E(x17251,x17252)+E(f604(x17253,x17254,x17251),f604(x17253,x17254,x17252))
% 11.41/11.20 [1726]~E(x17261,x17262)+E(f512(x17261,x17263,x17264,x17265,x17266,x17267,x17268),f512(x17262,x17263,x17264,x17265,x17266,x17267,x17268))
% 11.41/11.20 [1727]~E(x17271,x17272)+E(f512(x17273,x17271,x17274,x17275,x17276,x17277,x17278),f512(x17273,x17272,x17274,x17275,x17276,x17277,x17278))
% 11.41/11.20 [1728]~E(x17281,x17282)+E(f512(x17283,x17284,x17281,x17285,x17286,x17287,x17288),f512(x17283,x17284,x17282,x17285,x17286,x17287,x17288))
% 11.41/11.20 [1729]~E(x17291,x17292)+E(f512(x17293,x17294,x17295,x17291,x17296,x17297,x17298),f512(x17293,x17294,x17295,x17292,x17296,x17297,x17298))
% 11.41/11.20 [1730]~E(x17301,x17302)+E(f512(x17303,x17304,x17305,x17306,x17301,x17307,x17308),f512(x17303,x17304,x17305,x17306,x17302,x17307,x17308))
% 11.41/11.20 [1731]~E(x17311,x17312)+E(f512(x17313,x17314,x17315,x17316,x17317,x17311,x17318),f512(x17313,x17314,x17315,x17316,x17317,x17312,x17318))
% 11.41/11.20 [1732]~E(x17321,x17322)+E(f512(x17323,x17324,x17325,x17326,x17327,x17328,x17321),f512(x17323,x17324,x17325,x17326,x17327,x17328,x17322))
% 11.41/11.20 [1733]~E(x17331,x17332)+E(f610(x17331,x17333),f610(x17332,x17333))
% 11.41/11.20 [1734]~E(x17341,x17342)+E(f610(x17343,x17341),f610(x17343,x17342))
% 11.41/11.20 [1735]~E(x17351,x17352)+E(f489(x17351,x17353,x17354),f489(x17352,x17353,x17354))
% 11.41/11.20 [1736]~E(x17361,x17362)+E(f489(x17363,x17361,x17364),f489(x17363,x17362,x17364))
% 11.41/11.20 [1737]~E(x17371,x17372)+E(f489(x17373,x17374,x17371),f489(x17373,x17374,x17372))
% 11.41/11.20 [1738]~E(x17381,x17382)+E(f613(x17381,x17383),f613(x17382,x17383))
% 11.41/11.20 [1739]~E(x17391,x17392)+E(f613(x17393,x17391),f613(x17393,x17392))
% 11.41/11.20 [1740]~E(x17401,x17402)+E(f595(x17401,x17403,x17404,x17405),f595(x17402,x17403,x17404,x17405))
% 11.41/11.20 [1741]~E(x17411,x17412)+E(f595(x17413,x17411,x17414,x17415),f595(x17413,x17412,x17414,x17415))
% 11.41/11.20 [1742]~E(x17421,x17422)+E(f595(x17423,x17424,x17421,x17425),f595(x17423,x17424,x17422,x17425))
% 11.41/11.20 [1743]~E(x17431,x17432)+E(f595(x17433,x17434,x17435,x17431),f595(x17433,x17434,x17435,x17432))
% 11.41/11.20 [1744]~E(x17441,x17442)+E(f662(x17441,x17443,x17444),f662(x17442,x17443,x17444))
% 11.41/11.20 [1745]~E(x17451,x17452)+E(f662(x17453,x17451,x17454),f662(x17453,x17452,x17454))
% 11.41/11.20 [1746]~E(x17461,x17462)+E(f662(x17463,x17464,x17461),f662(x17463,x17464,x17462))
% 11.41/11.20 [1747]~E(x17471,x17472)+E(f472(x17471,x17473,x17474,x17475,x17476,x17477),f472(x17472,x17473,x17474,x17475,x17476,x17477))
% 11.41/11.20 [1748]~E(x17481,x17482)+E(f472(x17483,x17481,x17484,x17485,x17486,x17487),f472(x17483,x17482,x17484,x17485,x17486,x17487))
% 11.41/11.20 [1749]~E(x17491,x17492)+E(f472(x17493,x17494,x17491,x17495,x17496,x17497),f472(x17493,x17494,x17492,x17495,x17496,x17497))
% 11.41/11.20 [1750]~E(x17501,x17502)+E(f472(x17503,x17504,x17505,x17501,x17506,x17507),f472(x17503,x17504,x17505,x17502,x17506,x17507))
% 11.41/11.20 [1751]~E(x17511,x17512)+E(f472(x17513,x17514,x17515,x17516,x17511,x17517),f472(x17513,x17514,x17515,x17516,x17512,x17517))
% 11.41/11.20 [1752]~E(x17521,x17522)+E(f472(x17523,x17524,x17525,x17526,x17527,x17521),f472(x17523,x17524,x17525,x17526,x17527,x17522))
% 11.41/11.20 [1753]~E(x17531,x17532)+E(f140(x17531,x17533),f140(x17532,x17533))
% 11.41/11.20 [1754]~E(x17541,x17542)+E(f140(x17543,x17541),f140(x17543,x17542))
% 11.41/11.20 [1755]~E(x17551,x17552)+E(f228(x17551,x17553,x17554,x17555,x17556),f228(x17552,x17553,x17554,x17555,x17556))
% 11.41/11.20 [1756]~E(x17561,x17562)+E(f228(x17563,x17561,x17564,x17565,x17566),f228(x17563,x17562,x17564,x17565,x17566))
% 11.41/11.20 [1757]~E(x17571,x17572)+E(f228(x17573,x17574,x17571,x17575,x17576),f228(x17573,x17574,x17572,x17575,x17576))
% 11.41/11.20 [1758]~E(x17581,x17582)+E(f228(x17583,x17584,x17585,x17581,x17586),f228(x17583,x17584,x17585,x17582,x17586))
% 11.41/11.20 [1759]~E(x17591,x17592)+E(f228(x17593,x17594,x17595,x17596,x17591),f228(x17593,x17594,x17595,x17596,x17592))
% 11.41/11.20 [1760]~E(x17601,x17602)+E(f445(x17601,x17603,x17604,x17605),f445(x17602,x17603,x17604,x17605))
% 11.41/11.20 [1761]~E(x17611,x17612)+E(f445(x17613,x17611,x17614,x17615),f445(x17613,x17612,x17614,x17615))
% 11.41/11.20 [1762]~E(x17621,x17622)+E(f445(x17623,x17624,x17621,x17625),f445(x17623,x17624,x17622,x17625))
% 11.41/11.20 [1763]~E(x17631,x17632)+E(f445(x17633,x17634,x17635,x17631),f445(x17633,x17634,x17635,x17632))
% 11.41/11.20 [1764]~E(x17641,x17642)+E(f680(x17641,x17643,x17644,x17645,x17646),f680(x17642,x17643,x17644,x17645,x17646))
% 11.41/11.20 [1765]~E(x17651,x17652)+E(f680(x17653,x17651,x17654,x17655,x17656),f680(x17653,x17652,x17654,x17655,x17656))
% 11.41/11.20 [1766]~E(x17661,x17662)+E(f680(x17663,x17664,x17661,x17665,x17666),f680(x17663,x17664,x17662,x17665,x17666))
% 11.41/11.20 [1767]~E(x17671,x17672)+E(f680(x17673,x17674,x17675,x17671,x17676),f680(x17673,x17674,x17675,x17672,x17676))
% 11.41/11.20 [1768]~E(x17681,x17682)+E(f680(x17683,x17684,x17685,x17686,x17681),f680(x17683,x17684,x17685,x17686,x17682))
% 11.41/11.20 [1769]~E(x17691,x17692)+E(f419(x17691,x17693,x17694,x17695),f419(x17692,x17693,x17694,x17695))
% 11.41/11.20 [1770]~E(x17701,x17702)+E(f419(x17703,x17701,x17704,x17705),f419(x17703,x17702,x17704,x17705))
% 11.41/11.20 [1771]~E(x17711,x17712)+E(f419(x17713,x17714,x17711,x17715),f419(x17713,x17714,x17712,x17715))
% 11.41/11.20 [1772]~E(x17721,x17722)+E(f419(x17723,x17724,x17725,x17721),f419(x17723,x17724,x17725,x17722))
% 11.41/11.20 [1773]~E(x17731,x17732)+E(f572(x17731,x17733,x17734),f572(x17732,x17733,x17734))
% 11.41/11.20 [1774]~E(x17741,x17742)+E(f572(x17743,x17741,x17744),f572(x17743,x17742,x17744))
% 11.41/11.20 [1775]~E(x17751,x17752)+E(f572(x17753,x17754,x17751),f572(x17753,x17754,x17752))
% 11.41/11.20 [1776]~E(x17761,x17762)+E(f433(x17761,x17763,x17764),f433(x17762,x17763,x17764))
% 11.41/11.20 [1777]~E(x17771,x17772)+E(f433(x17773,x17771,x17774),f433(x17773,x17772,x17774))
% 11.41/11.20 [1778]~E(x17781,x17782)+E(f433(x17783,x17784,x17781),f433(x17783,x17784,x17782))
% 11.41/11.20 [1779]~E(x17791,x17792)+E(f699(x17791,x17793,x17794),f699(x17792,x17793,x17794))
% 11.41/11.20 [1780]~E(x17801,x17802)+E(f699(x17803,x17801,x17804),f699(x17803,x17802,x17804))
% 11.41/11.20 [1781]~E(x17811,x17812)+E(f699(x17813,x17814,x17811),f699(x17813,x17814,x17812))
% 11.41/11.20 [1782]~E(x17821,x17822)+E(f865(x17821,x17823),f865(x17822,x17823))
% 11.41/11.20 [1783]~E(x17831,x17832)+E(f865(x17833,x17831),f865(x17833,x17832))
% 11.41/11.20 [1784]~E(x17841,x17842)+E(f637(x17841,x17843,x17844,x17845,x17846,x17847),f637(x17842,x17843,x17844,x17845,x17846,x17847))
% 11.41/11.20 [1785]~E(x17851,x17852)+E(f637(x17853,x17851,x17854,x17855,x17856,x17857),f637(x17853,x17852,x17854,x17855,x17856,x17857))
% 11.41/11.20 [1786]~E(x17861,x17862)+E(f637(x17863,x17864,x17861,x17865,x17866,x17867),f637(x17863,x17864,x17862,x17865,x17866,x17867))
% 11.41/11.20 [1787]~E(x17871,x17872)+E(f637(x17873,x17874,x17875,x17871,x17876,x17877),f637(x17873,x17874,x17875,x17872,x17876,x17877))
% 11.41/11.20 [1788]~E(x17881,x17882)+E(f637(x17883,x17884,x17885,x17886,x17881,x17887),f637(x17883,x17884,x17885,x17886,x17882,x17887))
% 11.41/11.20 [1789]~E(x17891,x17892)+E(f637(x17893,x17894,x17895,x17896,x17897,x17891),f637(x17893,x17894,x17895,x17896,x17897,x17892))
% 11.41/11.20 [1790]~E(x17901,x17902)+E(f557(x17901,x17903,x17904,x17905,x17906,x17907),f557(x17902,x17903,x17904,x17905,x17906,x17907))
% 11.41/11.20 [1791]~E(x17911,x17912)+E(f557(x17913,x17911,x17914,x17915,x17916,x17917),f557(x17913,x17912,x17914,x17915,x17916,x17917))
% 11.41/11.20 [1792]~E(x17921,x17922)+E(f557(x17923,x17924,x17921,x17925,x17926,x17927),f557(x17923,x17924,x17922,x17925,x17926,x17927))
% 11.41/11.20 [1793]~E(x17931,x17932)+E(f557(x17933,x17934,x17935,x17931,x17936,x17937),f557(x17933,x17934,x17935,x17932,x17936,x17937))
% 11.41/11.20 [1794]~E(x17941,x17942)+E(f557(x17943,x17944,x17945,x17946,x17941,x17947),f557(x17943,x17944,x17945,x17946,x17942,x17947))
% 11.41/11.20 [1795]~E(x17951,x17952)+E(f557(x17953,x17954,x17955,x17956,x17957,x17951),f557(x17953,x17954,x17955,x17956,x17957,x17952))
% 11.41/11.20 [1796]~E(x17961,x17962)+E(f499(x17961,x17963,x17964,x17965),f499(x17962,x17963,x17964,x17965))
% 11.41/11.20 [1797]~E(x17971,x17972)+E(f499(x17973,x17971,x17974,x17975),f499(x17973,x17972,x17974,x17975))
% 11.41/11.20 [1798]~E(x17981,x17982)+E(f499(x17983,x17984,x17981,x17985),f499(x17983,x17984,x17982,x17985))
% 11.41/11.20 [1799]~E(x17991,x17992)+E(f499(x17993,x17994,x17995,x17991),f499(x17993,x17994,x17995,x17992))
% 11.41/11.20 [1800]~E(x18001,x18002)+E(f231(x18001,x18003),f231(x18002,x18003))
% 11.41/11.20 [1801]~E(x18011,x18012)+E(f231(x18013,x18011),f231(x18013,x18012))
% 11.41/11.20 [1802]~E(x18021,x18022)+E(f748(x18021,x18023,x18024,x18025,x18026),f748(x18022,x18023,x18024,x18025,x18026))
% 11.41/11.20 [1803]~E(x18031,x18032)+E(f748(x18033,x18031,x18034,x18035,x18036),f748(x18033,x18032,x18034,x18035,x18036))
% 11.41/11.20 [1804]~E(x18041,x18042)+E(f748(x18043,x18044,x18041,x18045,x18046),f748(x18043,x18044,x18042,x18045,x18046))
% 11.41/11.20 [1805]~E(x18051,x18052)+E(f748(x18053,x18054,x18055,x18051,x18056),f748(x18053,x18054,x18055,x18052,x18056))
% 11.41/11.20 [1806]~E(x18061,x18062)+E(f748(x18063,x18064,x18065,x18066,x18061),f748(x18063,x18064,x18065,x18066,x18062))
% 11.41/11.20 [1807]~E(x18071,x18072)+E(f462(x18071),f462(x18072))
% 11.41/11.20 [1808]~E(x18081,x18082)+E(f562(x18081,x18083),f562(x18082,x18083))
% 11.41/11.20 [1809]~E(x18091,x18092)+E(f562(x18093,x18091),f562(x18093,x18092))
% 11.41/11.20 [1810]~E(x18101,x18102)+E(f533(x18101,x18103,x18104,x18105),f533(x18102,x18103,x18104,x18105))
% 11.41/11.20 [1811]~E(x18111,x18112)+E(f533(x18113,x18111,x18114,x18115),f533(x18113,x18112,x18114,x18115))
% 11.41/11.20 [1812]~E(x18121,x18122)+E(f533(x18123,x18124,x18121,x18125),f533(x18123,x18124,x18122,x18125))
% 11.41/11.20 [1813]~E(x18131,x18132)+E(f533(x18133,x18134,x18135,x18131),f533(x18133,x18134,x18135,x18132))
% 11.41/11.20 [1814]~E(x18141,x18142)+E(f617(x18141,x18143,x18144),f617(x18142,x18143,x18144))
% 11.41/11.20 [1815]~E(x18151,x18152)+E(f617(x18153,x18151,x18154),f617(x18153,x18152,x18154))
% 11.41/11.20 [1816]~E(x18161,x18162)+E(f617(x18163,x18164,x18161),f617(x18163,x18164,x18162))
% 11.41/11.20 [1817]~E(x18171,x18172)+E(f590(x18171,x18173,x18174,x18175,x18176,x18177),f590(x18172,x18173,x18174,x18175,x18176,x18177))
% 11.41/11.20 [1818]~E(x18181,x18182)+E(f590(x18183,x18181,x18184,x18185,x18186,x18187),f590(x18183,x18182,x18184,x18185,x18186,x18187))
% 11.41/11.20 [1819]~E(x18191,x18192)+E(f590(x18193,x18194,x18191,x18195,x18196,x18197),f590(x18193,x18194,x18192,x18195,x18196,x18197))
% 11.41/11.20 [1820]~E(x18201,x18202)+E(f590(x18203,x18204,x18205,x18201,x18206,x18207),f590(x18203,x18204,x18205,x18202,x18206,x18207))
% 11.41/11.20 [1821]~E(x18211,x18212)+E(f590(x18213,x18214,x18215,x18216,x18211,x18217),f590(x18213,x18214,x18215,x18216,x18212,x18217))
% 11.41/11.20 [1822]~E(x18221,x18222)+E(f590(x18223,x18224,x18225,x18226,x18227,x18221),f590(x18223,x18224,x18225,x18226,x18227,x18222))
% 11.41/11.20 [1823]~E(x18231,x18232)+E(f245(x18231,x18233),f245(x18232,x18233))
% 11.41/11.20 [1824]~E(x18241,x18242)+E(f245(x18243,x18241),f245(x18243,x18242))
% 11.41/11.20 [1825]~E(x18251,x18252)+E(f638(x18251),f638(x18252))
% 11.41/11.20 [1826]~E(x18261,x18262)+E(f453(x18261,x18263),f453(x18262,x18263))
% 11.41/11.20 [1827]~E(x18271,x18272)+E(f453(x18273,x18271),f453(x18273,x18272))
% 11.41/11.20 [1828]~E(x18281,x18282)+E(f428(x18281,x18283,x18284),f428(x18282,x18283,x18284))
% 11.41/11.20 [1829]~E(x18291,x18292)+E(f428(x18293,x18291,x18294),f428(x18293,x18292,x18294))
% 11.41/11.20 [1830]~E(x18301,x18302)+E(f428(x18303,x18304,x18301),f428(x18303,x18304,x18302))
% 11.41/11.20 [1831]~E(x18311,x18312)+E(f804(x18311,x18313,x18314),f804(x18312,x18313,x18314))
% 11.41/11.20 [1832]~E(x18321,x18322)+E(f804(x18323,x18321,x18324),f804(x18323,x18322,x18324))
% 11.41/11.20 [1833]~E(x18331,x18332)+E(f804(x18333,x18334,x18331),f804(x18333,x18334,x18332))
% 11.41/11.20 [1834]~E(x18341,x18342)+E(f745(x18341,x18343,x18344,x18345),f745(x18342,x18343,x18344,x18345))
% 11.41/11.20 [1835]~E(x18351,x18352)+E(f745(x18353,x18351,x18354,x18355),f745(x18353,x18352,x18354,x18355))
% 11.41/11.20 [1836]~E(x18361,x18362)+E(f745(x18363,x18364,x18361,x18365),f745(x18363,x18364,x18362,x18365))
% 11.41/11.20 [1837]~E(x18371,x18372)+E(f745(x18373,x18374,x18375,x18371),f745(x18373,x18374,x18375,x18372))
% 11.41/11.20 [1838]~E(x18381,x18382)+E(f354(x18381,x18383),f354(x18382,x18383))
% 11.41/11.20 [1839]~E(x18391,x18392)+E(f354(x18393,x18391),f354(x18393,x18392))
% 11.41/11.20 [1840]~E(x18401,x18402)+E(f491(x18401,x18403,x18404),f491(x18402,x18403,x18404))
% 11.41/11.20 [1841]~E(x18411,x18412)+E(f491(x18413,x18411,x18414),f491(x18413,x18412,x18414))
% 11.41/11.20 [1842]~E(x18421,x18422)+E(f491(x18423,x18424,x18421),f491(x18423,x18424,x18422))
% 11.41/11.20 [1843]~E(x18431,x18432)+E(f841(x18431,x18433,x18434),f841(x18432,x18433,x18434))
% 11.41/11.20 [1844]~E(x18441,x18442)+E(f841(x18443,x18441,x18444),f841(x18443,x18442,x18444))
% 11.41/11.20 [1845]~E(x18451,x18452)+E(f841(x18453,x18454,x18451),f841(x18453,x18454,x18452))
% 11.41/11.20 [1846]~E(x18461,x18462)+E(f656(x18461,x18463,x18464,x18465,x18466),f656(x18462,x18463,x18464,x18465,x18466))
% 11.41/11.20 [1847]~E(x18471,x18472)+E(f656(x18473,x18471,x18474,x18475,x18476),f656(x18473,x18472,x18474,x18475,x18476))
% 11.41/11.20 [1848]~E(x18481,x18482)+E(f656(x18483,x18484,x18481,x18485,x18486),f656(x18483,x18484,x18482,x18485,x18486))
% 11.41/11.20 [1849]~E(x18491,x18492)+E(f656(x18493,x18494,x18495,x18491,x18496),f656(x18493,x18494,x18495,x18492,x18496))
% 11.41/11.20 [1850]~E(x18501,x18502)+E(f656(x18503,x18504,x18505,x18506,x18501),f656(x18503,x18504,x18505,x18506,x18502))
% 11.41/11.20 [1851]~E(x18511,x18512)+E(f582(x18511,x18513),f582(x18512,x18513))
% 11.41/11.20 [1852]~E(x18521,x18522)+E(f582(x18523,x18521),f582(x18523,x18522))
% 11.41/11.20 [1853]~E(x18531,x18532)+E(f405(x18531,x18533,x18534,x18535,x18536),f405(x18532,x18533,x18534,x18535,x18536))
% 11.41/11.20 [1854]~E(x18541,x18542)+E(f405(x18543,x18541,x18544,x18545,x18546),f405(x18543,x18542,x18544,x18545,x18546))
% 11.41/11.20 [1855]~E(x18551,x18552)+E(f405(x18553,x18554,x18551,x18555,x18556),f405(x18553,x18554,x18552,x18555,x18556))
% 11.41/11.20 [1856]~E(x18561,x18562)+E(f405(x18563,x18564,x18565,x18561,x18566),f405(x18563,x18564,x18565,x18562,x18566))
% 11.41/11.20 [1857]~E(x18571,x18572)+E(f405(x18573,x18574,x18575,x18576,x18571),f405(x18573,x18574,x18575,x18576,x18572))
% 11.41/11.20 [1858]~E(x18581,x18582)+E(f644(x18581,x18583,x18584),f644(x18582,x18583,x18584))
% 11.41/11.20 [1859]~E(x18591,x18592)+E(f644(x18593,x18591,x18594),f644(x18593,x18592,x18594))
% 11.41/11.20 [1860]~E(x18601,x18602)+E(f644(x18603,x18604,x18601),f644(x18603,x18604,x18602))
% 11.41/11.20 [1861]~E(x18611,x18612)+E(f571(x18611,x18613,x18614),f571(x18612,x18613,x18614))
% 11.41/11.20 [1862]~E(x18621,x18622)+E(f571(x18623,x18621,x18624),f571(x18623,x18622,x18624))
% 11.41/11.20 [1863]~E(x18631,x18632)+E(f571(x18633,x18634,x18631),f571(x18633,x18634,x18632))
% 11.41/11.20 [1864]~E(x18641,x18642)+E(f383(x18641,x18643),f383(x18642,x18643))
% 11.41/11.20 [1865]~E(x18651,x18652)+E(f383(x18653,x18651),f383(x18653,x18652))
% 11.41/11.20 [1866]~E(x18661,x18662)+E(f830(x18661,x18663,x18664),f830(x18662,x18663,x18664))
% 11.41/11.20 [1867]~E(x18671,x18672)+E(f830(x18673,x18671,x18674),f830(x18673,x18672,x18674))
% 11.41/11.20 [1868]~E(x18681,x18682)+E(f830(x18683,x18684,x18681),f830(x18683,x18684,x18682))
% 11.41/11.20 [1869]~E(x18691,x18692)+E(f473(x18691,x18693,x18694,x18695),f473(x18692,x18693,x18694,x18695))
% 11.41/11.20 [1870]~E(x18701,x18702)+E(f473(x18703,x18701,x18704,x18705),f473(x18703,x18702,x18704,x18705))
% 11.41/11.20 [1871]~E(x18711,x18712)+E(f473(x18713,x18714,x18711,x18715),f473(x18713,x18714,x18712,x18715))
% 11.41/11.20 [1872]~E(x18721,x18722)+E(f473(x18723,x18724,x18725,x18721),f473(x18723,x18724,x18725,x18722))
% 11.41/11.20 [1873]~E(x18731,x18732)+E(f814(x18731,x18733,x18734),f814(x18732,x18733,x18734))
% 11.41/11.20 [1874]~E(x18741,x18742)+E(f814(x18743,x18741,x18744),f814(x18743,x18742,x18744))
% 11.41/11.20 [1875]~E(x18751,x18752)+E(f814(x18753,x18754,x18751),f814(x18753,x18754,x18752))
% 11.41/11.20 [1876]~E(x18761,x18762)+E(f295(x18761,x18763),f295(x18762,x18763))
% 11.41/11.20 [1877]~E(x18771,x18772)+E(f295(x18773,x18771),f295(x18773,x18772))
% 11.41/11.20 [1878]~E(x18781,x18782)+E(f411(x18781,x18783,x18784),f411(x18782,x18783,x18784))
% 11.41/11.20 [1879]~E(x18791,x18792)+E(f411(x18793,x18791,x18794),f411(x18793,x18792,x18794))
% 11.41/11.20 [1880]~E(x18801,x18802)+E(f411(x18803,x18804,x18801),f411(x18803,x18804,x18802))
% 11.41/11.20 [1881]~E(x18811,x18812)+E(f396(x18811,x18813,x18814,x18815),f396(x18812,x18813,x18814,x18815))
% 11.41/11.20 [1882]~E(x18821,x18822)+E(f396(x18823,x18821,x18824,x18825),f396(x18823,x18822,x18824,x18825))
% 11.41/11.20 [1883]~E(x18831,x18832)+E(f396(x18833,x18834,x18831,x18835),f396(x18833,x18834,x18832,x18835))
% 11.41/11.20 [1884]~E(x18841,x18842)+E(f396(x18843,x18844,x18845,x18841),f396(x18843,x18844,x18845,x18842))
% 11.41/11.20 [1885]~E(x18851,x18852)+E(f704(x18851,x18853,x18854,x18855,x18856,x18857,x18858),f704(x18852,x18853,x18854,x18855,x18856,x18857,x18858))
% 11.41/11.20 [1886]~E(x18861,x18862)+E(f704(x18863,x18861,x18864,x18865,x18866,x18867,x18868),f704(x18863,x18862,x18864,x18865,x18866,x18867,x18868))
% 11.41/11.20 [1887]~E(x18871,x18872)+E(f704(x18873,x18874,x18871,x18875,x18876,x18877,x18878),f704(x18873,x18874,x18872,x18875,x18876,x18877,x18878))
% 11.41/11.20 [1888]~E(x18881,x18882)+E(f704(x18883,x18884,x18885,x18881,x18886,x18887,x18888),f704(x18883,x18884,x18885,x18882,x18886,x18887,x18888))
% 11.41/11.20 [1889]~E(x18891,x18892)+E(f704(x18893,x18894,x18895,x18896,x18891,x18897,x18898),f704(x18893,x18894,x18895,x18896,x18892,x18897,x18898))
% 11.41/11.20 [1890]~E(x18901,x18902)+E(f704(x18903,x18904,x18905,x18906,x18907,x18901,x18908),f704(x18903,x18904,x18905,x18906,x18907,x18902,x18908))
% 11.41/11.20 [1891]~E(x18911,x18912)+E(f704(x18913,x18914,x18915,x18916,x18917,x18918,x18911),f704(x18913,x18914,x18915,x18916,x18917,x18918,x18912))
% 11.41/11.20 [1892]~E(x18921,x18922)+E(f424(x18921,x18923,x18924,x18925,x18926),f424(x18922,x18923,x18924,x18925,x18926))
% 11.41/11.20 [1893]~E(x18931,x18932)+E(f424(x18933,x18931,x18934,x18935,x18936),f424(x18933,x18932,x18934,x18935,x18936))
% 11.41/11.20 [1894]~E(x18941,x18942)+E(f424(x18943,x18944,x18941,x18945,x18946),f424(x18943,x18944,x18942,x18945,x18946))
% 11.41/11.20 [1895]~E(x18951,x18952)+E(f424(x18953,x18954,x18955,x18951,x18956),f424(x18953,x18954,x18955,x18952,x18956))
% 11.41/11.20 [1896]~E(x18961,x18962)+E(f424(x18963,x18964,x18965,x18966,x18961),f424(x18963,x18964,x18965,x18966,x18962))
% 11.41/11.20 [1897]~E(x18971,x18972)+E(f549(x18971,x18973,x18974,x18975,x18976),f549(x18972,x18973,x18974,x18975,x18976))
% 11.41/11.20 [1898]~E(x18981,x18982)+E(f549(x18983,x18981,x18984,x18985,x18986),f549(x18983,x18982,x18984,x18985,x18986))
% 11.41/11.20 [1899]~E(x18991,x18992)+E(f549(x18993,x18994,x18991,x18995,x18996),f549(x18993,x18994,x18992,x18995,x18996))
% 11.41/11.20 [1900]~E(x19001,x19002)+E(f549(x19003,x19004,x19005,x19001,x19006),f549(x19003,x19004,x19005,x19002,x19006))
% 11.41/11.20 [1901]~E(x19011,x19012)+E(f549(x19013,x19014,x19015,x19016,x19011),f549(x19013,x19014,x19015,x19016,x19012))
% 11.41/11.20 [1902]~E(x19021,x19022)+E(f281(x19021,x19023,x19024,x19025),f281(x19022,x19023,x19024,x19025))
% 11.41/11.20 [1903]~E(x19031,x19032)+E(f281(x19033,x19031,x19034,x19035),f281(x19033,x19032,x19034,x19035))
% 11.41/11.20 [1904]~E(x19041,x19042)+E(f281(x19043,x19044,x19041,x19045),f281(x19043,x19044,x19042,x19045))
% 11.41/11.20 [1905]~E(x19051,x19052)+E(f281(x19053,x19054,x19055,x19051),f281(x19053,x19054,x19055,x19052))
% 11.41/11.20 [1906]~E(x19061,x19062)+E(f384(x19061,x19063,x19064,x19065,x19066,x19067,x19068,x19069),f384(x19062,x19063,x19064,x19065,x19066,x19067,x19068,x19069))
% 11.41/11.20 [1907]~E(x19071,x19072)+E(f384(x19073,x19071,x19074,x19075,x19076,x19077,x19078,x19079),f384(x19073,x19072,x19074,x19075,x19076,x19077,x19078,x19079))
% 11.41/11.20 [1908]~E(x19081,x19082)+E(f384(x19083,x19084,x19081,x19085,x19086,x19087,x19088,x19089),f384(x19083,x19084,x19082,x19085,x19086,x19087,x19088,x19089))
% 11.41/11.20 [1909]~E(x19091,x19092)+E(f384(x19093,x19094,x19095,x19091,x19096,x19097,x19098,x19099),f384(x19093,x19094,x19095,x19092,x19096,x19097,x19098,x19099))
% 11.41/11.20 [1910]~E(x19101,x19102)+E(f384(x19103,x19104,x19105,x19106,x19101,x19107,x19108,x19109),f384(x19103,x19104,x19105,x19106,x19102,x19107,x19108,x19109))
% 11.41/11.20 [1911]~E(x19111,x19112)+E(f384(x19113,x19114,x19115,x19116,x19117,x19111,x19118,x19119),f384(x19113,x19114,x19115,x19116,x19117,x19112,x19118,x19119))
% 11.41/11.20 [1912]~E(x19121,x19122)+E(f384(x19123,x19124,x19125,x19126,x19127,x19128,x19121,x19129),f384(x19123,x19124,x19125,x19126,x19127,x19128,x19122,x19129))
% 11.41/11.20 [1913]~E(x19131,x19132)+E(f384(x19133,x19134,x19135,x19136,x19137,x19138,x19139,x19131),f384(x19133,x19134,x19135,x19136,x19137,x19138,x19139,x19132))
% 11.41/11.20 [1914]~E(x19141,x19142)+E(f615(x19141,x19143,x19144),f615(x19142,x19143,x19144))
% 11.41/11.20 [1915]~E(x19151,x19152)+E(f615(x19153,x19151,x19154),f615(x19153,x19152,x19154))
% 11.41/11.20 [1916]~E(x19161,x19162)+E(f615(x19163,x19164,x19161),f615(x19163,x19164,x19162))
% 11.41/11.20 [1917]~E(x19171,x19172)+E(f189(x19171,x19173,x19174,x19175),f189(x19172,x19173,x19174,x19175))
% 11.41/11.20 [1918]~E(x19181,x19182)+E(f189(x19183,x19181,x19184,x19185),f189(x19183,x19182,x19184,x19185))
% 11.41/11.20 [1919]~E(x19191,x19192)+E(f189(x19193,x19194,x19191,x19195),f189(x19193,x19194,x19192,x19195))
% 11.41/11.20 [1920]~E(x19201,x19202)+E(f189(x19203,x19204,x19205,x19201),f189(x19203,x19204,x19205,x19202))
% 11.41/11.20 [1921]~E(x19211,x19212)+E(f278(x19211,x19213,x19214,x19215),f278(x19212,x19213,x19214,x19215))
% 11.41/11.20 [1922]~E(x19221,x19222)+E(f278(x19223,x19221,x19224,x19225),f278(x19223,x19222,x19224,x19225))
% 11.41/11.20 [1923]~E(x19231,x19232)+E(f278(x19233,x19234,x19231,x19235),f278(x19233,x19234,x19232,x19235))
% 11.41/11.20 [1924]~E(x19241,x19242)+E(f278(x19243,x19244,x19245,x19241),f278(x19243,x19244,x19245,x19242))
% 11.41/11.20 [1925]~E(x19251,x19252)+E(f128(x19251),f128(x19252))
% 11.41/11.20 [1926]~E(x19261,x19262)+E(f581(x19261,x19263,x19264,x19265,x19266),f581(x19262,x19263,x19264,x19265,x19266))
% 11.41/11.20 [1927]~E(x19271,x19272)+E(f581(x19273,x19271,x19274,x19275,x19276),f581(x19273,x19272,x19274,x19275,x19276))
% 11.41/11.20 [1928]~E(x19281,x19282)+E(f581(x19283,x19284,x19281,x19285,x19286),f581(x19283,x19284,x19282,x19285,x19286))
% 11.41/11.20 [1929]~E(x19291,x19292)+E(f581(x19293,x19294,x19295,x19291,x19296),f581(x19293,x19294,x19295,x19292,x19296))
% 11.41/11.20 [1930]~E(x19301,x19302)+E(f581(x19303,x19304,x19305,x19306,x19301),f581(x19303,x19304,x19305,x19306,x19302))
% 11.41/11.20 [1931]~E(x19311,x19312)+E(f556(x19311,x19313,x19314,x19315,x19316,x19317),f556(x19312,x19313,x19314,x19315,x19316,x19317))
% 11.41/11.20 [1932]~E(x19321,x19322)+E(f556(x19323,x19321,x19324,x19325,x19326,x19327),f556(x19323,x19322,x19324,x19325,x19326,x19327))
% 11.41/11.20 [1933]~E(x19331,x19332)+E(f556(x19333,x19334,x19331,x19335,x19336,x19337),f556(x19333,x19334,x19332,x19335,x19336,x19337))
% 11.41/11.20 [1934]~E(x19341,x19342)+E(f556(x19343,x19344,x19345,x19341,x19346,x19347),f556(x19343,x19344,x19345,x19342,x19346,x19347))
% 11.41/11.20 [1935]~E(x19351,x19352)+E(f556(x19353,x19354,x19355,x19356,x19351,x19357),f556(x19353,x19354,x19355,x19356,x19352,x19357))
% 11.41/11.20 [1936]~E(x19361,x19362)+E(f556(x19363,x19364,x19365,x19366,x19367,x19361),f556(x19363,x19364,x19365,x19366,x19367,x19362))
% 11.41/11.20 [1937]~E(x19371,x19372)+E(f318(x19371,x19373,x19374),f318(x19372,x19373,x19374))
% 11.41/11.20 [1938]~E(x19381,x19382)+E(f318(x19383,x19381,x19384),f318(x19383,x19382,x19384))
% 11.41/11.20 [1939]~E(x19391,x19392)+E(f318(x19393,x19394,x19391),f318(x19393,x19394,x19392))
% 11.41/11.20 [1940]~E(x19401,x19402)+E(f377(x19401,x19403,x19404,x19405,x19406),f377(x19402,x19403,x19404,x19405,x19406))
% 11.41/11.20 [1941]~E(x19411,x19412)+E(f377(x19413,x19411,x19414,x19415,x19416),f377(x19413,x19412,x19414,x19415,x19416))
% 11.41/11.20 [1942]~E(x19421,x19422)+E(f377(x19423,x19424,x19421,x19425,x19426),f377(x19423,x19424,x19422,x19425,x19426))
% 11.41/11.20 [1943]~E(x19431,x19432)+E(f377(x19433,x19434,x19435,x19431,x19436),f377(x19433,x19434,x19435,x19432,x19436))
% 11.41/11.20 [1944]~E(x19441,x19442)+E(f377(x19443,x19444,x19445,x19446,x19441),f377(x19443,x19444,x19445,x19446,x19442))
% 11.41/11.20 [1945]~E(x19451,x19452)+E(f653(x19451,x19453),f653(x19452,x19453))
% 11.41/11.20 [1946]~E(x19461,x19462)+E(f653(x19463,x19461),f653(x19463,x19462))
% 11.41/11.20 [1947]~E(x19471,x19472)+E(f167(x19471,x19473,x19474),f167(x19472,x19473,x19474))
% 11.41/11.20 [1948]~E(x19481,x19482)+E(f167(x19483,x19481,x19484),f167(x19483,x19482,x19484))
% 11.41/11.20 [1949]~E(x19491,x19492)+E(f167(x19493,x19494,x19491),f167(x19493,x19494,x19492))
% 11.41/11.20 [1950]~E(x19501,x19502)+E(f461(x19501,x19503,x19504,x19505,x19506,x19507,x19508),f461(x19502,x19503,x19504,x19505,x19506,x19507,x19508))
% 11.41/11.20 [1951]~E(x19511,x19512)+E(f461(x19513,x19511,x19514,x19515,x19516,x19517,x19518),f461(x19513,x19512,x19514,x19515,x19516,x19517,x19518))
% 11.41/11.20 [1952]~E(x19521,x19522)+E(f461(x19523,x19524,x19521,x19525,x19526,x19527,x19528),f461(x19523,x19524,x19522,x19525,x19526,x19527,x19528))
% 11.41/11.20 [1953]~E(x19531,x19532)+E(f461(x19533,x19534,x19535,x19531,x19536,x19537,x19538),f461(x19533,x19534,x19535,x19532,x19536,x19537,x19538))
% 11.41/11.20 [1954]~E(x19541,x19542)+E(f461(x19543,x19544,x19545,x19546,x19541,x19547,x19548),f461(x19543,x19544,x19545,x19546,x19542,x19547,x19548))
% 11.41/11.20 [1955]~E(x19551,x19552)+E(f461(x19553,x19554,x19555,x19556,x19557,x19551,x19558),f461(x19553,x19554,x19555,x19556,x19557,x19552,x19558))
% 11.41/11.20 [1956]~E(x19561,x19562)+E(f461(x19563,x19564,x19565,x19566,x19567,x19568,x19561),f461(x19563,x19564,x19565,x19566,x19567,x19568,x19562))
% 11.41/11.20 [1957]~E(x19571,x19572)+E(f464(x19571,x19573,x19574,x19575),f464(x19572,x19573,x19574,x19575))
% 11.41/11.20 [1958]~E(x19581,x19582)+E(f464(x19583,x19581,x19584,x19585),f464(x19583,x19582,x19584,x19585))
% 11.41/11.20 [1959]~E(x19591,x19592)+E(f464(x19593,x19594,x19591,x19595),f464(x19593,x19594,x19592,x19595))
% 11.41/11.20 [1960]~E(x19601,x19602)+E(f464(x19603,x19604,x19605,x19601),f464(x19603,x19604,x19605,x19602))
% 11.41/11.20 [1961]~E(x19611,x19612)+E(f708(x19611,x19613,x19614),f708(x19612,x19613,x19614))
% 11.41/11.20 [1962]~E(x19621,x19622)+E(f708(x19623,x19621,x19624),f708(x19623,x19622,x19624))
% 11.41/11.20 [1963]~E(x19631,x19632)+E(f708(x19633,x19634,x19631),f708(x19633,x19634,x19632))
% 11.41/11.20 [1964]~E(x19641,x19642)+E(f525(x19641,x19643),f525(x19642,x19643))
% 11.41/11.20 [1965]~E(x19651,x19652)+E(f525(x19653,x19651),f525(x19653,x19652))
% 11.41/11.20 [1966]~E(x19661,x19662)+E(f480(x19661,x19663,x19664),f480(x19662,x19663,x19664))
% 11.41/11.20 [1967]~E(x19671,x19672)+E(f480(x19673,x19671,x19674),f480(x19673,x19672,x19674))
% 11.41/11.20 [1968]~E(x19681,x19682)+E(f480(x19683,x19684,x19681),f480(x19683,x19684,x19682))
% 11.41/11.20 [1969]~E(x19691,x19692)+E(f214(x19691,x19693,x19694,x19695),f214(x19692,x19693,x19694,x19695))
% 11.41/11.20 [1970]~E(x19701,x19702)+E(f214(x19703,x19701,x19704,x19705),f214(x19703,x19702,x19704,x19705))
% 11.41/11.20 [1971]~E(x19711,x19712)+E(f214(x19713,x19714,x19711,x19715),f214(x19713,x19714,x19712,x19715))
% 11.41/11.20 [1972]~E(x19721,x19722)+E(f214(x19723,x19724,x19725,x19721),f214(x19723,x19724,x19725,x19722))
% 11.41/11.20 [1973]~E(x19731,x19732)+E(f400(x19731,x19733,x19734,x19735,x19736),f400(x19732,x19733,x19734,x19735,x19736))
% 11.41/11.20 [1974]~E(x19741,x19742)+E(f400(x19743,x19741,x19744,x19745,x19746),f400(x19743,x19742,x19744,x19745,x19746))
% 11.41/11.20 [1975]~E(x19751,x19752)+E(f400(x19753,x19754,x19751,x19755,x19756),f400(x19753,x19754,x19752,x19755,x19756))
% 11.41/11.20 [1976]~E(x19761,x19762)+E(f400(x19763,x19764,x19765,x19761,x19766),f400(x19763,x19764,x19765,x19762,x19766))
% 11.41/11.20 [1977]~E(x19771,x19772)+E(f400(x19773,x19774,x19775,x19776,x19771),f400(x19773,x19774,x19775,x19776,x19772))
% 11.41/11.20 [1978]~E(x19781,x19782)+E(f635(x19781,x19783,x19784,x19785),f635(x19782,x19783,x19784,x19785))
% 11.41/11.20 [1979]~E(x19791,x19792)+E(f635(x19793,x19791,x19794,x19795),f635(x19793,x19792,x19794,x19795))
% 11.41/11.20 [1980]~E(x19801,x19802)+E(f635(x19803,x19804,x19801,x19805),f635(x19803,x19804,x19802,x19805))
% 11.41/11.20 [1981]~E(x19811,x19812)+E(f635(x19813,x19814,x19815,x19811),f635(x19813,x19814,x19815,x19812))
% 11.41/11.20 [1982]~E(x19821,x19822)+E(f609(x19821),f609(x19822))
% 11.41/11.20 [1983]~E(x19831,x19832)+E(f374(x19831,x19833,x19834,x19835),f374(x19832,x19833,x19834,x19835))
% 11.41/11.20 [1984]~E(x19841,x19842)+E(f374(x19843,x19841,x19844,x19845),f374(x19843,x19842,x19844,x19845))
% 11.41/11.20 [1985]~E(x19851,x19852)+E(f374(x19853,x19854,x19851,x19855),f374(x19853,x19854,x19852,x19855))
% 11.41/11.20 [1986]~E(x19861,x19862)+E(f374(x19863,x19864,x19865,x19861),f374(x19863,x19864,x19865,x19862))
% 11.41/11.20 [1987]~E(x19871,x19872)+E(f208(x19871,x19873),f208(x19872,x19873))
% 11.41/11.20 [1988]~E(x19881,x19882)+E(f208(x19883,x19881),f208(x19883,x19882))
% 11.41/11.20 [1989]~E(x19891,x19892)+E(f664(x19891,x19893,x19894,x19895),f664(x19892,x19893,x19894,x19895))
% 11.41/11.20 [1990]~E(x19901,x19902)+E(f664(x19903,x19901,x19904,x19905),f664(x19903,x19902,x19904,x19905))
% 11.41/11.20 [1991]~E(x19911,x19912)+E(f664(x19913,x19914,x19911,x19915),f664(x19913,x19914,x19912,x19915))
% 11.41/11.20 [1992]~E(x19921,x19922)+E(f664(x19923,x19924,x19925,x19921),f664(x19923,x19924,x19925,x19922))
% 11.41/11.20 [1993]~E(x19931,x19932)+E(f540(x19931,x19933,x19934,x19935,x19936),f540(x19932,x19933,x19934,x19935,x19936))
% 11.41/11.20 [1994]~E(x19941,x19942)+E(f540(x19943,x19941,x19944,x19945,x19946),f540(x19943,x19942,x19944,x19945,x19946))
% 11.41/11.20 [1995]~E(x19951,x19952)+E(f540(x19953,x19954,x19951,x19955,x19956),f540(x19953,x19954,x19952,x19955,x19956))
% 11.41/11.20 [1996]~E(x19961,x19962)+E(f540(x19963,x19964,x19965,x19961,x19966),f540(x19963,x19964,x19965,x19962,x19966))
% 11.41/11.20 [1997]~E(x19971,x19972)+E(f540(x19973,x19974,x19975,x19976,x19971),f540(x19973,x19974,x19975,x19976,x19972))
% 11.41/11.20 [1998]~E(x19981,x19982)+E(f522(x19981,x19983,x19984,x19985,x19986),f522(x19982,x19983,x19984,x19985,x19986))
% 11.41/11.20 [1999]~E(x19991,x19992)+E(f522(x19993,x19991,x19994,x19995,x19996),f522(x19993,x19992,x19994,x19995,x19996))
% 11.41/11.20 [2000]~E(x20001,x20002)+E(f522(x20003,x20004,x20001,x20005,x20006),f522(x20003,x20004,x20002,x20005,x20006))
% 11.41/11.20 [2001]~E(x20011,x20012)+E(f522(x20013,x20014,x20015,x20011,x20016),f522(x20013,x20014,x20015,x20012,x20016))
% 11.41/11.20 [2002]~E(x20021,x20022)+E(f522(x20023,x20024,x20025,x20026,x20021),f522(x20023,x20024,x20025,x20026,x20022))
% 11.41/11.20 [2003]~E(x20031,x20032)+E(f678(x20031,x20033,x20034,x20035,x20036),f678(x20032,x20033,x20034,x20035,x20036))
% 11.41/11.20 [2004]~E(x20041,x20042)+E(f678(x20043,x20041,x20044,x20045,x20046),f678(x20043,x20042,x20044,x20045,x20046))
% 11.41/11.20 [2005]~E(x20051,x20052)+E(f678(x20053,x20054,x20051,x20055,x20056),f678(x20053,x20054,x20052,x20055,x20056))
% 11.41/11.20 [2006]~E(x20061,x20062)+E(f678(x20063,x20064,x20065,x20061,x20066),f678(x20063,x20064,x20065,x20062,x20066))
% 11.41/11.20 [2007]~E(x20071,x20072)+E(f678(x20073,x20074,x20075,x20076,x20071),f678(x20073,x20074,x20075,x20076,x20072))
% 11.41/11.20 [2008]~E(x20081,x20082)+E(f367(x20081,x20083,x20084,x20085),f367(x20082,x20083,x20084,x20085))
% 11.41/11.20 [2009]~E(x20091,x20092)+E(f367(x20093,x20091,x20094,x20095),f367(x20093,x20092,x20094,x20095))
% 11.41/11.20 [2010]~E(x20101,x20102)+E(f367(x20103,x20104,x20101,x20105),f367(x20103,x20104,x20102,x20105))
% 11.41/11.20 [2011]~E(x20111,x20112)+E(f367(x20113,x20114,x20115,x20111),f367(x20113,x20114,x20115,x20112))
% 11.41/11.20 [2012]~E(x20121,x20122)+E(f588(x20121,x20123),f588(x20122,x20123))
% 11.41/11.20 [2013]~E(x20131,x20132)+E(f588(x20133,x20131),f588(x20133,x20132))
% 11.41/11.20 [2014]~E(x20141,x20142)+E(f676(x20141,x20143,x20144,x20145,x20146,x20147,x20148),f676(x20142,x20143,x20144,x20145,x20146,x20147,x20148))
% 11.41/11.20 [2015]~E(x20151,x20152)+E(f676(x20153,x20151,x20154,x20155,x20156,x20157,x20158),f676(x20153,x20152,x20154,x20155,x20156,x20157,x20158))
% 11.41/11.20 [2016]~E(x20161,x20162)+E(f676(x20163,x20164,x20161,x20165,x20166,x20167,x20168),f676(x20163,x20164,x20162,x20165,x20166,x20167,x20168))
% 11.41/11.20 [2017]~E(x20171,x20172)+E(f676(x20173,x20174,x20175,x20171,x20176,x20177,x20178),f676(x20173,x20174,x20175,x20172,x20176,x20177,x20178))
% 11.41/11.20 [2018]~E(x20181,x20182)+E(f676(x20183,x20184,x20185,x20186,x20181,x20187,x20188),f676(x20183,x20184,x20185,x20186,x20182,x20187,x20188))
% 11.41/11.20 [2019]~E(x20191,x20192)+E(f676(x20193,x20194,x20195,x20196,x20197,x20191,x20198),f676(x20193,x20194,x20195,x20196,x20197,x20192,x20198))
% 11.41/11.20 [2020]~E(x20201,x20202)+E(f676(x20203,x20204,x20205,x20206,x20207,x20208,x20201),f676(x20203,x20204,x20205,x20206,x20207,x20208,x20202))
% 11.41/11.20 [2021]~E(x20211,x20212)+E(f553(x20211,x20213,x20214,x20215),f553(x20212,x20213,x20214,x20215))
% 11.41/11.20 [2022]~E(x20221,x20222)+E(f553(x20223,x20221,x20224,x20225),f553(x20223,x20222,x20224,x20225))
% 11.41/11.20 [2023]~E(x20231,x20232)+E(f553(x20233,x20234,x20231,x20235),f553(x20233,x20234,x20232,x20235))
% 11.41/11.20 [2024]~E(x20241,x20242)+E(f553(x20243,x20244,x20245,x20241),f553(x20243,x20244,x20245,x20242))
% 11.41/11.20 [2025]~E(x20251,x20252)+E(f526(x20251,x20253),f526(x20252,x20253))
% 11.41/11.20 [2026]~E(x20261,x20262)+E(f526(x20263,x20261),f526(x20263,x20262))
% 11.41/11.20 [2027]~E(x20271,x20272)+E(f715(x20271,x20273,x20274,x20275,x20276),f715(x20272,x20273,x20274,x20275,x20276))
% 11.41/11.20 [2028]~E(x20281,x20282)+E(f715(x20283,x20281,x20284,x20285,x20286),f715(x20283,x20282,x20284,x20285,x20286))
% 11.41/11.20 [2029]~E(x20291,x20292)+E(f715(x20293,x20294,x20291,x20295,x20296),f715(x20293,x20294,x20292,x20295,x20296))
% 11.41/11.20 [2030]~E(x20301,x20302)+E(f715(x20303,x20304,x20305,x20301,x20306),f715(x20303,x20304,x20305,x20302,x20306))
% 11.41/11.20 [2031]~E(x20311,x20312)+E(f715(x20313,x20314,x20315,x20316,x20311),f715(x20313,x20314,x20315,x20316,x20312))
% 11.41/11.20 [2032]~E(x20321,x20322)+E(f574(x20321,x20323,x20324),f574(x20322,x20323,x20324))
% 11.41/11.20 [2033]~E(x20331,x20332)+E(f574(x20333,x20331,x20334),f574(x20333,x20332,x20334))
% 11.41/11.20 [2034]~E(x20341,x20342)+E(f574(x20343,x20344,x20341),f574(x20343,x20344,x20342))
% 11.41/11.20 [2035]~E(x20351,x20352)+E(f781(x20351,x20353,x20354),f781(x20352,x20353,x20354))
% 11.41/11.20 [2036]~E(x20361,x20362)+E(f781(x20363,x20361,x20364),f781(x20363,x20362,x20364))
% 11.41/11.20 [2037]~E(x20371,x20372)+E(f781(x20373,x20374,x20371),f781(x20373,x20374,x20372))
% 11.41/11.20 [2038]~E(x20381,x20382)+E(f300(x20381,x20383,x20384),f300(x20382,x20383,x20384))
% 11.41/11.20 [2039]~E(x20391,x20392)+E(f300(x20393,x20391,x20394),f300(x20393,x20392,x20394))
% 11.41/11.20 [2040]~E(x20401,x20402)+E(f300(x20403,x20404,x20401),f300(x20403,x20404,x20402))
% 11.41/11.20 [2041]~E(x20411,x20412)+E(f519(x20411,x20413,x20414,x20415),f519(x20412,x20413,x20414,x20415))
% 11.41/11.20 [2042]~E(x20421,x20422)+E(f519(x20423,x20421,x20424,x20425),f519(x20423,x20422,x20424,x20425))
% 11.41/11.20 [2043]~E(x20431,x20432)+E(f519(x20433,x20434,x20431,x20435),f519(x20433,x20434,x20432,x20435))
% 11.41/11.20 [2044]~E(x20441,x20442)+E(f519(x20443,x20444,x20445,x20441),f519(x20443,x20444,x20445,x20442))
% 11.41/11.20 [2045]~E(x20451,x20452)+E(f19(x20451,x20453,x20454,x20455),f19(x20452,x20453,x20454,x20455))
% 11.41/11.20 [2046]~E(x20461,x20462)+E(f19(x20463,x20461,x20464,x20465),f19(x20463,x20462,x20464,x20465))
% 11.41/11.20 [2047]~E(x20471,x20472)+E(f19(x20473,x20474,x20471,x20475),f19(x20473,x20474,x20472,x20475))
% 11.41/11.20 [2048]~E(x20481,x20482)+E(f19(x20483,x20484,x20485,x20481),f19(x20483,x20484,x20485,x20482))
% 11.41/11.20 [2049]~E(x20491,x20492)+E(f735(x20491),f735(x20492))
% 11.41/11.20 [2050]~E(x20501,x20502)+E(f520(x20501,x20503,x20504,x20505,x20506),f520(x20502,x20503,x20504,x20505,x20506))
% 11.41/11.20 [2051]~E(x20511,x20512)+E(f520(x20513,x20511,x20514,x20515,x20516),f520(x20513,x20512,x20514,x20515,x20516))
% 11.41/11.20 [2052]~E(x20521,x20522)+E(f520(x20523,x20524,x20521,x20525,x20526),f520(x20523,x20524,x20522,x20525,x20526))
% 11.41/11.20 [2053]~E(x20531,x20532)+E(f520(x20533,x20534,x20535,x20531,x20536),f520(x20533,x20534,x20535,x20532,x20536))
% 11.41/11.20 [2054]~E(x20541,x20542)+E(f520(x20543,x20544,x20545,x20546,x20541),f520(x20543,x20544,x20545,x20546,x20542))
% 11.41/11.20 [2055]~E(x20551,x20552)+E(f641(x20551,x20553,x20554),f641(x20552,x20553,x20554))
% 11.41/11.20 [2056]~E(x20561,x20562)+E(f641(x20563,x20561,x20564),f641(x20563,x20562,x20564))
% 11.41/11.20 [2057]~E(x20571,x20572)+E(f641(x20573,x20574,x20571),f641(x20573,x20574,x20572))
% 11.41/11.20 [2058]~E(x20581,x20582)+E(f516(x20581,x20583),f516(x20582,x20583))
% 11.41/11.20 [2059]~E(x20591,x20592)+E(f516(x20593,x20591),f516(x20593,x20592))
% 11.41/11.20 [2060]~E(x20601,x20602)+E(f722(x20601,x20603,x20604,x20605),f722(x20602,x20603,x20604,x20605))
% 11.41/11.20 [2061]~E(x20611,x20612)+E(f722(x20613,x20611,x20614,x20615),f722(x20613,x20612,x20614,x20615))
% 11.41/11.20 [2062]~E(x20621,x20622)+E(f722(x20623,x20624,x20621,x20625),f722(x20623,x20624,x20622,x20625))
% 11.41/11.20 [2063]~E(x20631,x20632)+E(f722(x20633,x20634,x20635,x20631),f722(x20633,x20634,x20635,x20632))
% 11.41/11.20 [2064]~E(x20641,x20642)+E(f576(x20641,x20643,x20644),f576(x20642,x20643,x20644))
% 11.41/11.20 [2065]~E(x20651,x20652)+E(f576(x20653,x20651,x20654),f576(x20653,x20652,x20654))
% 11.41/11.20 [2066]~E(x20661,x20662)+E(f576(x20663,x20664,x20661),f576(x20663,x20664,x20662))
% 11.41/11.20 [2067]~E(x20671,x20672)+E(f202(x20671,x20673,x20674,x20675),f202(x20672,x20673,x20674,x20675))
% 11.41/11.20 [2068]~E(x20681,x20682)+E(f202(x20683,x20681,x20684,x20685),f202(x20683,x20682,x20684,x20685))
% 11.41/11.20 [2069]~E(x20691,x20692)+E(f202(x20693,x20694,x20691,x20695),f202(x20693,x20694,x20692,x20695))
% 11.41/11.20 [2070]~E(x20701,x20702)+E(f202(x20703,x20704,x20705,x20701),f202(x20703,x20704,x20705,x20702))
% 11.41/11.20 [2071]~E(x20711,x20712)+E(f388(x20711,x20713),f388(x20712,x20713))
% 11.41/11.20 [2072]~E(x20721,x20722)+E(f388(x20723,x20721),f388(x20723,x20722))
% 11.41/11.20 [2073]~E(x20731,x20732)+E(f435(x20731,x20733),f435(x20732,x20733))
% 11.41/11.20 [2074]~E(x20741,x20742)+E(f435(x20743,x20741),f435(x20743,x20742))
% 11.41/11.20 [2075]~E(x20751,x20752)+E(f838(x20751,x20753,x20754),f838(x20752,x20753,x20754))
% 11.41/11.20 [2076]~E(x20761,x20762)+E(f838(x20763,x20761,x20764),f838(x20763,x20762,x20764))
% 11.41/11.20 [2077]~E(x20771,x20772)+E(f838(x20773,x20774,x20771),f838(x20773,x20774,x20772))
% 11.41/11.20 [2078]~E(x20781,x20782)+E(f591(x20781,x20783,x20784,x20785,x20786,x20787),f591(x20782,x20783,x20784,x20785,x20786,x20787))
% 11.41/11.20 [2079]~E(x20791,x20792)+E(f591(x20793,x20791,x20794,x20795,x20796,x20797),f591(x20793,x20792,x20794,x20795,x20796,x20797))
% 11.41/11.20 [2080]~E(x20801,x20802)+E(f591(x20803,x20804,x20801,x20805,x20806,x20807),f591(x20803,x20804,x20802,x20805,x20806,x20807))
% 11.41/11.20 [2081]~E(x20811,x20812)+E(f591(x20813,x20814,x20815,x20811,x20816,x20817),f591(x20813,x20814,x20815,x20812,x20816,x20817))
% 11.41/11.20 [2082]~E(x20821,x20822)+E(f591(x20823,x20824,x20825,x20826,x20821,x20827),f591(x20823,x20824,x20825,x20826,x20822,x20827))
% 11.41/11.20 [2083]~E(x20831,x20832)+E(f591(x20833,x20834,x20835,x20836,x20837,x20831),f591(x20833,x20834,x20835,x20836,x20837,x20832))
% 11.41/11.20 [2084]~E(x20841,x20842)+E(f607(x20841,x20843,x20844,x20845),f607(x20842,x20843,x20844,x20845))
% 11.41/11.20 [2085]~E(x20851,x20852)+E(f607(x20853,x20851,x20854,x20855),f607(x20853,x20852,x20854,x20855))
% 11.41/11.20 [2086]~E(x20861,x20862)+E(f607(x20863,x20864,x20861,x20865),f607(x20863,x20864,x20862,x20865))
% 11.41/11.20 [2087]~E(x20871,x20872)+E(f607(x20873,x20874,x20875,x20871),f607(x20873,x20874,x20875,x20872))
% 11.41/11.20 [2088]~E(x20881,x20882)+E(f596(x20881,x20883),f596(x20882,x20883))
% 11.41/11.20 [2089]~E(x20891,x20892)+E(f596(x20893,x20891),f596(x20893,x20892))
% 11.41/11.20 [2090]~E(x20901,x20902)+E(f389(x20901),f389(x20902))
% 11.41/11.20 [2091]~E(x20911,x20912)+E(f421(x20911,x20913,x20914,x20915,x20916,x20917),f421(x20912,x20913,x20914,x20915,x20916,x20917))
% 11.41/11.20 [2092]~E(x20921,x20922)+E(f421(x20923,x20921,x20924,x20925,x20926,x20927),f421(x20923,x20922,x20924,x20925,x20926,x20927))
% 11.41/11.20 [2093]~E(x20931,x20932)+E(f421(x20933,x20934,x20931,x20935,x20936,x20937),f421(x20933,x20934,x20932,x20935,x20936,x20937))
% 11.41/11.20 [2094]~E(x20941,x20942)+E(f421(x20943,x20944,x20945,x20941,x20946,x20947),f421(x20943,x20944,x20945,x20942,x20946,x20947))
% 11.41/11.20 [2095]~E(x20951,x20952)+E(f421(x20953,x20954,x20955,x20956,x20951,x20957),f421(x20953,x20954,x20955,x20956,x20952,x20957))
% 11.41/11.20 [2096]~E(x20961,x20962)+E(f421(x20963,x20964,x20965,x20966,x20967,x20961),f421(x20963,x20964,x20965,x20966,x20967,x20962))
% 11.41/11.20 [2097]~E(x20971,x20972)+E(f397(x20971,x20973,x20974,x20975),f397(x20972,x20973,x20974,x20975))
% 11.41/11.20 [2098]~E(x20981,x20982)+E(f397(x20983,x20981,x20984,x20985),f397(x20983,x20982,x20984,x20985))
% 11.41/11.20 [2099]~E(x20991,x20992)+E(f397(x20993,x20994,x20991,x20995),f397(x20993,x20994,x20992,x20995))
% 11.41/11.20 [2100]~E(x21001,x21002)+E(f397(x21003,x21004,x21005,x21001),f397(x21003,x21004,x21005,x21002))
% 11.41/11.20 [2101]~E(x21011,x21012)+E(f546(x21011,x21013,x21014,x21015,x21016),f546(x21012,x21013,x21014,x21015,x21016))
% 11.41/11.20 [2102]~E(x21021,x21022)+E(f546(x21023,x21021,x21024,x21025,x21026),f546(x21023,x21022,x21024,x21025,x21026))
% 11.41/11.20 [2103]~E(x21031,x21032)+E(f546(x21033,x21034,x21031,x21035,x21036),f546(x21033,x21034,x21032,x21035,x21036))
% 11.41/11.20 [2104]~E(x21041,x21042)+E(f546(x21043,x21044,x21045,x21041,x21046),f546(x21043,x21044,x21045,x21042,x21046))
% 11.41/11.20 [2105]~E(x21051,x21052)+E(f546(x21053,x21054,x21055,x21056,x21051),f546(x21053,x21054,x21055,x21056,x21052))
% 11.41/11.20 [2106]~E(x21061,x21062)+E(f669(x21061,x21063,x21064,x21065,x21066),f669(x21062,x21063,x21064,x21065,x21066))
% 11.41/11.20 [2107]~E(x21071,x21072)+E(f669(x21073,x21071,x21074,x21075,x21076),f669(x21073,x21072,x21074,x21075,x21076))
% 11.41/11.20 [2108]~E(x21081,x21082)+E(f669(x21083,x21084,x21081,x21085,x21086),f669(x21083,x21084,x21082,x21085,x21086))
% 11.41/11.20 [2109]~E(x21091,x21092)+E(f669(x21093,x21094,x21095,x21091,x21096),f669(x21093,x21094,x21095,x21092,x21096))
% 11.41/11.20 [2110]~E(x21101,x21102)+E(f669(x21103,x21104,x21105,x21106,x21101),f669(x21103,x21104,x21105,x21106,x21102))
% 11.41/11.20 [2111]~E(x21111,x21112)+E(f349(x21111,x21113,x21114,x21115),f349(x21112,x21113,x21114,x21115))
% 11.41/11.20 [2112]~E(x21121,x21122)+E(f349(x21123,x21121,x21124,x21125),f349(x21123,x21122,x21124,x21125))
% 11.41/11.20 [2113]~E(x21131,x21132)+E(f349(x21133,x21134,x21131,x21135),f349(x21133,x21134,x21132,x21135))
% 11.41/11.20 [2114]~E(x21141,x21142)+E(f349(x21143,x21144,x21145,x21141),f349(x21143,x21144,x21145,x21142))
% 11.41/11.20 [2115]~E(x21151,x21152)+E(f584(x21151,x21153),f584(x21152,x21153))
% 11.41/11.20 [2116]~E(x21161,x21162)+E(f584(x21163,x21161),f584(x21163,x21162))
% 11.41/11.20 [2117]~E(x21171,x21172)+E(f817(x21171,x21173,x21174),f817(x21172,x21173,x21174))
% 11.41/11.20 [2118]~E(x21181,x21182)+E(f817(x21183,x21181,x21184),f817(x21183,x21182,x21184))
% 11.41/11.20 [2119]~E(x21191,x21192)+E(f817(x21193,x21194,x21191),f817(x21193,x21194,x21192))
% 11.41/11.20 [2120]~E(x21201,x21202)+E(f503(x21201),f503(x21202))
% 11.41/11.20 [2121]~E(x21211,x21212)+E(f776(x21211,x21213,x21214),f776(x21212,x21213,x21214))
% 11.41/11.20 [2122]~E(x21221,x21222)+E(f776(x21223,x21221,x21224),f776(x21223,x21222,x21224))
% 11.41/11.20 [2123]~E(x21231,x21232)+E(f776(x21233,x21234,x21231),f776(x21233,x21234,x21232))
% 11.41/11.20 [2124]~E(x21241,x21242)+E(f510(x21241,x21243,x21244),f510(x21242,x21243,x21244))
% 11.41/11.20 [2125]~E(x21251,x21252)+E(f510(x21253,x21251,x21254),f510(x21253,x21252,x21254))
% 11.41/11.20 [2126]~E(x21261,x21262)+E(f510(x21263,x21264,x21261),f510(x21263,x21264,x21262))
% 11.41/11.20 [2127]~E(x21271,x21272)+E(f56(x21271),f56(x21272))
% 11.41/11.20 [2128]~E(x21281,x21282)+E(f215(x21281,x21283,x21284,x21285),f215(x21282,x21283,x21284,x21285))
% 11.41/11.20 [2129]~E(x21291,x21292)+E(f215(x21293,x21291,x21294,x21295),f215(x21293,x21292,x21294,x21295))
% 11.41/11.20 [2130]~E(x21301,x21302)+E(f215(x21303,x21304,x21301,x21305),f215(x21303,x21304,x21302,x21305))
% 11.41/11.20 [2131]~E(x21311,x21312)+E(f215(x21313,x21314,x21315,x21311),f215(x21313,x21314,x21315,x21312))
% 11.41/11.20 [2132]~E(x21321,x21322)+E(f437(x21321,x21323,x21324,x21325),f437(x21322,x21323,x21324,x21325))
% 11.41/11.20 [2133]~E(x21331,x21332)+E(f437(x21333,x21331,x21334,x21335),f437(x21333,x21332,x21334,x21335))
% 11.41/11.20 [2134]~E(x21341,x21342)+E(f437(x21343,x21344,x21341,x21345),f437(x21343,x21344,x21342,x21345))
% 11.41/11.20 [2135]~E(x21351,x21352)+E(f437(x21353,x21354,x21355,x21351),f437(x21353,x21354,x21355,x21352))
% 11.41/11.20 [2136]~E(x21361,x21362)+E(f713(x21361,x21363,x21364,x21365),f713(x21362,x21363,x21364,x21365))
% 11.41/11.20 [2137]~E(x21371,x21372)+E(f713(x21373,x21371,x21374,x21375),f713(x21373,x21372,x21374,x21375))
% 11.41/11.20 [2138]~E(x21381,x21382)+E(f713(x21383,x21384,x21381,x21385),f713(x21383,x21384,x21382,x21385))
% 11.41/11.20 [2139]~E(x21391,x21392)+E(f713(x21393,x21394,x21395,x21391),f713(x21393,x21394,x21395,x21392))
% 11.41/11.20 [2140]~E(x21401,x21402)+E(f703(x21401,x21403,x21404,x21405,x21406,x21407),f703(x21402,x21403,x21404,x21405,x21406,x21407))
% 11.41/11.20 [2141]~E(x21411,x21412)+E(f703(x21413,x21411,x21414,x21415,x21416,x21417),f703(x21413,x21412,x21414,x21415,x21416,x21417))
% 11.41/11.20 [2142]~E(x21421,x21422)+E(f703(x21423,x21424,x21421,x21425,x21426,x21427),f703(x21423,x21424,x21422,x21425,x21426,x21427))
% 11.41/11.20 [2143]~E(x21431,x21432)+E(f703(x21433,x21434,x21435,x21431,x21436,x21437),f703(x21433,x21434,x21435,x21432,x21436,x21437))
% 11.41/11.20 [2144]~E(x21441,x21442)+E(f703(x21443,x21444,x21445,x21446,x21441,x21447),f703(x21443,x21444,x21445,x21446,x21442,x21447))
% 11.41/11.20 [2145]~E(x21451,x21452)+E(f703(x21453,x21454,x21455,x21456,x21457,x21451),f703(x21453,x21454,x21455,x21456,x21457,x21452))
% 11.41/11.20 [2146]~E(x21461,x21462)+E(f714(x21461,x21463,x21464,x21465,x21466),f714(x21462,x21463,x21464,x21465,x21466))
% 11.41/11.20 [2147]~E(x21471,x21472)+E(f714(x21473,x21471,x21474,x21475,x21476),f714(x21473,x21472,x21474,x21475,x21476))
% 11.41/11.20 [2148]~E(x21481,x21482)+E(f714(x21483,x21484,x21481,x21485,x21486),f714(x21483,x21484,x21482,x21485,x21486))
% 11.41/11.20 [2149]~E(x21491,x21492)+E(f714(x21493,x21494,x21495,x21491,x21496),f714(x21493,x21494,x21495,x21492,x21496))
% 11.41/11.20 [2150]~E(x21501,x21502)+E(f714(x21503,x21504,x21505,x21506,x21501),f714(x21503,x21504,x21505,x21506,x21502))
% 11.41/11.20 [2151]~E(x21511,x21512)+E(f463(x21511,x21513,x21514),f463(x21512,x21513,x21514))
% 11.41/11.20 [2152]~E(x21521,x21522)+E(f463(x21523,x21521,x21524),f463(x21523,x21522,x21524))
% 11.41/11.20 [2153]~E(x21531,x21532)+E(f463(x21533,x21534,x21531),f463(x21533,x21534,x21532))
% 11.41/11.20 [2154]~E(x21541,x21542)+E(f580(x21541,x21543,x21544,x21545,x21546),f580(x21542,x21543,x21544,x21545,x21546))
% 11.41/11.20 [2155]~E(x21551,x21552)+E(f580(x21553,x21551,x21554,x21555,x21556),f580(x21553,x21552,x21554,x21555,x21556))
% 11.41/11.20 [2156]~E(x21561,x21562)+E(f580(x21563,x21564,x21561,x21565,x21566),f580(x21563,x21564,x21562,x21565,x21566))
% 11.41/11.20 [2157]~E(x21571,x21572)+E(f580(x21573,x21574,x21575,x21571,x21576),f580(x21573,x21574,x21575,x21572,x21576))
% 11.41/11.20 [2158]~E(x21581,x21582)+E(f580(x21583,x21584,x21585,x21586,x21581),f580(x21583,x21584,x21585,x21586,x21582))
% 11.41/11.20 [2159]~E(x21591,x21592)+E(f777(x21591,x21593,x21594),f777(x21592,x21593,x21594))
% 11.41/11.20 [2160]~E(x21601,x21602)+E(f777(x21603,x21601,x21604),f777(x21603,x21602,x21604))
% 11.41/11.20 [2161]~E(x21611,x21612)+E(f777(x21613,x21614,x21611),f777(x21613,x21614,x21612))
% 11.41/11.20 [2162]~E(x21621,x21622)+E(f548(x21621,x21623,x21624,x21625,x21626),f548(x21622,x21623,x21624,x21625,x21626))
% 11.41/11.20 [2163]~E(x21631,x21632)+E(f548(x21633,x21631,x21634,x21635,x21636),f548(x21633,x21632,x21634,x21635,x21636))
% 11.41/11.20 [2164]~E(x21641,x21642)+E(f548(x21643,x21644,x21641,x21645,x21646),f548(x21643,x21644,x21642,x21645,x21646))
% 11.41/11.20 [2165]~E(x21651,x21652)+E(f548(x21653,x21654,x21655,x21651,x21656),f548(x21653,x21654,x21655,x21652,x21656))
% 11.41/11.20 [2166]~E(x21661,x21662)+E(f548(x21663,x21664,x21665,x21666,x21661),f548(x21663,x21664,x21665,x21666,x21662))
% 11.41/11.20 [2167]~E(x21671,x21672)+E(f732(x21671,x21673,x21674,x21675,x21676),f732(x21672,x21673,x21674,x21675,x21676))
% 11.41/11.20 [2168]~E(x21681,x21682)+E(f732(x21683,x21681,x21684,x21685,x21686),f732(x21683,x21682,x21684,x21685,x21686))
% 11.41/11.20 [2169]~E(x21691,x21692)+E(f732(x21693,x21694,x21691,x21695,x21696),f732(x21693,x21694,x21692,x21695,x21696))
% 11.41/11.20 [2170]~E(x21701,x21702)+E(f732(x21703,x21704,x21705,x21701,x21706),f732(x21703,x21704,x21705,x21702,x21706))
% 11.41/11.20 [2171]~E(x21711,x21712)+E(f732(x21713,x21714,x21715,x21716,x21711),f732(x21713,x21714,x21715,x21716,x21712))
% 11.41/11.20 [2172]~E(x21721,x21722)+E(f677(x21721,x21723,x21724,x21725,x21726),f677(x21722,x21723,x21724,x21725,x21726))
% 11.41/11.20 [2173]~E(x21731,x21732)+E(f677(x21733,x21731,x21734,x21735,x21736),f677(x21733,x21732,x21734,x21735,x21736))
% 11.41/11.20 [2174]~E(x21741,x21742)+E(f677(x21743,x21744,x21741,x21745,x21746),f677(x21743,x21744,x21742,x21745,x21746))
% 11.41/11.20 [2175]~E(x21751,x21752)+E(f677(x21753,x21754,x21755,x21751,x21756),f677(x21753,x21754,x21755,x21752,x21756))
% 11.41/11.20 [2176]~E(x21761,x21762)+E(f677(x21763,x21764,x21765,x21766,x21761),f677(x21763,x21764,x21765,x21766,x21762))
% 11.41/11.20 [2177]~E(x21771,x21772)+E(f575(x21771,x21773,x21774,x21775),f575(x21772,x21773,x21774,x21775))
% 11.41/11.20 [2178]~E(x21781,x21782)+E(f575(x21783,x21781,x21784,x21785),f575(x21783,x21782,x21784,x21785))
% 11.41/11.20 [2179]~E(x21791,x21792)+E(f575(x21793,x21794,x21791,x21795),f575(x21793,x21794,x21792,x21795))
% 11.41/11.20 [2180]~E(x21801,x21802)+E(f575(x21803,x21804,x21805,x21801),f575(x21803,x21804,x21805,x21802))
% 11.41/11.20 [2181]~E(x21811,x21812)+E(f643(x21811,x21813,x21814),f643(x21812,x21813,x21814))
% 11.41/11.20 [2182]~E(x21821,x21822)+E(f643(x21823,x21821,x21824),f643(x21823,x21822,x21824))
% 11.41/11.20 [2183]~E(x21831,x21832)+E(f643(x21833,x21834,x21831),f643(x21833,x21834,x21832))
% 11.41/11.20 [2184]~E(x21841,x21842)+E(f727(x21841,x21843,x21844,x21845,x21846),f727(x21842,x21843,x21844,x21845,x21846))
% 11.41/11.20 [2185]~E(x21851,x21852)+E(f727(x21853,x21851,x21854,x21855,x21856),f727(x21853,x21852,x21854,x21855,x21856))
% 11.41/11.20 [2186]~E(x21861,x21862)+E(f727(x21863,x21864,x21861,x21865,x21866),f727(x21863,x21864,x21862,x21865,x21866))
% 11.41/11.20 [2187]~E(x21871,x21872)+E(f727(x21873,x21874,x21875,x21871,x21876),f727(x21873,x21874,x21875,x21872,x21876))
% 11.41/11.20 [2188]~E(x21881,x21882)+E(f727(x21883,x21884,x21885,x21886,x21881),f727(x21883,x21884,x21885,x21886,x21882))
% 11.41/11.20 [2189]~E(x21891,x21892)+E(f536(x21891,x21893,x21894,x21895),f536(x21892,x21893,x21894,x21895))
% 11.41/11.20 [2190]~E(x21901,x21902)+E(f536(x21903,x21901,x21904,x21905),f536(x21903,x21902,x21904,x21905))
% 11.41/11.20 [2191]~E(x21911,x21912)+E(f536(x21913,x21914,x21911,x21915),f536(x21913,x21914,x21912,x21915))
% 11.41/11.20 [2192]~E(x21921,x21922)+E(f536(x21923,x21924,x21925,x21921),f536(x21923,x21924,x21925,x21922))
% 11.41/11.20 [2193]~E(x21931,x21932)+E(f505(x21931,x21933),f505(x21932,x21933))
% 11.41/11.20 [2194]~E(x21941,x21942)+E(f505(x21943,x21941),f505(x21943,x21942))
% 11.41/11.20 [2195]~E(x21951,x21952)+E(f379(x21951,x21953,x21954,x21955,x21956),f379(x21952,x21953,x21954,x21955,x21956))
% 11.41/11.20 [2196]~E(x21961,x21962)+E(f379(x21963,x21961,x21964,x21965,x21966),f379(x21963,x21962,x21964,x21965,x21966))
% 11.41/11.20 [2197]~E(x21971,x21972)+E(f379(x21973,x21974,x21971,x21975,x21976),f379(x21973,x21974,x21972,x21975,x21976))
% 11.41/11.20 [2198]~E(x21981,x21982)+E(f379(x21983,x21984,x21985,x21981,x21986),f379(x21983,x21984,x21985,x21982,x21986))
% 11.41/11.20 [2199]~E(x21991,x21992)+E(f379(x21993,x21994,x21995,x21996,x21991),f379(x21993,x21994,x21995,x21996,x21992))
% 11.41/11.20 [2200]~E(x22001,x22002)+E(f829(x22001,x22003,x22004),f829(x22002,x22003,x22004))
% 11.41/11.20 [2201]~E(x22011,x22012)+E(f829(x22013,x22011,x22014),f829(x22013,x22012,x22014))
% 11.41/11.20 [2202]~E(x22021,x22022)+E(f829(x22023,x22024,x22021),f829(x22023,x22024,x22022))
% 11.41/11.20 [2203]~E(x22031,x22032)+E(f391(x22031,x22033,x22034),f391(x22032,x22033,x22034))
% 11.41/11.20 [2204]~E(x22041,x22042)+E(f391(x22043,x22041,x22044),f391(x22043,x22042,x22044))
% 11.41/11.20 [2205]~E(x22051,x22052)+E(f391(x22053,x22054,x22051),f391(x22053,x22054,x22052))
% 11.41/11.20 [2206]~E(x22061,x22062)+E(f726(x22061,x22063,x22064),f726(x22062,x22063,x22064))
% 11.41/11.20 [2207]~E(x22071,x22072)+E(f726(x22073,x22071,x22074),f726(x22073,x22072,x22074))
% 11.41/11.20 [2208]~E(x22081,x22082)+E(f726(x22083,x22084,x22081),f726(x22083,x22084,x22082))
% 11.41/11.20 [2209]~E(x22091,x22092)+E(f842(x22091,x22093,x22094,x22095,x22096),f842(x22092,x22093,x22094,x22095,x22096))
% 11.41/11.20 [2210]~E(x22101,x22102)+E(f842(x22103,x22101,x22104,x22105,x22106),f842(x22103,x22102,x22104,x22105,x22106))
% 11.41/11.20 [2211]~E(x22111,x22112)+E(f842(x22113,x22114,x22111,x22115,x22116),f842(x22113,x22114,x22112,x22115,x22116))
% 11.41/11.20 [2212]~E(x22121,x22122)+E(f842(x22123,x22124,x22125,x22121,x22126),f842(x22123,x22124,x22125,x22122,x22126))
% 11.41/11.20 [2213]~E(x22131,x22132)+E(f842(x22133,x22134,x22135,x22136,x22131),f842(x22133,x22134,x22135,x22136,x22132))
% 11.41/11.20 [2214]~E(x22141,x22142)+E(f616(x22141,x22143,x22144,x22145),f616(x22142,x22143,x22144,x22145))
% 11.41/11.20 [2215]~E(x22151,x22152)+E(f616(x22153,x22151,x22154,x22155),f616(x22153,x22152,x22154,x22155))
% 11.41/11.20 [2216]~E(x22161,x22162)+E(f616(x22163,x22164,x22161,x22165),f616(x22163,x22164,x22162,x22165))
% 11.41/11.20 [2217]~E(x22171,x22172)+E(f616(x22173,x22174,x22175,x22171),f616(x22173,x22174,x22175,x22172))
% 11.41/11.20 [2218]~E(x22181,x22182)+E(f660(x22181,x22183,x22184,x22185,x22186),f660(x22182,x22183,x22184,x22185,x22186))
% 11.41/11.20 [2219]~E(x22191,x22192)+E(f660(x22193,x22191,x22194,x22195,x22196),f660(x22193,x22192,x22194,x22195,x22196))
% 11.41/11.20 [2220]~E(x22201,x22202)+E(f660(x22203,x22204,x22201,x22205,x22206),f660(x22203,x22204,x22202,x22205,x22206))
% 11.41/11.20 [2221]~E(x22211,x22212)+E(f660(x22213,x22214,x22215,x22211,x22216),f660(x22213,x22214,x22215,x22212,x22216))
% 11.41/11.20 [2222]~E(x22221,x22222)+E(f660(x22223,x22224,x22225,x22226,x22221),f660(x22223,x22224,x22225,x22226,x22222))
% 11.41/11.20 [2223]~E(x22231,x22232)+E(f754(x22231,x22233,x22234,x22235),f754(x22232,x22233,x22234,x22235))
% 11.41/11.20 [2224]~E(x22241,x22242)+E(f754(x22243,x22241,x22244,x22245),f754(x22243,x22242,x22244,x22245))
% 11.41/11.20 [2225]~E(x22251,x22252)+E(f754(x22253,x22254,x22251,x22255),f754(x22253,x22254,x22252,x22255))
% 11.41/11.20 [2226]~E(x22261,x22262)+E(f754(x22263,x22264,x22265,x22261),f754(x22263,x22264,x22265,x22262))
% 11.41/11.20 [2227]~E(x22271,x22272)+E(f213(x22271,x22273,x22274,x22275,x22276,x22277,x22278),f213(x22272,x22273,x22274,x22275,x22276,x22277,x22278))
% 11.41/11.20 [2228]~E(x22281,x22282)+E(f213(x22283,x22281,x22284,x22285,x22286,x22287,x22288),f213(x22283,x22282,x22284,x22285,x22286,x22287,x22288))
% 11.41/11.20 [2229]~E(x22291,x22292)+E(f213(x22293,x22294,x22291,x22295,x22296,x22297,x22298),f213(x22293,x22294,x22292,x22295,x22296,x22297,x22298))
% 11.41/11.20 [2230]~E(x22301,x22302)+E(f213(x22303,x22304,x22305,x22301,x22306,x22307,x22308),f213(x22303,x22304,x22305,x22302,x22306,x22307,x22308))
% 11.41/11.20 [2231]~E(x22311,x22312)+E(f213(x22313,x22314,x22315,x22316,x22311,x22317,x22318),f213(x22313,x22314,x22315,x22316,x22312,x22317,x22318))
% 11.41/11.20 [2232]~E(x22321,x22322)+E(f213(x22323,x22324,x22325,x22326,x22327,x22321,x22328),f213(x22323,x22324,x22325,x22326,x22327,x22322,x22328))
% 11.41/11.20 [2233]~E(x22331,x22332)+E(f213(x22333,x22334,x22335,x22336,x22337,x22338,x22331),f213(x22333,x22334,x22335,x22336,x22337,x22338,x22332))
% 11.41/11.20 [2234]~E(x22341,x22342)+E(f454(x22341,x22343),f454(x22342,x22343))
% 11.41/11.20 [2235]~E(x22351,x22352)+E(f454(x22353,x22351),f454(x22353,x22352))
% 11.41/11.20 [2236]~E(x22361,x22362)+E(f631(x22361,x22363,x22364),f631(x22362,x22363,x22364))
% 11.41/11.20 [2237]~E(x22371,x22372)+E(f631(x22373,x22371,x22374),f631(x22373,x22372,x22374))
% 11.41/11.20 [2238]~E(x22381,x22382)+E(f631(x22383,x22384,x22381),f631(x22383,x22384,x22382))
% 11.41/11.20 [2239]~E(x22391,x22392)+E(f729(x22391,x22393,x22394,x22395,x22396),f729(x22392,x22393,x22394,x22395,x22396))
% 11.41/11.20 [2240]~E(x22401,x22402)+E(f729(x22403,x22401,x22404,x22405,x22406),f729(x22403,x22402,x22404,x22405,x22406))
% 11.41/11.20 [2241]~E(x22411,x22412)+E(f729(x22413,x22414,x22411,x22415,x22416),f729(x22413,x22414,x22412,x22415,x22416))
% 11.41/11.20 [2242]~E(x22421,x22422)+E(f729(x22423,x22424,x22425,x22421,x22426),f729(x22423,x22424,x22425,x22422,x22426))
% 11.41/11.20 [2243]~E(x22431,x22432)+E(f729(x22433,x22434,x22435,x22436,x22431),f729(x22433,x22434,x22435,x22436,x22432))
% 11.41/11.20 [2244]~E(x22441,x22442)+E(f59(x22441),f59(x22442))
% 11.41/11.20 [2245]~E(x22451,x22452)+E(f550(x22451,x22453,x22454,x22455,x22456),f550(x22452,x22453,x22454,x22455,x22456))
% 11.41/11.20 [2246]~E(x22461,x22462)+E(f550(x22463,x22461,x22464,x22465,x22466),f550(x22463,x22462,x22464,x22465,x22466))
% 11.41/11.20 [2247]~E(x22471,x22472)+E(f550(x22473,x22474,x22471,x22475,x22476),f550(x22473,x22474,x22472,x22475,x22476))
% 11.41/11.20 [2248]~E(x22481,x22482)+E(f550(x22483,x22484,x22485,x22481,x22486),f550(x22483,x22484,x22485,x22482,x22486))
% 11.41/11.20 [2249]~E(x22491,x22492)+E(f550(x22493,x22494,x22495,x22496,x22491),f550(x22493,x22494,x22495,x22496,x22492))
% 11.41/11.20 [2250]~E(x22501,x22502)+E(f488(x22501,x22503,x22504),f488(x22502,x22503,x22504))
% 11.41/11.20 [2251]~E(x22511,x22512)+E(f488(x22513,x22511,x22514),f488(x22513,x22512,x22514))
% 11.41/11.20 [2252]~E(x22521,x22522)+E(f488(x22523,x22524,x22521),f488(x22523,x22524,x22522))
% 11.41/11.20 [2253]~E(x22531,x22532)+E(f439(x22531,x22533,x22534,x22535),f439(x22532,x22533,x22534,x22535))
% 11.41/11.20 [2254]~E(x22541,x22542)+E(f439(x22543,x22541,x22544,x22545),f439(x22543,x22542,x22544,x22545))
% 11.41/11.20 [2255]~E(x22551,x22552)+E(f439(x22553,x22554,x22551,x22555),f439(x22553,x22554,x22552,x22555))
% 11.41/11.20 [2256]~E(x22561,x22562)+E(f439(x22563,x22564,x22565,x22561),f439(x22563,x22564,x22565,x22562))
% 11.41/11.20 [2257]~E(x22571,x22572)+E(f731(x22571,x22573,x22574,x22575,x22576),f731(x22572,x22573,x22574,x22575,x22576))
% 11.41/11.20 [2258]~E(x22581,x22582)+E(f731(x22583,x22581,x22584,x22585,x22586),f731(x22583,x22582,x22584,x22585,x22586))
% 11.41/11.20 [2259]~E(x22591,x22592)+E(f731(x22593,x22594,x22591,x22595,x22596),f731(x22593,x22594,x22592,x22595,x22596))
% 11.41/11.20 [2260]~E(x22601,x22602)+E(f731(x22603,x22604,x22605,x22601,x22606),f731(x22603,x22604,x22605,x22602,x22606))
% 11.41/11.20 [2261]~E(x22611,x22612)+E(f731(x22613,x22614,x22615,x22616,x22611),f731(x22613,x22614,x22615,x22616,x22612))
% 11.41/11.20 [2262]~E(x22621,x22622)+E(f474(x22621,x22623,x22624,x22625),f474(x22622,x22623,x22624,x22625))
% 11.41/11.20 [2263]~E(x22631,x22632)+E(f474(x22633,x22631,x22634,x22635),f474(x22633,x22632,x22634,x22635))
% 11.41/11.20 [2264]~E(x22641,x22642)+E(f474(x22643,x22644,x22641,x22645),f474(x22643,x22644,x22642,x22645))
% 11.41/11.20 [2265]~E(x22651,x22652)+E(f474(x22653,x22654,x22655,x22651),f474(x22653,x22654,x22655,x22652))
% 11.41/11.20 [2266]~E(x22661,x22662)+E(f272(x22661,x22663,x22664),f272(x22662,x22663,x22664))
% 11.41/11.20 [2267]~E(x22671,x22672)+E(f272(x22673,x22671,x22674),f272(x22673,x22672,x22674))
% 11.41/11.20 [2268]~E(x22681,x22682)+E(f272(x22683,x22684,x22681),f272(x22683,x22684,x22682))
% 11.41/11.20 [2269]~E(x22691,x22692)+E(f264(x22691,x22693,x22694,x22695,x22696),f264(x22692,x22693,x22694,x22695,x22696))
% 11.41/11.20 [2270]~E(x22701,x22702)+E(f264(x22703,x22701,x22704,x22705,x22706),f264(x22703,x22702,x22704,x22705,x22706))
% 11.41/11.20 [2271]~E(x22711,x22712)+E(f264(x22713,x22714,x22711,x22715,x22716),f264(x22713,x22714,x22712,x22715,x22716))
% 11.41/11.20 [2272]~E(x22721,x22722)+E(f264(x22723,x22724,x22725,x22721,x22726),f264(x22723,x22724,x22725,x22722,x22726))
% 11.41/11.20 [2273]~E(x22731,x22732)+E(f264(x22733,x22734,x22735,x22736,x22731),f264(x22733,x22734,x22735,x22736,x22732))
% 11.41/11.20 [2274]~E(x22741,x22742)+E(f642(x22741,x22743,x22744,x22745,x22746,x22747),f642(x22742,x22743,x22744,x22745,x22746,x22747))
% 11.41/11.20 [2275]~E(x22751,x22752)+E(f642(x22753,x22751,x22754,x22755,x22756,x22757),f642(x22753,x22752,x22754,x22755,x22756,x22757))
% 11.41/11.20 [2276]~E(x22761,x22762)+E(f642(x22763,x22764,x22761,x22765,x22766,x22767),f642(x22763,x22764,x22762,x22765,x22766,x22767))
% 11.41/11.20 [2277]~E(x22771,x22772)+E(f642(x22773,x22774,x22775,x22771,x22776,x22777),f642(x22773,x22774,x22775,x22772,x22776,x22777))
% 11.41/11.20 [2278]~E(x22781,x22782)+E(f642(x22783,x22784,x22785,x22786,x22781,x22787),f642(x22783,x22784,x22785,x22786,x22782,x22787))
% 11.41/11.20 [2279]~E(x22791,x22792)+E(f642(x22793,x22794,x22795,x22796,x22797,x22791),f642(x22793,x22794,x22795,x22796,x22797,x22792))
% 11.41/11.20 [2280]~E(x22801,x22802)+E(f555(x22801,x22803,x22804,x22805),f555(x22802,x22803,x22804,x22805))
% 11.41/11.20 [2281]~E(x22811,x22812)+E(f555(x22813,x22811,x22814,x22815),f555(x22813,x22812,x22814,x22815))
% 11.41/11.20 [2282]~E(x22821,x22822)+E(f555(x22823,x22824,x22821,x22825),f555(x22823,x22824,x22822,x22825))
% 11.41/11.20 [2283]~E(x22831,x22832)+E(f555(x22833,x22834,x22835,x22831),f555(x22833,x22834,x22835,x22832))
% 11.41/11.20 [2284]~E(x22841,x22842)+E(f545(x22841,x22843,x22844,x22845),f545(x22842,x22843,x22844,x22845))
% 11.41/11.20 [2285]~E(x22851,x22852)+E(f545(x22853,x22851,x22854,x22855),f545(x22853,x22852,x22854,x22855))
% 11.41/11.20 [2286]~E(x22861,x22862)+E(f545(x22863,x22864,x22861,x22865),f545(x22863,x22864,x22862,x22865))
% 11.41/11.20 [2287]~E(x22871,x22872)+E(f545(x22873,x22874,x22875,x22871),f545(x22873,x22874,x22875,x22872))
% 11.41/11.20 [2288]~E(x22881,x22882)+E(f467(x22881,x22883,x22884,x22885),f467(x22882,x22883,x22884,x22885))
% 11.41/11.20 [2289]~E(x22891,x22892)+E(f467(x22893,x22891,x22894,x22895),f467(x22893,x22892,x22894,x22895))
% 11.41/11.20 [2290]~E(x22901,x22902)+E(f467(x22903,x22904,x22901,x22905),f467(x22903,x22904,x22902,x22905))
% 11.41/11.20 [2291]~E(x22911,x22912)+E(f467(x22913,x22914,x22915,x22911),f467(x22913,x22914,x22915,x22912))
% 11.41/11.20 [2292]~E(x22921,x22922)+E(f171(x22921),f171(x22922))
% 11.41/11.20 [2293]~E(x22931,x22932)+E(f828(x22931,x22933,x22934),f828(x22932,x22933,x22934))
% 11.41/11.20 [2294]~E(x22941,x22942)+E(f828(x22943,x22941,x22944),f828(x22943,x22942,x22944))
% 11.41/11.20 [2295]~E(x22951,x22952)+E(f828(x22953,x22954,x22951),f828(x22953,x22954,x22952))
% 11.41/11.20 [2296]~E(x22961,x22962)+E(f670(x22961,x22963,x22964,x22965,x22966),f670(x22962,x22963,x22964,x22965,x22966))
% 11.41/11.20 [2297]~E(x22971,x22972)+E(f670(x22973,x22971,x22974,x22975,x22976),f670(x22973,x22972,x22974,x22975,x22976))
% 11.41/11.20 [2298]~E(x22981,x22982)+E(f670(x22983,x22984,x22981,x22985,x22986),f670(x22983,x22984,x22982,x22985,x22986))
% 11.41/11.20 [2299]~E(x22991,x22992)+E(f670(x22993,x22994,x22995,x22991,x22996),f670(x22993,x22994,x22995,x22992,x22996))
% 11.41/11.20 [2300]~E(x23001,x23002)+E(f670(x23003,x23004,x23005,x23006,x23001),f670(x23003,x23004,x23005,x23006,x23002))
% 11.41/11.20 [2301]~E(x23011,x23012)+E(f380(x23011,x23013,x23014,x23015,x23016),f380(x23012,x23013,x23014,x23015,x23016))
% 11.41/11.20 [2302]~E(x23021,x23022)+E(f380(x23023,x23021,x23024,x23025,x23026),f380(x23023,x23022,x23024,x23025,x23026))
% 11.41/11.20 [2303]~E(x23031,x23032)+E(f380(x23033,x23034,x23031,x23035,x23036),f380(x23033,x23034,x23032,x23035,x23036))
% 11.41/11.20 [2304]~E(x23041,x23042)+E(f380(x23043,x23044,x23045,x23041,x23046),f380(x23043,x23044,x23045,x23042,x23046))
% 11.41/11.20 [2305]~E(x23051,x23052)+E(f380(x23053,x23054,x23055,x23056,x23051),f380(x23053,x23054,x23055,x23056,x23052))
% 11.41/11.20 [2306]~E(x23061,x23062)+E(f701(x23061,x23063,x23064,x23065),f701(x23062,x23063,x23064,x23065))
% 11.41/11.20 [2307]~E(x23071,x23072)+E(f701(x23073,x23071,x23074,x23075),f701(x23073,x23072,x23074,x23075))
% 11.41/11.20 [2308]~E(x23081,x23082)+E(f701(x23083,x23084,x23081,x23085),f701(x23083,x23084,x23082,x23085))
% 11.41/11.20 [2309]~E(x23091,x23092)+E(f701(x23093,x23094,x23095,x23091),f701(x23093,x23094,x23095,x23092))
% 11.41/11.20 [2310]~E(x23101,x23102)+E(f368(x23101,x23103,x23104,x23105),f368(x23102,x23103,x23104,x23105))
% 11.41/11.20 [2311]~E(x23111,x23112)+E(f368(x23113,x23111,x23114,x23115),f368(x23113,x23112,x23114,x23115))
% 11.41/11.20 [2312]~E(x23121,x23122)+E(f368(x23123,x23124,x23121,x23125),f368(x23123,x23124,x23122,x23125))
% 11.41/11.20 [2313]~E(x23131,x23132)+E(f368(x23133,x23134,x23135,x23131),f368(x23133,x23134,x23135,x23132))
% 11.41/11.20 [2314]~E(x23141,x23142)+E(f466(x23141,x23143,x23144,x23145),f466(x23142,x23143,x23144,x23145))
% 11.41/11.20 [2315]~E(x23151,x23152)+E(f466(x23153,x23151,x23154,x23155),f466(x23153,x23152,x23154,x23155))
% 11.41/11.20 [2316]~E(x23161,x23162)+E(f466(x23163,x23164,x23161,x23165),f466(x23163,x23164,x23162,x23165))
% 11.41/11.20 [2317]~E(x23171,x23172)+E(f466(x23173,x23174,x23175,x23171),f466(x23173,x23174,x23175,x23172))
% 11.41/11.20 [2318]~E(x23181,x23182)+E(f663(x23181,x23183,x23184),f663(x23182,x23183,x23184))
% 11.41/11.20 [2319]~E(x23191,x23192)+E(f663(x23193,x23191,x23194),f663(x23193,x23192,x23194))
% 11.41/11.20 [2320]~E(x23201,x23202)+E(f663(x23203,x23204,x23201),f663(x23203,x23204,x23202))
% 11.41/11.20 [2321]~E(x23211,x23212)+E(f832(x23211,x23213,x23214),f832(x23212,x23213,x23214))
% 11.41/11.20 [2322]~E(x23221,x23222)+E(f832(x23223,x23221,x23224),f832(x23223,x23222,x23224))
% 11.41/11.20 [2323]~E(x23231,x23232)+E(f832(x23233,x23234,x23231),f832(x23233,x23234,x23232))
% 11.41/11.20 [2324]~E(x23241,x23242)+E(f441(x23241,x23243,x23244,x23245),f441(x23242,x23243,x23244,x23245))
% 11.41/11.20 [2325]~E(x23251,x23252)+E(f441(x23253,x23251,x23254,x23255),f441(x23253,x23252,x23254,x23255))
% 11.41/11.20 [2326]~E(x23261,x23262)+E(f441(x23263,x23264,x23261,x23265),f441(x23263,x23264,x23262,x23265))
% 11.41/11.20 [2327]~E(x23271,x23272)+E(f441(x23273,x23274,x23275,x23271),f441(x23273,x23274,x23275,x23272))
% 11.41/11.20 [2328]~E(x23281,x23282)+E(f283(x23281),f283(x23282))
% 11.41/11.20 [2329]~E(x23291,x23292)+E(f763(x23291,x23293,x23294),f763(x23292,x23293,x23294))
% 11.41/11.20 [2330]~E(x23301,x23302)+E(f763(x23303,x23301,x23304),f763(x23303,x23302,x23304))
% 11.41/11.20 [2331]~E(x23311,x23312)+E(f763(x23313,x23314,x23311),f763(x23313,x23314,x23312))
% 11.41/11.20 [2332]~E(x23321,x23322)+E(f507(x23321,x23323,x23324,x23325),f507(x23322,x23323,x23324,x23325))
% 11.41/11.20 [2333]~E(x23331,x23332)+E(f507(x23333,x23331,x23334,x23335),f507(x23333,x23332,x23334,x23335))
% 11.41/11.20 [2334]~E(x23341,x23342)+E(f507(x23343,x23344,x23341,x23345),f507(x23343,x23344,x23342,x23345))
% 11.41/11.20 [2335]~E(x23351,x23352)+E(f507(x23353,x23354,x23355,x23351),f507(x23353,x23354,x23355,x23352))
% 11.41/11.20 [2336]~E(x23361,x23362)+E(f716(x23361,x23363,x23364,x23365),f716(x23362,x23363,x23364,x23365))
% 11.41/11.20 [2337]~E(x23371,x23372)+E(f716(x23373,x23371,x23374,x23375),f716(x23373,x23372,x23374,x23375))
% 11.41/11.20 [2338]~E(x23381,x23382)+E(f716(x23383,x23384,x23381,x23385),f716(x23383,x23384,x23382,x23385))
% 11.41/11.20 [2339]~E(x23391,x23392)+E(f716(x23393,x23394,x23395,x23391),f716(x23393,x23394,x23395,x23392))
% 11.41/11.20 [2340]~E(x23401,x23402)+E(f768(x23401,x23403,x23404),f768(x23402,x23403,x23404))
% 11.41/11.20 [2341]~E(x23411,x23412)+E(f768(x23413,x23411,x23414),f768(x23413,x23412,x23414))
% 11.41/11.20 [2342]~E(x23421,x23422)+E(f768(x23423,x23424,x23421),f768(x23423,x23424,x23422))
% 11.41/11.20 [2343]~E(x23431,x23432)+E(f209(x23431),f209(x23432))
% 11.41/11.20 [2344]~E(x23441,x23442)+E(f524(x23441,x23443,x23444,x23445,x23446),f524(x23442,x23443,x23444,x23445,x23446))
% 11.41/11.20 [2345]~E(x23451,x23452)+E(f524(x23453,x23451,x23454,x23455,x23456),f524(x23453,x23452,x23454,x23455,x23456))
% 11.41/11.20 [2346]~E(x23461,x23462)+E(f524(x23463,x23464,x23461,x23465,x23466),f524(x23463,x23464,x23462,x23465,x23466))
% 11.41/11.20 [2347]~E(x23471,x23472)+E(f524(x23473,x23474,x23475,x23471,x23476),f524(x23473,x23474,x23475,x23472,x23476))
% 11.41/11.20 [2348]~E(x23481,x23482)+E(f524(x23483,x23484,x23485,x23486,x23481),f524(x23483,x23484,x23485,x23486,x23482))
% 11.41/11.20 [2349]~E(x23491,x23492)+E(f600(x23491,x23493),f600(x23492,x23493))
% 11.41/11.20 [2350]~E(x23501,x23502)+E(f600(x23503,x23501),f600(x23503,x23502))
% 11.41/11.20 [2351]~E(x23511,x23512)+E(f482(x23511,x23513,x23514),f482(x23512,x23513,x23514))
% 11.41/11.20 [2352]~E(x23521,x23522)+E(f482(x23523,x23521,x23524),f482(x23523,x23522,x23524))
% 11.41/11.20 [2353]~E(x23531,x23532)+E(f482(x23533,x23534,x23531),f482(x23533,x23534,x23532))
% 11.41/11.20 [2354]~E(x23541,x23542)+E(f679(x23541,x23543,x23544,x23545,x23546),f679(x23542,x23543,x23544,x23545,x23546))
% 11.41/11.20 [2355]~E(x23551,x23552)+E(f679(x23553,x23551,x23554,x23555,x23556),f679(x23553,x23552,x23554,x23555,x23556))
% 11.41/11.20 [2356]~E(x23561,x23562)+E(f679(x23563,x23564,x23561,x23565,x23566),f679(x23563,x23564,x23562,x23565,x23566))
% 11.41/11.20 [2357]~E(x23571,x23572)+E(f679(x23573,x23574,x23575,x23571,x23576),f679(x23573,x23574,x23575,x23572,x23576))
% 11.41/11.20 [2358]~E(x23581,x23582)+E(f679(x23583,x23584,x23585,x23586,x23581),f679(x23583,x23584,x23585,x23586,x23582))
% 11.41/11.20 [2359]~E(x23591,x23592)+E(f730(x23591,x23593,x23594,x23595,x23596),f730(x23592,x23593,x23594,x23595,x23596))
% 11.41/11.20 [2360]~E(x23601,x23602)+E(f730(x23603,x23601,x23604,x23605,x23606),f730(x23603,x23602,x23604,x23605,x23606))
% 11.41/11.20 [2361]~E(x23611,x23612)+E(f730(x23613,x23614,x23611,x23615,x23616),f730(x23613,x23614,x23612,x23615,x23616))
% 11.41/11.20 [2362]~E(x23621,x23622)+E(f730(x23623,x23624,x23625,x23621,x23626),f730(x23623,x23624,x23625,x23622,x23626))
% 11.41/11.20 [2363]~E(x23631,x23632)+E(f730(x23633,x23634,x23635,x23636,x23631),f730(x23633,x23634,x23635,x23636,x23632))
% 11.41/11.20 [2364]~E(x23641,x23642)+E(f770(x23641,x23643,x23644,x23645),f770(x23642,x23643,x23644,x23645))
% 11.41/11.20 [2365]~E(x23651,x23652)+E(f770(x23653,x23651,x23654,x23655),f770(x23653,x23652,x23654,x23655))
% 11.41/11.20 [2366]~E(x23661,x23662)+E(f770(x23663,x23664,x23661,x23665),f770(x23663,x23664,x23662,x23665))
% 11.41/11.20 [2367]~E(x23671,x23672)+E(f770(x23673,x23674,x23675,x23671),f770(x23673,x23674,x23675,x23672))
% 11.41/11.20 [2368]~E(x23681,x23682)+E(f627(x23681,x23683,x23684,x23685,x23686,x23687),f627(x23682,x23683,x23684,x23685,x23686,x23687))
% 11.41/11.20 [2369]~E(x23691,x23692)+E(f627(x23693,x23691,x23694,x23695,x23696,x23697),f627(x23693,x23692,x23694,x23695,x23696,x23697))
% 11.41/11.20 [2370]~E(x23701,x23702)+E(f627(x23703,x23704,x23701,x23705,x23706,x23707),f627(x23703,x23704,x23702,x23705,x23706,x23707))
% 11.41/11.20 [2371]~E(x23711,x23712)+E(f627(x23713,x23714,x23715,x23711,x23716,x23717),f627(x23713,x23714,x23715,x23712,x23716,x23717))
% 11.41/11.20 [2372]~E(x23721,x23722)+E(f627(x23723,x23724,x23725,x23726,x23721,x23727),f627(x23723,x23724,x23725,x23726,x23722,x23727))
% 11.41/11.20 [2373]~E(x23731,x23732)+E(f627(x23733,x23734,x23735,x23736,x23737,x23731),f627(x23733,x23734,x23735,x23736,x23737,x23732))
% 11.41/11.20 [2374]~E(x23741,x23742)+E(f706(x23741,x23743,x23744,x23745),f706(x23742,x23743,x23744,x23745))
% 11.41/11.20 [2375]~E(x23751,x23752)+E(f706(x23753,x23751,x23754,x23755),f706(x23753,x23752,x23754,x23755))
% 11.41/11.20 [2376]~E(x23761,x23762)+E(f706(x23763,x23764,x23761,x23765),f706(x23763,x23764,x23762,x23765))
% 11.41/11.20 [2377]~E(x23771,x23772)+E(f706(x23773,x23774,x23775,x23771),f706(x23773,x23774,x23775,x23772))
% 11.41/11.20 [2378]~E(x23781,x23782)+E(f724(x23781,x23783,x23784,x23785,x23786,x23787,x23788),f724(x23782,x23783,x23784,x23785,x23786,x23787,x23788))
% 11.41/11.20 [2379]~E(x23791,x23792)+E(f724(x23793,x23791,x23794,x23795,x23796,x23797,x23798),f724(x23793,x23792,x23794,x23795,x23796,x23797,x23798))
% 11.41/11.20 [2380]~E(x23801,x23802)+E(f724(x23803,x23804,x23801,x23805,x23806,x23807,x23808),f724(x23803,x23804,x23802,x23805,x23806,x23807,x23808))
% 11.41/11.20 [2381]~E(x23811,x23812)+E(f724(x23813,x23814,x23815,x23811,x23816,x23817,x23818),f724(x23813,x23814,x23815,x23812,x23816,x23817,x23818))
% 11.41/11.20 [2382]~E(x23821,x23822)+E(f724(x23823,x23824,x23825,x23826,x23821,x23827,x23828),f724(x23823,x23824,x23825,x23826,x23822,x23827,x23828))
% 11.41/11.20 [2383]~E(x23831,x23832)+E(f724(x23833,x23834,x23835,x23836,x23837,x23831,x23838),f724(x23833,x23834,x23835,x23836,x23837,x23832,x23838))
% 11.41/11.20 [2384]~E(x23841,x23842)+E(f724(x23843,x23844,x23845,x23846,x23847,x23848,x23841),f724(x23843,x23844,x23845,x23846,x23847,x23848,x23842))
% 11.41/11.20 [2385]~E(x23851,x23852)+E(f805(x23851,x23853,x23854),f805(x23852,x23853,x23854))
% 11.41/11.20 [2386]~E(x23861,x23862)+E(f805(x23863,x23861,x23864),f805(x23863,x23862,x23864))
% 11.41/11.20 [2387]~E(x23871,x23872)+E(f805(x23873,x23874,x23871),f805(x23873,x23874,x23872))
% 11.41/11.20 [2388]~E(x23881,x23882)+E(f831(x23881,x23883,x23884),f831(x23882,x23883,x23884))
% 11.41/11.20 [2389]~E(x23891,x23892)+E(f831(x23893,x23891,x23894),f831(x23893,x23892,x23894))
% 11.41/11.20 [2390]~E(x23901,x23902)+E(f831(x23903,x23904,x23901),f831(x23903,x23904,x23902))
% 11.41/11.20 [2391]~E(x23911,x23912)+E(f205(x23911),f205(x23912))
% 11.41/11.20 [2392]~E(x23921,x23922)+E(f471(x23921,x23923),f471(x23922,x23923))
% 11.41/11.20 [2393]~E(x23931,x23932)+E(f471(x23933,x23931),f471(x23933,x23932))
% 11.41/11.20 [2394]~E(x23941,x23942)+E(f483(x23941,x23943,x23944),f483(x23942,x23943,x23944))
% 11.41/11.20 [2395]~E(x23951,x23952)+E(f483(x23953,x23951,x23954),f483(x23953,x23952,x23954))
% 11.41/11.20 [2396]~E(x23961,x23962)+E(f483(x23963,x23964,x23961),f483(x23963,x23964,x23962))
% 11.41/11.20 [2397]~E(x23971,x23972)+E(f373(x23971,x23973,x23974,x23975,x23976),f373(x23972,x23973,x23974,x23975,x23976))
% 11.41/11.20 [2398]~E(x23981,x23982)+E(f373(x23983,x23981,x23984,x23985,x23986),f373(x23983,x23982,x23984,x23985,x23986))
% 11.41/11.20 [2399]~E(x23991,x23992)+E(f373(x23993,x23994,x23991,x23995,x23996),f373(x23993,x23994,x23992,x23995,x23996))
% 11.41/11.20 [2400]~E(x24001,x24002)+E(f373(x24003,x24004,x24005,x24001,x24006),f373(x24003,x24004,x24005,x24002,x24006))
% 11.41/11.20 [2401]~E(x24011,x24012)+E(f373(x24013,x24014,x24015,x24016,x24011),f373(x24013,x24014,x24015,x24016,x24012))
% 11.41/11.20 [2402]~E(x24021,x24022)+E(f233(x24021,x24023,x24024,x24025),f233(x24022,x24023,x24024,x24025))
% 11.41/11.20 [2403]~E(x24031,x24032)+E(f233(x24033,x24031,x24034,x24035),f233(x24033,x24032,x24034,x24035))
% 11.41/11.20 [2404]~E(x24041,x24042)+E(f233(x24043,x24044,x24041,x24045),f233(x24043,x24044,x24042,x24045))
% 11.41/11.20 [2405]~E(x24051,x24052)+E(f233(x24053,x24054,x24055,x24051),f233(x24053,x24054,x24055,x24052))
% 11.41/11.20 [2406]~E(x24061,x24062)+E(f561(x24061),f561(x24062))
% 11.41/11.20 [2407]~E(x24071,x24072)+E(f598(x24071,x24073,x24074,x24075),f598(x24072,x24073,x24074,x24075))
% 11.41/11.20 [2408]~E(x24081,x24082)+E(f598(x24083,x24081,x24084,x24085),f598(x24083,x24082,x24084,x24085))
% 11.41/11.20 [2409]~E(x24091,x24092)+E(f598(x24093,x24094,x24091,x24095),f598(x24093,x24094,x24092,x24095))
% 11.41/11.20 [2410]~E(x24101,x24102)+E(f598(x24103,x24104,x24105,x24101),f598(x24103,x24104,x24105,x24102))
% 11.41/11.20 [2411]~E(x24111,x24112)+E(f847(x24111,x24113),f847(x24112,x24113))
% 11.41/11.20 [2412]~E(x24121,x24122)+E(f847(x24123,x24121),f847(x24123,x24122))
% 11.41/11.20 [2413]~E(x24131,x24132)+E(f586(x24131,x24133),f586(x24132,x24133))
% 11.41/11.20 [2414]~E(x24141,x24142)+E(f586(x24143,x24141),f586(x24143,x24142))
% 11.41/11.20 [2415]~E(x24151,x24152)+E(f370(x24151,x24153,x24154,x24155),f370(x24152,x24153,x24154,x24155))
% 11.41/11.20 [2416]~E(x24161,x24162)+E(f370(x24163,x24161,x24164,x24165),f370(x24163,x24162,x24164,x24165))
% 11.41/11.20 [2417]~E(x24171,x24172)+E(f370(x24173,x24174,x24171,x24175),f370(x24173,x24174,x24172,x24175))
% 11.41/11.20 [2418]~E(x24181,x24182)+E(f370(x24183,x24184,x24185,x24181),f370(x24183,x24184,x24185,x24182))
% 11.41/11.20 [2419]~E(x24191,x24192)+E(f630(x24191,x24193),f630(x24192,x24193))
% 11.41/11.20 [2420]~E(x24201,x24202)+E(f630(x24203,x24201),f630(x24203,x24202))
% 11.41/11.20 [2421]~E(x24211,x24212)+E(f500(x24211,x24213,x24214,x24215,x24216),f500(x24212,x24213,x24214,x24215,x24216))
% 11.41/11.20 [2422]~E(x24221,x24222)+E(f500(x24223,x24221,x24224,x24225,x24226),f500(x24223,x24222,x24224,x24225,x24226))
% 11.41/11.20 [2423]~E(x24231,x24232)+E(f500(x24233,x24234,x24231,x24235,x24236),f500(x24233,x24234,x24232,x24235,x24236))
% 11.41/11.20 [2424]~E(x24241,x24242)+E(f500(x24243,x24244,x24245,x24241,x24246),f500(x24243,x24244,x24245,x24242,x24246))
% 11.41/11.20 [2425]~E(x24251,x24252)+E(f500(x24253,x24254,x24255,x24256,x24251),f500(x24253,x24254,x24255,x24256,x24252))
% 11.41/11.20 [2426]~E(x24261,x24262)+E(f570(x24261,x24263,x24264),f570(x24262,x24263,x24264))
% 11.41/11.20 [2427]~E(x24271,x24272)+E(f570(x24273,x24271,x24274),f570(x24273,x24272,x24274))
% 11.41/11.20 [2428]~E(x24281,x24282)+E(f570(x24283,x24284,x24281),f570(x24283,x24284,x24282))
% 11.41/11.20 [2429]~E(x24291,x24292)+E(f559(x24291),f559(x24292))
% 11.41/11.20 [2430]~E(x24301,x24302)+E(f787(x24301),f787(x24302))
% 11.41/11.20 [2431]~E(x24311,x24312)+E(f589(x24311,x24313,x24314,x24315),f589(x24312,x24313,x24314,x24315))
% 11.41/11.20 [2432]~E(x24321,x24322)+E(f589(x24323,x24321,x24324,x24325),f589(x24323,x24322,x24324,x24325))
% 11.41/11.20 [2433]~E(x24331,x24332)+E(f589(x24333,x24334,x24331,x24335),f589(x24333,x24334,x24332,x24335))
% 11.41/11.20 [2434]~E(x24341,x24342)+E(f589(x24343,x24344,x24345,x24341),f589(x24343,x24344,x24345,x24342))
% 11.41/11.20 [2435]~E(x24351,x24352)+E(f414(x24351),f414(x24352))
% 11.41/11.20 [2436]~E(x24361,x24362)+E(f587(x24361,x24363),f587(x24362,x24363))
% 11.41/11.20 [2437]~E(x24371,x24372)+E(f587(x24373,x24371),f587(x24373,x24372))
% 11.41/11.20 [2438]~E(x24381,x24382)+E(f542(x24381,x24383,x24384,x24385,x24386),f542(x24382,x24383,x24384,x24385,x24386))
% 11.41/11.20 [2439]~E(x24391,x24392)+E(f542(x24393,x24391,x24394,x24395,x24396),f542(x24393,x24392,x24394,x24395,x24396))
% 11.41/11.20 [2440]~E(x24401,x24402)+E(f542(x24403,x24404,x24401,x24405,x24406),f542(x24403,x24404,x24402,x24405,x24406))
% 11.41/11.20 [2441]~E(x24411,x24412)+E(f542(x24413,x24414,x24415,x24411,x24416),f542(x24413,x24414,x24415,x24412,x24416))
% 11.41/11.20 [2442]~E(x24421,x24422)+E(f542(x24423,x24424,x24425,x24426,x24421),f542(x24423,x24424,x24425,x24426,x24422))
% 11.41/11.20 [2443]~E(x24431,x24432)+E(f674(x24431,x24433,x24434,x24435,x24436),f674(x24432,x24433,x24434,x24435,x24436))
% 11.41/11.20 [2444]~E(x24441,x24442)+E(f674(x24443,x24441,x24444,x24445,x24446),f674(x24443,x24442,x24444,x24445,x24446))
% 11.41/11.20 [2445]~E(x24451,x24452)+E(f674(x24453,x24454,x24451,x24455,x24456),f674(x24453,x24454,x24452,x24455,x24456))
% 11.41/11.20 [2446]~E(x24461,x24462)+E(f674(x24463,x24464,x24465,x24461,x24466),f674(x24463,x24464,x24465,x24462,x24466))
% 11.41/11.20 [2447]~E(x24471,x24472)+E(f674(x24473,x24474,x24475,x24476,x24471),f674(x24473,x24474,x24475,x24476,x24472))
% 11.41/11.20 [2448]~E(x24481,x24482)+E(f737(x24481,x24483,x24484),f737(x24482,x24483,x24484))
% 11.41/11.20 [2449]~E(x24491,x24492)+E(f737(x24493,x24491,x24494),f737(x24493,x24492,x24494))
% 11.41/11.20 [2450]~E(x24501,x24502)+E(f737(x24503,x24504,x24501),f737(x24503,x24504,x24502))
% 11.41/11.20 [2451]~E(x24511,x24512)+E(f612(x24511,x24513),f612(x24512,x24513))
% 11.41/11.20 [2452]~E(x24521,x24522)+E(f612(x24523,x24521),f612(x24523,x24522))
% 11.41/11.20 [2453]~E(x24531,x24532)+E(f210(x24531),f210(x24532))
% 11.41/11.20 [2454]~E(x24541,x24542)+E(f760(x24541),f760(x24542))
% 11.41/11.20 [2455]~E(x24551,x24552)+E(f328(x24551,x24553,x24554),f328(x24552,x24553,x24554))
% 11.41/11.20 [2456]~E(x24561,x24562)+E(f328(x24563,x24561,x24564),f328(x24563,x24562,x24564))
% 11.41/11.20 [2457]~E(x24571,x24572)+E(f328(x24573,x24574,x24571),f328(x24573,x24574,x24572))
% 11.41/11.20 [2458]~E(x24581,x24582)+E(f693(x24581,x24583),f693(x24582,x24583))
% 11.41/11.20 [2459]~E(x24591,x24592)+E(f693(x24593,x24591),f693(x24593,x24592))
% 11.41/11.20 [2460]~E(x24601,x24602)+E(f450(x24601,x24603,x24604,x24605,x24606),f450(x24602,x24603,x24604,x24605,x24606))
% 11.41/11.20 [2461]~E(x24611,x24612)+E(f450(x24613,x24611,x24614,x24615,x24616),f450(x24613,x24612,x24614,x24615,x24616))
% 11.41/11.20 [2462]~E(x24621,x24622)+E(f450(x24623,x24624,x24621,x24625,x24626),f450(x24623,x24624,x24622,x24625,x24626))
% 11.41/11.20 [2463]~E(x24631,x24632)+E(f450(x24633,x24634,x24635,x24631,x24636),f450(x24633,x24634,x24635,x24632,x24636))
% 11.41/11.20 [2464]~E(x24641,x24642)+E(f450(x24643,x24644,x24645,x24646,x24641),f450(x24643,x24644,x24645,x24646,x24642))
% 11.41/11.20 [2465]~E(x24651,x24652)+E(f659(x24651,x24653,x24654,x24655,x24656),f659(x24652,x24653,x24654,x24655,x24656))
% 11.41/11.20 [2466]~E(x24661,x24662)+E(f659(x24663,x24661,x24664,x24665,x24666),f659(x24663,x24662,x24664,x24665,x24666))
% 11.41/11.20 [2467]~E(x24671,x24672)+E(f659(x24673,x24674,x24671,x24675,x24676),f659(x24673,x24674,x24672,x24675,x24676))
% 11.41/11.20 [2468]~E(x24681,x24682)+E(f659(x24683,x24684,x24685,x24681,x24686),f659(x24683,x24684,x24685,x24682,x24686))
% 11.41/11.20 [2469]~E(x24691,x24692)+E(f659(x24693,x24694,x24695,x24696,x24691),f659(x24693,x24694,x24695,x24696,x24692))
% 11.41/11.20 [2470]~E(x24701,x24702)+E(f619(x24701,x24703),f619(x24702,x24703))
% 11.41/11.20 [2471]~E(x24711,x24712)+E(f619(x24713,x24711),f619(x24713,x24712))
% 11.41/11.20 [2472]~E(x24721,x24722)+E(f594(x24721,x24723),f594(x24722,x24723))
% 11.41/11.20 [2473]~E(x24731,x24732)+E(f594(x24733,x24731),f594(x24733,x24732))
% 11.41/11.20 [2474]~E(x24741,x24742)+E(f494(x24741,x24743,x24744,x24745,x24746),f494(x24742,x24743,x24744,x24745,x24746))
% 11.41/11.20 [2475]~E(x24751,x24752)+E(f494(x24753,x24751,x24754,x24755,x24756),f494(x24753,x24752,x24754,x24755,x24756))
% 11.41/11.20 [2476]~E(x24761,x24762)+E(f494(x24763,x24764,x24761,x24765,x24766),f494(x24763,x24764,x24762,x24765,x24766))
% 11.41/11.20 [2477]~E(x24771,x24772)+E(f494(x24773,x24774,x24775,x24771,x24776),f494(x24773,x24774,x24775,x24772,x24776))
% 11.41/11.20 [2478]~E(x24781,x24782)+E(f494(x24783,x24784,x24785,x24786,x24781),f494(x24783,x24784,x24785,x24786,x24782))
% 11.41/11.20 [2479]~E(x24791,x24792)+E(f504(x24791,x24793),f504(x24792,x24793))
% 11.41/11.20 [2480]~E(x24801,x24802)+E(f504(x24803,x24801),f504(x24803,x24802))
% 11.41/11.20 [2481]~E(x24811,x24812)+E(f123(x24811,x24813,x24814,x24815),f123(x24812,x24813,x24814,x24815))
% 11.41/11.20 [2482]~E(x24821,x24822)+E(f123(x24823,x24821,x24824,x24825),f123(x24823,x24822,x24824,x24825))
% 11.41/11.20 [2483]~E(x24831,x24832)+E(f123(x24833,x24834,x24831,x24835),f123(x24833,x24834,x24832,x24835))
% 11.41/11.20 [2484]~E(x24841,x24842)+E(f123(x24843,x24844,x24845,x24841),f123(x24843,x24844,x24845,x24842))
% 11.41/11.20 [2485]~E(x24851,x24852)+E(f352(x24851,x24853),f352(x24852,x24853))
% 11.41/11.20 [2486]~E(x24861,x24862)+E(f352(x24863,x24861),f352(x24863,x24862))
% 11.41/11.20 [2487]~E(x24871,x24872)+E(f378(x24871,x24873,x24874,x24875,x24876),f378(x24872,x24873,x24874,x24875,x24876))
% 11.41/11.20 [2488]~E(x24881,x24882)+E(f378(x24883,x24881,x24884,x24885,x24886),f378(x24883,x24882,x24884,x24885,x24886))
% 11.41/11.20 [2489]~E(x24891,x24892)+E(f378(x24893,x24894,x24891,x24895,x24896),f378(x24893,x24894,x24892,x24895,x24896))
% 11.41/11.20 [2490]~E(x24901,x24902)+E(f378(x24903,x24904,x24905,x24901,x24906),f378(x24903,x24904,x24905,x24902,x24906))
% 11.41/11.20 [2491]~E(x24911,x24912)+E(f378(x24913,x24914,x24915,x24916,x24911),f378(x24913,x24914,x24915,x24916,x24912))
% 11.41/11.20 [2492]~E(x24921,x24922)+E(f230(x24921,x24923,x24924,x24925,x24926),f230(x24922,x24923,x24924,x24925,x24926))
% 11.41/11.20 [2493]~E(x24931,x24932)+E(f230(x24933,x24931,x24934,x24935,x24936),f230(x24933,x24932,x24934,x24935,x24936))
% 11.41/11.20 [2494]~E(x24941,x24942)+E(f230(x24943,x24944,x24941,x24945,x24946),f230(x24943,x24944,x24942,x24945,x24946))
% 11.41/11.20 [2495]~E(x24951,x24952)+E(f230(x24953,x24954,x24955,x24951,x24956),f230(x24953,x24954,x24955,x24952,x24956))
% 11.41/11.20 [2496]~E(x24961,x24962)+E(f230(x24963,x24964,x24965,x24966,x24961),f230(x24963,x24964,x24965,x24966,x24962))
% 11.41/11.20 [2497]~E(x24971,x24972)+E(f232(x24971,x24973,x24974),f232(x24972,x24973,x24974))
% 11.41/11.20 [2498]~E(x24981,x24982)+E(f232(x24983,x24981,x24984),f232(x24983,x24982,x24984))
% 11.41/11.20 [2499]~E(x24991,x24992)+E(f232(x24993,x24994,x24991),f232(x24993,x24994,x24992))
% 11.41/11.20 [2500]~E(x25001,x25002)+E(f629(x25001),f629(x25002))
% 11.41/11.20 [2501]~E(x25011,x25012)+E(f449(x25011,x25013,x25014,x25015),f449(x25012,x25013,x25014,x25015))
% 11.41/11.20 [2502]~E(x25021,x25022)+E(f449(x25023,x25021,x25024,x25025),f449(x25023,x25022,x25024,x25025))
% 11.41/11.20 [2503]~E(x25031,x25032)+E(f449(x25033,x25034,x25031,x25035),f449(x25033,x25034,x25032,x25035))
% 11.41/11.20 [2504]~E(x25041,x25042)+E(f449(x25043,x25044,x25045,x25041),f449(x25043,x25044,x25045,x25042))
% 11.41/11.20 [2505]~E(x25051,x25052)+E(f325(x25051,x25053,x25054),f325(x25052,x25053,x25054))
% 11.41/11.20 [2506]~E(x25061,x25062)+E(f325(x25063,x25061,x25064),f325(x25063,x25062,x25064))
% 11.41/11.20 [2507]~E(x25071,x25072)+E(f325(x25073,x25074,x25071),f325(x25073,x25074,x25072))
% 11.41/11.20 [2508]~E(x25081,x25082)+E(f103(x25081,x25083,x25084,x25085),f103(x25082,x25083,x25084,x25085))
% 11.41/11.20 [2509]~E(x25091,x25092)+E(f103(x25093,x25091,x25094,x25095),f103(x25093,x25092,x25094,x25095))
% 11.41/11.20 [2510]~E(x25101,x25102)+E(f103(x25103,x25104,x25101,x25105),f103(x25103,x25104,x25102,x25105))
% 11.41/11.20 [2511]~E(x25111,x25112)+E(f103(x25113,x25114,x25115,x25111),f103(x25113,x25114,x25115,x25112))
% 11.41/11.20 [2512]~E(x25121,x25122)+E(f697(x25121,x25123,x25124),f697(x25122,x25123,x25124))
% 11.41/11.20 [2513]~E(x25131,x25132)+E(f697(x25133,x25131,x25134),f697(x25133,x25132,x25134))
% 11.41/11.20 [2514]~E(x25141,x25142)+E(f697(x25143,x25144,x25141),f697(x25143,x25144,x25142))
% 11.41/11.20 [2515]~E(x25151,x25152)+E(f798(x25151,x25153),f798(x25152,x25153))
% 11.41/11.20 [2516]~E(x25161,x25162)+E(f798(x25163,x25161),f798(x25163,x25162))
% 11.41/11.20 [2517]~E(x25171,x25172)+E(f426(x25171,x25173),f426(x25172,x25173))
% 11.41/11.20 [2518]~E(x25181,x25182)+E(f426(x25183,x25181),f426(x25183,x25182))
% 11.41/11.20 [2519]~E(x25191,x25192)+E(f415(x25191,x25193),f415(x25192,x25193))
% 11.41/11.20 [2520]~E(x25201,x25202)+E(f415(x25203,x25201),f415(x25203,x25202))
% 11.41/11.20 [2521]~E(x25211,x25212)+E(f815(x25211,x25213,x25214),f815(x25212,x25213,x25214))
% 11.41/11.20 [2522]~E(x25221,x25222)+E(f815(x25223,x25221,x25224),f815(x25223,x25222,x25224))
% 11.41/11.20 [2523]~E(x25231,x25232)+E(f815(x25233,x25234,x25231),f815(x25233,x25234,x25232))
% 11.41/11.20 [2524]~E(x25241,x25242)+E(f427(x25241,x25243,x25244,x25245),f427(x25242,x25243,x25244,x25245))
% 11.41/11.20 [2525]~E(x25251,x25252)+E(f427(x25253,x25251,x25254,x25255),f427(x25253,x25252,x25254,x25255))
% 11.41/11.20 [2526]~E(x25261,x25262)+E(f427(x25263,x25264,x25261,x25265),f427(x25263,x25264,x25262,x25265))
% 11.41/11.20 [2527]~E(x25271,x25272)+E(f427(x25273,x25274,x25275,x25271),f427(x25273,x25274,x25275,x25272))
% 11.41/11.20 [2528]~E(x25281,x25282)+E(f541(x25281,x25283,x25284,x25285,x25286),f541(x25282,x25283,x25284,x25285,x25286))
% 11.41/11.20 [2529]~E(x25291,x25292)+E(f541(x25293,x25291,x25294,x25295,x25296),f541(x25293,x25292,x25294,x25295,x25296))
% 11.41/11.20 [2530]~E(x25301,x25302)+E(f541(x25303,x25304,x25301,x25305,x25306),f541(x25303,x25304,x25302,x25305,x25306))
% 11.41/11.20 [2531]~E(x25311,x25312)+E(f541(x25313,x25314,x25315,x25311,x25316),f541(x25313,x25314,x25315,x25312,x25316))
% 11.41/11.20 [2532]~E(x25321,x25322)+E(f541(x25323,x25324,x25325,x25326,x25321),f541(x25323,x25324,x25325,x25326,x25322))
% 11.41/11.20 [2533]~E(x25331,x25332)+E(f532(x25331,x25333,x25334),f532(x25332,x25333,x25334))
% 11.41/11.20 [2534]~E(x25341,x25342)+E(f532(x25343,x25341,x25344),f532(x25343,x25342,x25344))
% 11.41/11.20 [2535]~E(x25351,x25352)+E(f532(x25353,x25354,x25351),f532(x25353,x25354,x25352))
% 11.41/11.20 [2536]~E(x25361,x25362)+E(f758(x25361,x25363,x25364),f758(x25362,x25363,x25364))
% 11.41/11.20 [2537]~E(x25371,x25372)+E(f758(x25373,x25371,x25374),f758(x25373,x25372,x25374))
% 11.41/11.20 [2538]~E(x25381,x25382)+E(f758(x25383,x25384,x25381),f758(x25383,x25384,x25382))
% 11.41/11.20 [2539]~E(x25391,x25392)+E(f788(x25391),f788(x25392))
% 11.41/11.20 [2540]~E(x25401,x25402)+E(f487(x25401,x25403,x25404),f487(x25402,x25403,x25404))
% 11.41/11.20 [2541]~E(x25411,x25412)+E(f487(x25413,x25411,x25414),f487(x25413,x25412,x25414))
% 11.41/11.20 [2542]~E(x25421,x25422)+E(f487(x25423,x25424,x25421),f487(x25423,x25424,x25422))
% 11.41/11.20 [2543]~E(x25431,x25432)+E(f839(x25431,x25433,x25434),f839(x25432,x25433,x25434))
% 11.41/11.20 [2544]~E(x25441,x25442)+E(f839(x25443,x25441,x25444),f839(x25443,x25442,x25444))
% 11.41/11.20 [2545]~E(x25451,x25452)+E(f839(x25453,x25454,x25451),f839(x25453,x25454,x25452))
% 11.41/11.20 [2546]~E(x25461,x25462)+E(f518(x25461,x25463,x25464),f518(x25462,x25463,x25464))
% 11.41/11.20 [2547]~E(x25471,x25472)+E(f518(x25473,x25471,x25474),f518(x25473,x25472,x25474))
% 11.41/11.20 [2548]~E(x25481,x25482)+E(f518(x25483,x25484,x25481),f518(x25483,x25484,x25482))
% 11.41/11.20 [2549]~E(x25491,x25492)+E(f774(x25491,x25493,x25494),f774(x25492,x25493,x25494))
% 11.41/11.20 [2550]~E(x25501,x25502)+E(f774(x25503,x25501,x25504),f774(x25503,x25502,x25504))
% 11.41/11.20 [2551]~E(x25511,x25512)+E(f774(x25513,x25514,x25511),f774(x25513,x25514,x25512))
% 11.41/11.20 [2552]~E(x25521,x25522)+E(f539(x25521,x25523,x25524,x25525),f539(x25522,x25523,x25524,x25525))
% 11.41/11.20 [2553]~E(x25531,x25532)+E(f539(x25533,x25531,x25534,x25535),f539(x25533,x25532,x25534,x25535))
% 11.41/11.20 [2554]~E(x25541,x25542)+E(f539(x25543,x25544,x25541,x25545),f539(x25543,x25544,x25542,x25545))
% 11.41/11.20 [2555]~E(x25551,x25552)+E(f539(x25553,x25554,x25555,x25551),f539(x25553,x25554,x25555,x25552))
% 11.41/11.20 [2556]~P1(x25561)+P1(x25562)+~E(x25561,x25562)
% 11.41/11.20 [2557]~P85(x25571)+P85(x25572)+~E(x25571,x25572)
% 11.41/11.20 [2558]P14(x25582,x25583,x25584,x25585,x25586,x25587)+~E(x25581,x25582)+~P14(x25581,x25583,x25584,x25585,x25586,x25587)
% 11.41/11.20 [2559]P14(x25593,x25592,x25594,x25595,x25596,x25597)+~E(x25591,x25592)+~P14(x25593,x25591,x25594,x25595,x25596,x25597)
% 11.41/11.20 [2560]P14(x25603,x25604,x25602,x25605,x25606,x25607)+~E(x25601,x25602)+~P14(x25603,x25604,x25601,x25605,x25606,x25607)
% 11.41/11.20 [2561]P14(x25613,x25614,x25615,x25612,x25616,x25617)+~E(x25611,x25612)+~P14(x25613,x25614,x25615,x25611,x25616,x25617)
% 11.41/11.20 [2562]P14(x25623,x25624,x25625,x25626,x25622,x25627)+~E(x25621,x25622)+~P14(x25623,x25624,x25625,x25626,x25621,x25627)
% 11.41/11.20 [2563]P14(x25633,x25634,x25635,x25636,x25637,x25632)+~E(x25631,x25632)+~P14(x25633,x25634,x25635,x25636,x25637,x25631)
% 11.41/11.20 [2564]P9(x25642,x25643,x25644)+~E(x25641,x25642)+~P9(x25641,x25643,x25644)
% 11.41/11.20 [2565]P9(x25653,x25652,x25654)+~E(x25651,x25652)+~P9(x25653,x25651,x25654)
% 11.41/11.20 [2566]P9(x25663,x25664,x25662)+~E(x25661,x25662)+~P9(x25663,x25664,x25661)
% 11.41/11.20 [2567]~P2(x25671)+P2(x25672)+~E(x25671,x25672)
% 11.41/11.20 [2568]~P101(x25681)+P101(x25682)+~E(x25681,x25682)
% 11.41/11.20 [2569]~P99(x25691)+P99(x25692)+~E(x25691,x25692)
% 11.41/11.20 [2570]~P63(x25701)+P63(x25702)+~E(x25701,x25702)
% 11.41/11.20 [2571]P38(x25712,x25713,x25714,x25715)+~E(x25711,x25712)+~P38(x25711,x25713,x25714,x25715)
% 11.41/11.20 [2572]P38(x25723,x25722,x25724,x25725)+~E(x25721,x25722)+~P38(x25723,x25721,x25724,x25725)
% 11.41/11.20 [2573]P38(x25733,x25734,x25732,x25735)+~E(x25731,x25732)+~P38(x25733,x25734,x25731,x25735)
% 11.41/11.20 [2574]P38(x25743,x25744,x25745,x25742)+~E(x25741,x25742)+~P38(x25743,x25744,x25745,x25741)
% 11.41/11.20 [2575]P15(x25752,x25753)+~E(x25751,x25752)+~P15(x25751,x25753)
% 11.41/11.20 [2576]P15(x25763,x25762)+~E(x25761,x25762)+~P15(x25763,x25761)
% 11.41/11.20 [2577]~P64(x25771)+P64(x25772)+~E(x25771,x25772)
% 11.41/11.20 [2578]~P80(x25781)+P80(x25782)+~E(x25781,x25782)
% 11.41/11.20 [2579]~P74(x25791)+P74(x25792)+~E(x25791,x25792)
% 11.41/11.20 [2580]~P67(x25801)+P67(x25802)+~E(x25801,x25802)
% 11.41/11.20 [2581]~P6(x25811)+P6(x25812)+~E(x25811,x25812)
% 11.41/11.20 [2582]P142(x25822,x25823,x25824)+~E(x25821,x25822)+~P142(x25821,x25823,x25824)
% 11.41/11.20 [2583]P142(x25833,x25832,x25834)+~E(x25831,x25832)+~P142(x25833,x25831,x25834)
% 11.41/11.20 [2584]P142(x25843,x25844,x25842)+~E(x25841,x25842)+~P142(x25843,x25844,x25841)
% 11.41/11.20 [2585]~P68(x25851)+P68(x25852)+~E(x25851,x25852)
% 11.41/11.20 [2586]P33(x25862,x25863,x25864,x25865)+~E(x25861,x25862)+~P33(x25861,x25863,x25864,x25865)
% 11.41/11.20 [2587]P33(x25873,x25872,x25874,x25875)+~E(x25871,x25872)+~P33(x25873,x25871,x25874,x25875)
% 11.41/11.20 [2588]P33(x25883,x25884,x25882,x25885)+~E(x25881,x25882)+~P33(x25883,x25884,x25881,x25885)
% 11.41/11.20 [2589]P33(x25893,x25894,x25895,x25892)+~E(x25891,x25892)+~P33(x25893,x25894,x25895,x25891)
% 11.41/11.20 [2590]P26(x25902,x25903,x25904,x25905)+~E(x25901,x25902)+~P26(x25901,x25903,x25904,x25905)
% 11.41/11.20 [2591]P26(x25913,x25912,x25914,x25915)+~E(x25911,x25912)+~P26(x25913,x25911,x25914,x25915)
% 11.41/11.20 [2592]P26(x25923,x25924,x25922,x25925)+~E(x25921,x25922)+~P26(x25923,x25924,x25921,x25925)
% 11.41/11.20 [2593]P26(x25933,x25934,x25935,x25932)+~E(x25931,x25932)+~P26(x25933,x25934,x25935,x25931)
% 11.41/11.20 [2594]~P69(x25941)+P69(x25942)+~E(x25941,x25942)
% 11.41/11.20 [2595]~P86(x25951)+P86(x25952)+~E(x25951,x25952)
% 11.41/11.20 [2596]P143(x25962,x25963,x25964)+~E(x25961,x25962)+~P143(x25961,x25963,x25964)
% 11.41/11.20 [2597]P143(x25973,x25972,x25974)+~E(x25971,x25972)+~P143(x25973,x25971,x25974)
% 11.41/11.20 [2598]P143(x25983,x25984,x25982)+~E(x25981,x25982)+~P143(x25983,x25984,x25981)
% 11.41/11.20 [2599]~P89(x25991)+P89(x25992)+~E(x25991,x25992)
% 11.41/11.20 [2600]~P111(x26001)+P111(x26002)+~E(x26001,x26002)
% 11.41/11.20 [2601]~P122(x26011)+P122(x26012)+~E(x26011,x26012)
% 11.41/11.20 [2602]~P112(x26021)+P112(x26022)+~E(x26021,x26022)
% 11.41/11.20 [2603]~P127(x26031)+P127(x26032)+~E(x26031,x26032)
% 11.41/11.20 [2604]~P125(x26041)+P125(x26042)+~E(x26041,x26042)
% 11.41/11.20 [2605]~P61(x26051)+P61(x26052)+~E(x26051,x26052)
% 11.41/11.20 [2606]P35(x26062,x26063)+~E(x26061,x26062)+~P35(x26061,x26063)
% 11.41/11.20 [2607]P35(x26073,x26072)+~E(x26071,x26072)+~P35(x26073,x26071)
% 11.41/11.20 [2608]~P90(x26081)+P90(x26082)+~E(x26081,x26082)
% 11.41/11.20 [2609]~P93(x26091)+P93(x26092)+~E(x26091,x26092)
% 11.41/11.20 [2610]~P78(x26101)+P78(x26102)+~E(x26101,x26102)
% 11.41/11.20 [2611]~P91(x26111)+P91(x26112)+~E(x26111,x26112)
% 11.41/11.20 [2612]~P81(x26121)+P81(x26122)+~E(x26121,x26122)
% 11.41/11.20 [2613]~P7(x26131)+P7(x26132)+~E(x26131,x26132)
% 11.41/11.20 [2614]~P88(x26141)+P88(x26142)+~E(x26141,x26142)
% 11.41/11.20 [2615]~P113(x26151)+P113(x26152)+~E(x26151,x26152)
% 11.41/11.20 [2616]~P120(x26161)+P120(x26162)+~E(x26161,x26162)
% 11.41/11.20 [2617]~P62(x26171)+P62(x26172)+~E(x26171,x26172)
% 11.41/11.20 [2618]P53(x26182,x26183,x26184)+~E(x26181,x26182)+~P53(x26181,x26183,x26184)
% 11.41/11.20 [2619]P53(x26193,x26192,x26194)+~E(x26191,x26192)+~P53(x26193,x26191,x26194)
% 11.41/11.20 [2620]P53(x26203,x26204,x26202)+~E(x26201,x26202)+~P53(x26203,x26204,x26201)
% 11.41/11.20 [2621]~P87(x26211)+P87(x26212)+~E(x26211,x26212)
% 11.41/11.20 [2622]~P4(x26221)+P4(x26222)+~E(x26221,x26222)
% 11.41/11.20 [2623]P55(x26232,x26233)+~E(x26231,x26232)+~P55(x26231,x26233)
% 11.41/11.20 [2624]P55(x26243,x26242)+~E(x26241,x26242)+~P55(x26243,x26241)
% 11.41/11.20 [2625]~P100(x26251)+P100(x26252)+~E(x26251,x26252)
% 11.41/11.20 [2626]~P77(x26261)+P77(x26262)+~E(x26261,x26262)
% 11.41/11.20 [2627]P20(x26272,x26273,x26274,x26275)+~E(x26271,x26272)+~P20(x26271,x26273,x26274,x26275)
% 11.41/11.20 [2628]P20(x26283,x26282,x26284,x26285)+~E(x26281,x26282)+~P20(x26283,x26281,x26284,x26285)
% 11.41/11.20 [2629]P20(x26293,x26294,x26292,x26295)+~E(x26291,x26292)+~P20(x26293,x26294,x26291,x26295)
% 11.41/11.20 [2630]P20(x26303,x26304,x26305,x26302)+~E(x26301,x26302)+~P20(x26303,x26304,x26305,x26301)
% 11.41/11.20 [2631]~P136(x26311)+P136(x26312)+~E(x26311,x26312)
% 11.41/11.20 [2632]P47(x26322,x26323)+~E(x26321,x26322)+~P47(x26321,x26323)
% 11.41/11.20 [2633]P47(x26333,x26332)+~E(x26331,x26332)+~P47(x26333,x26331)
% 11.41/11.20 [2634]~P131(x26341)+P131(x26342)+~E(x26341,x26342)
% 11.41/11.20 [2635]~P139(x26351)+P139(x26352)+~E(x26351,x26352)
% 11.41/11.20 [2636]~P104(x26361)+P104(x26362)+~E(x26361,x26362)
% 11.41/11.20 [2637]~P71(x26371)+P71(x26372)+~E(x26371,x26372)
% 11.41/11.20 [2638]P22(x26382,x26383,x26384,x26385,x26386)+~E(x26381,x26382)+~P22(x26381,x26383,x26384,x26385,x26386)
% 11.41/11.20 [2639]P22(x26393,x26392,x26394,x26395,x26396)+~E(x26391,x26392)+~P22(x26393,x26391,x26394,x26395,x26396)
% 11.41/11.20 [2640]P22(x26403,x26404,x26402,x26405,x26406)+~E(x26401,x26402)+~P22(x26403,x26404,x26401,x26405,x26406)
% 11.41/11.20 [2641]P22(x26413,x26414,x26415,x26412,x26416)+~E(x26411,x26412)+~P22(x26413,x26414,x26415,x26411,x26416)
% 11.41/11.20 [2642]P22(x26423,x26424,x26425,x26426,x26422)+~E(x26421,x26422)+~P22(x26423,x26424,x26425,x26426,x26421)
% 11.41/11.20 [2643]~P79(x26431)+P79(x26432)+~E(x26431,x26432)
% 11.41/11.20 [2644]~P103(x26441)+P103(x26442)+~E(x26441,x26442)
% 11.41/11.20 [2645]~P3(x26451)+P3(x26452)+~E(x26451,x26452)
% 11.41/11.20 [2646]~P98(x26461)+P98(x26462)+~E(x26461,x26462)
% 11.41/11.20 [2647]~P116(x26471)+P116(x26472)+~E(x26471,x26472)
% 11.41/11.20 [2648]~P123(x26481)+P123(x26482)+~E(x26481,x26482)
% 11.41/11.20 [2649]~P135(x26491)+P135(x26492)+~E(x26491,x26492)
% 11.41/11.20 [2650]~P114(x26501)+P114(x26502)+~E(x26501,x26502)
% 11.41/11.20 [2651]P18(x26512,x26513,x26514)+~E(x26511,x26512)+~P18(x26511,x26513,x26514)
% 11.41/11.20 [2652]P18(x26523,x26522,x26524)+~E(x26521,x26522)+~P18(x26523,x26521,x26524)
% 11.41/11.20 [2653]P18(x26533,x26534,x26532)+~E(x26531,x26532)+~P18(x26533,x26534,x26531)
% 11.41/11.20 [2654]~P105(x26541)+P105(x26542)+~E(x26541,x26542)
% 11.41/11.20 [2655]~P70(x26551)+P70(x26552)+~E(x26551,x26552)
% 11.41/11.20 [2656]P46(x26562,x26563,x26564)+~E(x26561,x26562)+~P46(x26561,x26563,x26564)
% 11.41/11.20 [2657]P46(x26573,x26572,x26574)+~E(x26571,x26572)+~P46(x26573,x26571,x26574)
% 11.41/11.20 [2658]P46(x26583,x26584,x26582)+~E(x26581,x26582)+~P46(x26583,x26584,x26581)
% 11.41/11.20 [2659]~P75(x26591)+P75(x26592)+~E(x26591,x26592)
% 11.41/11.20 [2660]P50(x26602,x26603,x26604,x26605,x26606,x26607,x26608)+~E(x26601,x26602)+~P50(x26601,x26603,x26604,x26605,x26606,x26607,x26608)
% 11.41/11.20 [2661]P50(x26613,x26612,x26614,x26615,x26616,x26617,x26618)+~E(x26611,x26612)+~P50(x26613,x26611,x26614,x26615,x26616,x26617,x26618)
% 11.41/11.20 [2662]P50(x26623,x26624,x26622,x26625,x26626,x26627,x26628)+~E(x26621,x26622)+~P50(x26623,x26624,x26621,x26625,x26626,x26627,x26628)
% 11.41/11.20 [2663]P50(x26633,x26634,x26635,x26632,x26636,x26637,x26638)+~E(x26631,x26632)+~P50(x26633,x26634,x26635,x26631,x26636,x26637,x26638)
% 11.41/11.20 [2664]P50(x26643,x26644,x26645,x26646,x26642,x26647,x26648)+~E(x26641,x26642)+~P50(x26643,x26644,x26645,x26646,x26641,x26647,x26648)
% 11.41/11.20 [2665]P50(x26653,x26654,x26655,x26656,x26657,x26652,x26658)+~E(x26651,x26652)+~P50(x26653,x26654,x26655,x26656,x26657,x26651,x26658)
% 11.41/11.20 [2666]P50(x26663,x26664,x26665,x26666,x26667,x26668,x26662)+~E(x26661,x26662)+~P50(x26663,x26664,x26665,x26666,x26667,x26668,x26661)
% 11.41/11.20 [2667]P23(x26672,x26673,x26674,x26675,x26676,x26677)+~E(x26671,x26672)+~P23(x26671,x26673,x26674,x26675,x26676,x26677)
% 11.41/11.20 [2668]P23(x26683,x26682,x26684,x26685,x26686,x26687)+~E(x26681,x26682)+~P23(x26683,x26681,x26684,x26685,x26686,x26687)
% 11.41/11.20 [2669]P23(x26693,x26694,x26692,x26695,x26696,x26697)+~E(x26691,x26692)+~P23(x26693,x26694,x26691,x26695,x26696,x26697)
% 11.41/11.20 [2670]P23(x26703,x26704,x26705,x26702,x26706,x26707)+~E(x26701,x26702)+~P23(x26703,x26704,x26705,x26701,x26706,x26707)
% 11.41/11.20 [2671]P23(x26713,x26714,x26715,x26716,x26712,x26717)+~E(x26711,x26712)+~P23(x26713,x26714,x26715,x26716,x26711,x26717)
% 11.41/11.20 [2672]P23(x26723,x26724,x26725,x26726,x26727,x26722)+~E(x26721,x26722)+~P23(x26723,x26724,x26725,x26726,x26727,x26721)
% 11.41/11.20 [2673]~P66(x26731)+P66(x26732)+~E(x26731,x26732)
% 11.41/11.20 [2674]P24(x26742,x26743,x26744,x26745,x26746,x26747)+~E(x26741,x26742)+~P24(x26741,x26743,x26744,x26745,x26746,x26747)
% 11.41/11.20 [2675]P24(x26753,x26752,x26754,x26755,x26756,x26757)+~E(x26751,x26752)+~P24(x26753,x26751,x26754,x26755,x26756,x26757)
% 11.41/11.20 [2676]P24(x26763,x26764,x26762,x26765,x26766,x26767)+~E(x26761,x26762)+~P24(x26763,x26764,x26761,x26765,x26766,x26767)
% 11.41/11.20 [2677]P24(x26773,x26774,x26775,x26772,x26776,x26777)+~E(x26771,x26772)+~P24(x26773,x26774,x26775,x26771,x26776,x26777)
% 11.41/11.20 [2678]P24(x26783,x26784,x26785,x26786,x26782,x26787)+~E(x26781,x26782)+~P24(x26783,x26784,x26785,x26786,x26781,x26787)
% 11.41/11.20 [2679]P24(x26793,x26794,x26795,x26796,x26797,x26792)+~E(x26791,x26792)+~P24(x26793,x26794,x26795,x26796,x26797,x26791)
% 11.41/11.20 [2680]P13(x26802,x26803,x26804,x26805)+~E(x26801,x26802)+~P13(x26801,x26803,x26804,x26805)
% 11.41/11.20 [2681]P13(x26813,x26812,x26814,x26815)+~E(x26811,x26812)+~P13(x26813,x26811,x26814,x26815)
% 11.41/11.20 [2682]P13(x26823,x26824,x26822,x26825)+~E(x26821,x26822)+~P13(x26823,x26824,x26821,x26825)
% 11.41/11.20 [2683]P13(x26833,x26834,x26835,x26832)+~E(x26831,x26832)+~P13(x26833,x26834,x26835,x26831)
% 11.41/11.20 [2684]~P76(x26841)+P76(x26842)+~E(x26841,x26842)
% 11.41/11.20 [2685]~P94(x26851)+P94(x26852)+~E(x26851,x26852)
% 11.41/11.20 [2686]~P95(x26861)+P95(x26862)+~E(x26861,x26862)
% 11.41/11.20 [2687]~P65(x26871)+P65(x26872)+~E(x26871,x26872)
% 11.41/11.20 [2688]~P115(x26881)+P115(x26882)+~E(x26881,x26882)
% 11.41/11.20 [2689]~P121(x26891)+P121(x26892)+~E(x26891,x26892)
% 11.41/11.20 [2690]P32(x26902,x26903,x26904)+~E(x26901,x26902)+~P32(x26901,x26903,x26904)
% 11.41/11.20 [2691]P32(x26913,x26912,x26914)+~E(x26911,x26912)+~P32(x26913,x26911,x26914)
% 11.41/11.20 [2692]P32(x26923,x26924,x26922)+~E(x26921,x26922)+~P32(x26923,x26924,x26921)
% 11.41/11.20 [2693]~P59(x26931)+P59(x26932)+~E(x26931,x26932)
% 11.41/11.20 [2694]~P124(x26941)+P124(x26942)+~E(x26941,x26942)
% 11.41/11.20 [2695]P56(x26952,x26953,x26954,x26955)+~E(x26951,x26952)+~P56(x26951,x26953,x26954,x26955)
% 11.41/11.20 [2696]P56(x26963,x26962,x26964,x26965)+~E(x26961,x26962)+~P56(x26963,x26961,x26964,x26965)
% 11.41/11.20 [2697]P56(x26973,x26974,x26972,x26975)+~E(x26971,x26972)+~P56(x26973,x26974,x26971,x26975)
% 11.41/11.20 [2698]P56(x26983,x26984,x26985,x26982)+~E(x26981,x26982)+~P56(x26983,x26984,x26985,x26981)
% 11.41/11.20 [2699]P17(x26992,x26993,x26994)+~E(x26991,x26992)+~P17(x26991,x26993,x26994)
% 11.41/11.20 [2700]P17(x27003,x27002,x27004)+~E(x27001,x27002)+~P17(x27003,x27001,x27004)
% 11.41/11.20 [2701]P17(x27013,x27014,x27012)+~E(x27011,x27012)+~P17(x27013,x27014,x27011)
% 11.41/11.20 [2702]~P137(x27021)+P137(x27022)+~E(x27021,x27022)
% 11.41/11.20 [2703]~P129(x27031)+P129(x27032)+~E(x27031,x27032)
% 11.41/11.20 [2704]P27(x27042,x27043)+~E(x27041,x27042)+~P27(x27041,x27043)
% 11.41/11.20 [2705]P27(x27053,x27052)+~E(x27051,x27052)+~P27(x27053,x27051)
% 11.41/11.20 [2706]P57(x27062,x27063)+~E(x27061,x27062)+~P57(x27061,x27063)
% 11.41/11.20 [2707]P57(x27073,x27072)+~E(x27071,x27072)+~P57(x27073,x27071)
% 11.41/11.20 [2708]~P140(x27081)+P140(x27082)+~E(x27081,x27082)
% 11.41/11.20 [2709]~P42(x27091)+P42(x27092)+~E(x27091,x27092)
% 11.41/11.20 [2710]P41(x27102,x27103)+~E(x27101,x27102)+~P41(x27101,x27103)
% 11.41/11.20 [2711]P41(x27113,x27112)+~E(x27111,x27112)+~P41(x27113,x27111)
% 11.41/11.20 [2712]~P138(x27121)+P138(x27122)+~E(x27121,x27122)
% 11.41/11.20 [2713]P21(x27132,x27133,x27134,x27135)+~E(x27131,x27132)+~P21(x27131,x27133,x27134,x27135)
% 11.41/11.20 [2714]P21(x27143,x27142,x27144,x27145)+~E(x27141,x27142)+~P21(x27143,x27141,x27144,x27145)
% 11.41/11.20 [2715]P21(x27153,x27154,x27152,x27155)+~E(x27151,x27152)+~P21(x27153,x27154,x27151,x27155)
% 11.41/11.20 [2716]P21(x27163,x27164,x27165,x27162)+~E(x27161,x27162)+~P21(x27163,x27164,x27165,x27161)
% 11.41/11.20 [2717]~P106(x27171)+P106(x27172)+~E(x27171,x27172)
% 11.41/11.20 [2718]~P110(x27181)+P110(x27182)+~E(x27181,x27182)
% 11.41/11.20 [2719]P28(x27192,x27193,x27194)+~E(x27191,x27192)+~P28(x27191,x27193,x27194)
% 11.41/11.20 [2720]P28(x27203,x27202,x27204)+~E(x27201,x27202)+~P28(x27203,x27201,x27204)
% 11.41/11.20 [2721]P28(x27213,x27214,x27212)+~E(x27211,x27212)+~P28(x27213,x27214,x27211)
% 11.41/11.20 [2722]P44(x27222,x27223,x27224)+~E(x27221,x27222)+~P44(x27221,x27223,x27224)
% 11.41/11.20 [2723]P44(x27233,x27232,x27234)+~E(x27231,x27232)+~P44(x27233,x27231,x27234)
% 11.41/11.20 [2724]P44(x27243,x27244,x27242)+~E(x27241,x27242)+~P44(x27243,x27244,x27241)
% 11.41/11.20 [2725]P52(x27252,x27253,x27254)+~E(x27251,x27252)+~P52(x27251,x27253,x27254)
% 11.41/11.20 [2726]P52(x27263,x27262,x27264)+~E(x27261,x27262)+~P52(x27263,x27261,x27264)
% 11.41/11.20 [2727]P52(x27273,x27274,x27272)+~E(x27271,x27272)+~P52(x27273,x27274,x27271)
% 11.41/11.20 [2728]~P133(x27281)+P133(x27282)+~E(x27281,x27282)
% 11.41/11.20 [2729]~P60(x27291)+P60(x27292)+~E(x27291,x27292)
% 11.41/11.20 [2730]P54(x27302,x27303,x27304,x27305,x27306)+~E(x27301,x27302)+~P54(x27301,x27303,x27304,x27305,x27306)
% 11.41/11.20 [2731]P54(x27313,x27312,x27314,x27315,x27316)+~E(x27311,x27312)+~P54(x27313,x27311,x27314,x27315,x27316)
% 11.41/11.20 [2732]P54(x27323,x27324,x27322,x27325,x27326)+~E(x27321,x27322)+~P54(x27323,x27324,x27321,x27325,x27326)
% 11.41/11.20 [2733]P54(x27333,x27334,x27335,x27332,x27336)+~E(x27331,x27332)+~P54(x27333,x27334,x27335,x27331,x27336)
% 11.41/11.20 [2734]P54(x27343,x27344,x27345,x27346,x27342)+~E(x27341,x27342)+~P54(x27343,x27344,x27345,x27346,x27341)
% 11.41/11.20 [2735]~P58(x27351)+P58(x27352)+~E(x27351,x27352)
% 11.41/11.20 [2736]~P118(x27361)+P118(x27362)+~E(x27361,x27362)
% 11.41/11.20 [2737]P19(x27372,x27373,x27374)+~E(x27371,x27372)+~P19(x27371,x27373,x27374)
% 11.41/11.20 [2738]P19(x27383,x27382,x27384)+~E(x27381,x27382)+~P19(x27383,x27381,x27384)
% 11.41/11.20 [2739]P19(x27393,x27394,x27392)+~E(x27391,x27392)+~P19(x27393,x27394,x27391)
% 11.41/11.20 [2740]P25(x27402,x27403,x27404)+~E(x27401,x27402)+~P25(x27401,x27403,x27404)
% 11.41/11.20 [2741]P25(x27413,x27412,x27414)+~E(x27411,x27412)+~P25(x27413,x27411,x27414)
% 11.41/11.20 [2742]P25(x27423,x27424,x27422)+~E(x27421,x27422)+~P25(x27423,x27424,x27421)
% 11.41/11.20 [2743]~P82(x27431)+P82(x27432)+~E(x27431,x27432)
% 11.41/11.20 [2744]~P126(x27441)+P126(x27442)+~E(x27441,x27442)
% 11.41/11.20 [2745]~P84(x27451)+P84(x27452)+~E(x27451,x27452)
% 11.41/11.20 [2746]~P37(x27461)+P37(x27462)+~E(x27461,x27462)
% 11.41/11.20 [2747]P31(x27472,x27473,x27474)+~E(x27471,x27472)+~P31(x27471,x27473,x27474)
% 11.41/11.20 [2748]P31(x27483,x27482,x27484)+~E(x27481,x27482)+~P31(x27483,x27481,x27484)
% 11.41/11.20 [2749]P31(x27493,x27494,x27492)+~E(x27491,x27492)+~P31(x27493,x27494,x27491)
% 11.41/11.20 [2750]~P130(x27501)+P130(x27502)+~E(x27501,x27502)
% 11.41/11.20 [2751]P11(x27512,x27513,x27514)+~E(x27511,x27512)+~P11(x27511,x27513,x27514)
% 11.41/11.20 [2752]P11(x27523,x27522,x27524)+~E(x27521,x27522)+~P11(x27523,x27521,x27524)
% 11.41/11.20 [2753]P11(x27533,x27534,x27532)+~E(x27531,x27532)+~P11(x27533,x27534,x27531)
% 11.41/11.20 [2754]~P92(x27541)+P92(x27542)+~E(x27541,x27542)
% 11.41/11.20 [2755]P16(x27552,x27553,x27554)+~E(x27551,x27552)+~P16(x27551,x27553,x27554)
% 11.41/11.20 [2756]P16(x27563,x27562,x27564)+~E(x27561,x27562)+~P16(x27563,x27561,x27564)
% 11.41/11.20 [2757]P16(x27573,x27574,x27572)+~E(x27571,x27572)+~P16(x27573,x27574,x27571)
% 11.41/11.20 [2758]~P141(x27581)+P141(x27582)+~E(x27581,x27582)
% 11.41/11.20 [2759]P51(x27592,x27593,x27594,x27595)+~E(x27591,x27592)+~P51(x27591,x27593,x27594,x27595)
% 11.41/11.20 [2760]P51(x27603,x27602,x27604,x27605)+~E(x27601,x27602)+~P51(x27603,x27601,x27604,x27605)
% 11.41/11.20 [2761]P51(x27613,x27614,x27612,x27615)+~E(x27611,x27612)+~P51(x27613,x27614,x27611,x27615)
% 11.41/11.20 [2762]P51(x27623,x27624,x27625,x27622)+~E(x27621,x27622)+~P51(x27623,x27624,x27625,x27621)
% 11.41/11.20 [2763]P43(x27632,x27633)+~E(x27631,x27632)+~P43(x27631,x27633)
% 11.41/11.20 [2764]P43(x27643,x27642)+~E(x27641,x27642)+~P43(x27643,x27641)
% 11.41/11.20 [2765]~P132(x27651)+P132(x27652)+~E(x27651,x27652)
% 11.41/11.20 [2766]P40(x27662,x27663,x27664,x27665,x27666,x27667)+~E(x27661,x27662)+~P40(x27661,x27663,x27664,x27665,x27666,x27667)
% 11.41/11.20 [2767]P40(x27673,x27672,x27674,x27675,x27676,x27677)+~E(x27671,x27672)+~P40(x27673,x27671,x27674,x27675,x27676,x27677)
% 11.41/11.20 [2768]P40(x27683,x27684,x27682,x27685,x27686,x27687)+~E(x27681,x27682)+~P40(x27683,x27684,x27681,x27685,x27686,x27687)
% 11.41/11.20 [2769]P40(x27693,x27694,x27695,x27692,x27696,x27697)+~E(x27691,x27692)+~P40(x27693,x27694,x27695,x27691,x27696,x27697)
% 11.41/11.20 [2770]P40(x27703,x27704,x27705,x27706,x27702,x27707)+~E(x27701,x27702)+~P40(x27703,x27704,x27705,x27706,x27701,x27707)
% 11.41/11.20 [2771]P40(x27713,x27714,x27715,x27716,x27717,x27712)+~E(x27711,x27712)+~P40(x27713,x27714,x27715,x27716,x27717,x27711)
% 11.41/11.20 [2772]~P117(x27721)+P117(x27722)+~E(x27721,x27722)
% 11.41/11.20 [2773]P30(x27732,x27733)+~E(x27731,x27732)+~P30(x27731,x27733)
% 11.41/11.20 [2774]P30(x27743,x27742)+~E(x27741,x27742)+~P30(x27743,x27741)
% 11.41/11.20 [2775]P39(x27752,x27753,x27754,x27755)+~E(x27751,x27752)+~P39(x27751,x27753,x27754,x27755)
% 11.41/11.20 [2776]P39(x27763,x27762,x27764,x27765)+~E(x27761,x27762)+~P39(x27763,x27761,x27764,x27765)
% 11.41/11.20 [2777]P39(x27773,x27774,x27772,x27775)+~E(x27771,x27772)+~P39(x27773,x27774,x27771,x27775)
% 11.41/11.20 [2778]P39(x27783,x27784,x27785,x27782)+~E(x27781,x27782)+~P39(x27783,x27784,x27785,x27781)
% 11.41/11.20 [2779]~P97(x27791)+P97(x27792)+~E(x27791,x27792)
% 11.41/11.20 [2780]~P128(x27801)+P128(x27802)+~E(x27801,x27802)
% 11.41/11.20 [2781]~P72(x27811)+P72(x27812)+~E(x27811,x27812)
% 11.41/11.20 [2782]~P134(x27821)+P134(x27822)+~E(x27821,x27822)
% 11.41/11.20 [2783]~P119(x27831)+P119(x27832)+~E(x27831,x27832)
% 11.41/11.20 [2784]~P96(x27841)+P96(x27842)+~E(x27841,x27842)
% 11.41/11.20 [2785]~P5(x27851)+P5(x27852)+~E(x27851,x27852)
% 11.41/11.20 [2786]~P107(x27861)+P107(x27862)+~E(x27861,x27862)
% 11.41/11.20 [2787]P48(x27872,x27873)+~E(x27871,x27872)+~P48(x27871,x27873)
% 11.41/11.20 [2788]P48(x27883,x27882)+~E(x27881,x27882)+~P48(x27883,x27881)
% 11.41/11.20 [2789]~P109(x27891)+P109(x27892)+~E(x27891,x27892)
% 11.41/11.20 [2790]P49(x27902,x27903,x27904,x27905)+~E(x27901,x27902)+~P49(x27901,x27903,x27904,x27905)
% 11.41/11.20 [2791]P49(x27913,x27912,x27914,x27915)+~E(x27911,x27912)+~P49(x27913,x27911,x27914,x27915)
% 11.41/11.20 [2792]P49(x27923,x27924,x27922,x27925)+~E(x27921,x27922)+~P49(x27923,x27924,x27921,x27925)
% 11.41/11.20 [2793]P49(x27933,x27934,x27935,x27932)+~E(x27931,x27932)+~P49(x27933,x27934,x27935,x27931)
% 11.41/11.20 [2794]~P83(x27941)+P83(x27942)+~E(x27941,x27942)
% 11.41/11.20 [2795]P8(x27952,x27953)+~E(x27951,x27952)+~P8(x27951,x27953)
% 11.41/11.20 [2796]P8(x27963,x27962)+~E(x27961,x27962)+~P8(x27963,x27961)
% 11.41/11.20 [2797]~P73(x27971)+P73(x27972)+~E(x27971,x27972)
% 11.41/11.20 [2798]~P102(x27981)+P102(x27982)+~E(x27981,x27982)
% 11.41/11.20 [2799]P29(x27992,x27993)+~E(x27991,x27992)+~P29(x27991,x27993)
% 11.41/11.20 [2800]P29(x28003,x28002)+~E(x28001,x28002)+~P29(x28003,x28001)
% 11.41/11.20 [2801]P36(x28012,x28013)+~E(x28011,x28012)+~P36(x28011,x28013)
% 11.41/11.20 [2802]P36(x28023,x28022)+~E(x28021,x28022)+~P36(x28023,x28021)
% 11.41/11.20 [2803]P45(x28032,x28033,x28034)+~E(x28031,x28032)+~P45(x28031,x28033,x28034)
% 11.41/11.20 [2804]P45(x28043,x28042,x28044)+~E(x28041,x28042)+~P45(x28043,x28041,x28044)
% 11.41/11.20 [2805]P45(x28053,x28054,x28052)+~E(x28051,x28052)+~P45(x28053,x28054,x28051)
% 11.41/11.20 [2806]~P10(x28061)+P10(x28062)+~E(x28061,x28062)
% 11.41/11.20 [2807]P12(x28072,x28073,x28074,x28075,x28076)+~E(x28071,x28072)+~P12(x28071,x28073,x28074,x28075,x28076)
% 11.41/11.20 [2808]P12(x28083,x28082,x28084,x28085,x28086)+~E(x28081,x28082)+~P12(x28083,x28081,x28084,x28085,x28086)
% 11.41/11.20 [2809]P12(x28093,x28094,x28092,x28095,x28096)+~E(x28091,x28092)+~P12(x28093,x28094,x28091,x28095,x28096)
% 11.41/11.20 [2810]P12(x28103,x28104,x28105,x28102,x28106)+~E(x28101,x28102)+~P12(x28103,x28104,x28105,x28101,x28106)
% 11.41/11.20 [2811]P12(x28113,x28114,x28115,x28116,x28112)+~E(x28111,x28112)+~P12(x28113,x28114,x28115,x28116,x28111)
% 11.41/11.20 [2812]~P34(x28121)+P34(x28122)+~E(x28121,x28122)
% 11.41/11.20 [2813]~P108(x28131)+P108(x28132)+~E(x28131,x28132)
% 11.41/11.20 [2814]P144(x28142,x28143)+~E(x28141,x28142)+~P144(x28141,x28143)
% 11.41/11.20 [2815]P144(x28153,x28152)+~E(x28151,x28152)+~P144(x28153,x28151)
% 11.41/11.20 [2816]P145(x28162,x28163)+~E(x28161,x28162)+~P145(x28161,x28163)
% 11.41/11.20 [2817]P145(x28173,x28172)+~E(x28171,x28172)+~P145(x28173,x28171)
% 11.41/11.20
% 11.41/11.20 %-------------------------------------------
% 11.41/11.21 cnf(10052,plain,
% 11.41/11.21 ($false),
% 11.41/11.21 inference(scs_inference,[],[3470,4393,7575]),
% 11.41/11.21 ['proof']).
% 11.41/11.21 % SZS output end Proof
% 11.41/11.21 % Total time :6.950000s
%------------------------------------------------------------------------------